hypothesis on stress

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Article Contents

The challenge of defining stress, current models of stress in the behavioral literature, stress in a systems perspective, extensions and future directions, acknowledgments, glossary of control theory terms, what is stress a systems perspective.

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Marco Del Giudice, C Loren Buck, Lauren E Chaby, Brenna M Gormally, Conor C Taff, Christopher J Thawley, Maren N Vitousek, Haruka Wada, What Is Stress? A Systems Perspective, Integrative and Comparative Biology , Volume 58, Issue 6, December 2018, Pages 1019–1032, https://doi.org/10.1093/icb/icy114

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The term “stress” is used to describe important phenomena at multiple levels of biological organization, but finding a general and rigorous definition of the concept has proven challenging. Current models in the behavioral literature emphasize the cognitive aspects of stress, which is said to occur when threats to the organism are perceived as uncontrollable and/or unpredictable. Here we adopt the perspective of systems biology and take a step toward a general definition of stress by unpacking the concept in light of control theory. Our goal is to clarify the concept so as to facilitate integrative research and formal analysis. We argue that stress occurs when a biological control system detects a failure to control a fitness-critical variable, which may be either internal or external to the organism. Biological control systems typically include both feedback (reactive, compensatory) and feedforward (predictive, anticipatory) components; their interplay accounts for the complex phenomenology of stress in living organisms. The simple and abstract definition we propose applies to animals, plants, and single cells, highlighting connections across levels of organization. In the final section of the paper we explore some extensions of our approach and suggest directions for future research. Specifically, we discuss the classic concepts of conditioning and hormesis and review relevant work on cellular stress responses; show how control theory suggests the existence of fundamental trade-offs in the design of stress responses; and point to potential insights into the effects of novel environmental conditions, including those resulting from anthropogenic change.

My chapter defines the concept of stress. I am not certain whether one who undertakes this task either has an enormous ego, is immeasurably stupid, or is totally mad. ( Levine 1985 )

Ever since Selye (1950) introduced the term in biology, the task of defining stress has been fraught with difficulties and ambiguities ( Le Moal 2007 ; Romero et al. 2009 ; Koolhaas et al. 2011 ). Selye used the word “stress” to denote the specific physiological response that organisms mount to nonspecific demands, including both negative challenges (e.g., starvation, infection) and positive challenges (e.g., foraging or mating opportunities; Selye 1976 ). The initial definition has been narrowed in later research, first with the notion that stressors are actual or perceived threats to the homeostasis of the organism, and then with the emphasis—particularly strong in the behavioral literature—that stress is specifically triggered by perceptions of unpredictability and/or uncontrollability ( Levine and Ursin 1991 ; McEwen and Wingfield 2003 ; Ursin and Eriksen 2004 ; Romero et al. 2009 ; Ursin and Eriksen 2010 ; Koolhaas et al. 2011 ). These ideas are rooted in concepts from control theory, such as feedback and feedforward regulation ( Bechhoefer 2005 ; Albertos and Mareels 2010 ; Åström and Murray 2012 ; Frank 2018a ). However, the connections between biological models of stress and the formal theory of control systems are seldom discussed explicitly, and their implications have not been explored in any detail. Moreover, the increasing emphasis of behavioral models on the cognitive aspects of prediction and coping ( Ursin and Eriksen 2010 ; Koolhaas et al. 2011 ) makes them ill-suited to describe stress in organisms that lack a nervous system (e.g., plants; Hirt 2009 ), or even at the level of individual cells ( Kültz 2005 ). When researchers in animal, plant, and cellular physiology describe responses to threats and challenges as stress, they may be referring to entirely different phenomena—or, alternatively, the convergent vocabulary may reflect the existence of a shared conceptual core. An integrated perspective on stress has been hindered by the fact that stress is typically studied at a single biological scale, and the interaction with other scales is rarely investigated ( Romero et al. 2015 ).

In this paper we adopt the perspective of systems biology ( Kitano 2002 ), and take a step toward a general definition of stress by unpacking the concept in light of control theory. Specifically, we argue that stress occurs when a biological control system detects a failure to control a fitness-critical variable , which may be either internal or external to the organism. As we detail below, detection does not imply a cognitive appraisal but merely a measured discrepancy between the target state of the variable and its actual state. To qualify as control failures, discrepancies must be large and/or persistent, reflecting the system’s inability to anticipate or rapidly address the challenge (what counts as “large” and “persistent” necessarily depends on the particular variable and its relation to fitness). Biological control systems typically include both feedback (reactive, compensatory) and feedforward (predictive, anticipatory) components; their interplay accounts for the complex phenomenology of stress in living organisms.

Our goal is not to advance a new theory of stress or propose an alternative to existing models, but to clarify the concept so as to facilitate integrative research and—ultimately—formal analysis. The definition of stress we propose is meant to be as simple and abstract as possible; it does not depend on the cognitive, physiological, and molecular mechanisms that mediate or respond to challenges in any particular case. For instance, feedforward anticipatory responses do not require a nervous system and can be implemented by relatively simple biochemical pathways ( Zhang et al. 2009 ). Thus, our definition is consistent with current models of stress in the behavioral literature (reviewed in the next section); these models will be the main focus of this paper, since our expertise lies mainly in vertebrate systems. However, the same definition applies equally well to cellular stress responses, highlighting connections across levels of biological organization and facilitating integration between different disciplinary traditions. We believe that explicitly redefining stress in the language of control theory will promote conceptual clarity in a field marred by redundant and often ambiguous terminology. Even more importantly, this approach suggests several interesting implications and novel directions for research, as we discuss in the final section of the paper.

In this preliminary section we briefly survey current conceptions of stress in the behavioral literature, describing their main concepts, and highlight some recurring themes. We begin with the allostasis model proposed by McEwen and Wingfield (2003) , which has profoundly influenced subsequent theorizing in this area. This model focuses on the physiological adjustments required to maintain stability through change, or allostasis ( Sterling and Eyer 1988 ). Allostatic responses adaptively shift the set point of homeostatic systems to match anticipated changes in the environment or in the organism’s state (including transitions between life history stages). For example, the homeostatic set points of metabolism and body temperature shift between day and night, and even more dramatically during hibernation. When a prey spots a predator nearby, the autonomic system increases the set point of heart rate in anticipation of flight, even before actual escape behavior is initiated. In the model, stress is defined as a threatening event that elicits a physiological and/or behavioral allostatic response in addition to those imposed by the normal life cycle. Allostatic responses tend to have immediate benefits and long-term costs. Rising levels of physiological mediators such as glucocorticoids increase energy availability to deal with present challenges, but deplete the individual’s reserves and may result in tissue damage, particularly if exposure to stress is severe and/or chronic. The cumulative effect of allostasis is called allostatic load . When environmental conditions require more work to be done to maintain physiological stability, allostatic load increases and can lead to two types of overload. If the energy necessary to maintain homeostasis exceeds the energy available to an organism, an “emergency life history stage” will be initiated. If energetic demands are not exceeded and allostatic responses are sustained for too long, metabolic imbalances and pathological damage can result.

The concept of allostasis has been revised and extended in what is perhaps the most comprehensive model of stress to date, the reactive scope model ( Romero et al. 2009 ). This model is less focused on energetic expenditures, applies to a greater range of contexts (including those in which energy is not the limiting factor), and allows for more explicit predictions about individual differences in stress susceptibility. Mediators of the stress response (e.g., glucocorticoids, heart rate, behavioral responses such as aggression and locomotion) have a normal range termed the reactive scope, which encompasses anticipatory changes that follow circadian and seasonal fluctuations ( predictive homeostasis ), as well as temporary increases following unpredictable threats ( reactive homeostasis ). If levels of mediators (e.g., hormone concentrations) exceed the normal reactive scope too often or for too long they begin to induce pathological damage ( homeostatic overload ); if they fall too low they become insufficient to maintain homeostasis ( homeostatic failure ). Both outcomes should lead to diminished fitness. Genetic and developmental factors as well as prior experiences may narrow or expand the reactive scope, leading to individual differences in stress susceptibility. The development of individual differences is also the focus of the adaptive calibration model advanced by Del Giudice et al. (2011) and Ellis and Del Giudice (2014) . This model combines the concept of allostasis with the insight that repeated, chronic stress carries important information about life history-relevant features of the environment (e.g., danger, unpredictability, availability of resources). As the organism develops, the stress response system integrates this information and contributes to the regulation of key life history trade-offs, with broad-ranging effects on maturation, behavior, and physiology—including physiological reactivity to future stressors.

Whereas the allostasis and reactive scope models tend to focus mainly on physiological processes, the cognitive activation theory of stress (CATS; Ursin and Eriksen 2004 , 2010 ) takes an explicitly cognitive perspective on stress. The model defines stress as a general alarm response that occurs when there is a discrepancy between expectancy and reality. Expectancies correspond to the homeostatic set values of motivational systems and can be violated by threats to the organism, homeostatic imbalances, novelties, and so on. The alarm response triggered by discrepancies involves non-specific physiological arousal and persists until the discrepancy is resolved. The CATS quantifies expectancies by their strength, by the perceived probability of the expected event, and by the event’s positive or negative affective connotation (valence). Building on these notions, the model attempts to formalize intuitive concepts such as anxiety, helplessness, and hopelessness based on the perceived probability and valence of future events, coupled with learned expectations about the relationships between coping responses and outcomes.

As is apparent from this brief overview, a common thread of many current models of stress is that they do not exclusively focus on reactive or compensatory responses (those deployed after the challenge has occurred), but place considerable emphasis on the importance of anticipatory responses. The latter have been described by different authors as “allostasis,” “predictive homeostasis,” or “adaptive homeostasis” (with somewhat different implications; see Romero et al. 2009 ; Davies 2016 ). In a recent effort to clarify the concept of stress, Koolhaas et al. (2011) argued that stressors should be clearly distinguished from everyday challenges, and narrowly defined as fitness-threatening situations that involve significant unpredictability and/or uncontrollability. Unpredictable events can be identified by the lack of anticipatory responses, whereas uncontrollable events are marked by absent or delayed physiological recovery. In this perspective, the most stressful events for an animal are those in which previously predictable/controllable situations suddenly deteriorate, causing a rapid failure of both anticipatory and reactive processes. This framework synthesizes many key aspects of the existing approaches, including the allostasis model, reactive scope model, and CATS. It also inherits a markedly cognitive conception of stress: adopting the CATS formulation, the authors frame prediction as expectancies about probable outcomes, and note that the occurrence of stress is crucially influenced by the animal’s perception, internal representations, and memory of previous experiences. As noted above, defining stress in cognitive terms permits a sophisticated analysis of behavioral and physiological responses to challenges (for details see Koolhaas et al. 2011 ), but further separates the study of stress in animals from that of analogous phenomena that occur at the cellular level or in organisms without a nervous system. In the next section we show how, by explicitly considering the control-theoretic underpinnings of current models of stress, one can formulate their main insights in a more general way that does not rely on cognitive assumptions (while also accounting for the role of cognitive processes when they are relevant).

To survive and reproduce, organisms need to constantly control the state of myriad dynamic processes at multiple levels of organization, from single cells and their components (e.g., cellular respiration) to multicellular individuals (e.g., temperature control, circulation) to interactions between organisms (e.g., predator avoidance, competition for social rank). From this vantage point, organisms can be viewed as intricate collections of nested control systems. In the simplest cases, biological control systems maintain homeostasis by keeping a well-defined physiological variable (e.g., temperature, blood pressure, glucose concentration) within an optimal range around a set point. In more general terms, biological control can be framed as the pursuit of fitness-relevant goals which may depend on the state of complex variables such as social rank or offspring health and survival. Such variables are often partly or fully external to the organism (as illustrated by offspring survival); the effective regulation of both “internal” and “external” variables may require the organism to interact with its environment and sometimes modify it (e.g., searching for food, protecting offspring, choosing a location with appropriate temperature). Regardless of their nature and complexity, all control systems ultimately rely on two basic strategies, that is, feedback and feedforward control. The properties and limitations of these two types of regulation have been worked out in control theory, which is one of the main contributors to systems biology (see Kitano 2002 ; Bechhoefer 2005 ; Albertos and Mareels 2010 ; Åström and Murray 2012 ; Khammash 2016 ; Frank 2018a ). In what follows, we review some basic concepts of control theory (see also the Glossary at the end of the paper) before applying them to the problem of defining and understanding stress.

Feedback and feedforward control

In feedback or closed-loop control, the current set point or goal ( reference input ) is compared with the actual state of the system (i.e., the system’s output ) to obtain an error signal. For example, a thermostat may detect a discrepancy between the room temperature (output) and the temperature set point. The error signal is used to generate an action, so as to bring the state of the system closer to the reference input (e.g., the thermostat may activate a heater). However, other causal factors ( disturbances ) may be acting on the system at the same time; for example, someone may open a window, letting cold air into the room. The joint effect of control actions and disturbances determines the system’s output, which is then measured and compared with the reference, closing the control loop ( Fig. 1A ). The weight assigned to the feedback channel ( feedback gain ) determines the effect of error signals on the controller’s behavior, so that a higher-gain controller responds to a the same amount of discrepancy with a larger corrective action. In total, feedback controllers track the system’s output in real time, progressively narrowing the gap between the goal and the state of the world through moment-to-moment self-correction. As a rule, the system’s output is not directly available for comparison but has to be estimated or measured indirectly, for example through cascades of chemical reactions or sensory organs. Measurement processes—broadly defined to include sensory processes and the associated neural computations—inevitably introduce some stochastic error (or noise ) in the loop, and engender a fundamental trade-off between the controller’s tracking speed and its ability to reject unwanted noise. If the output is measured with higher temporal resolution—thus increasing the ability to track rapid changes in the state of the system—more irrelevant noise will enter the feedback channel and be amplified, causing undesired fluctuations in the response. Conversely, effective filtering of unwanted noise reduces the tracking speed of the control system ( Bechhoefer 2005 ; Albertos and Mareels 2010 ). A powerful way to employ feedback controllers is to nest multiple feedback loops within one another, yielding a feedback cascade . In this type of hierarchical arrangement, the inner control loop regulates a lower-order variable (i.e., pursues a lower-order goal) and thus simplifies the control problem faced by the controller in the outer loop. For example, regulation of blood pressure (the higher-order variable) depends on nested feedback loops that control lower-order variables such as heart rate, stroke volume, and vasoconstriction ( Sterling and Eyer 1988 ).

Schematic representation of ( A ) a feedback or closed-loop control system and ( B ) a feedforward or open-loop control system. Feedforward controllers may employ information about past and present disturbances (dashed box and arrows) to predict future states of the system and determine the appropriate control actions. FB, feedback; FF, feedforward.

The main strength of feedback control lies in its flexibility, that is, the ability to respond to unknown or unanticipated disturbances. More generally, feedback control has an intrinsically self-correcting nature; for this reason, it does not require an accurate preexisting model of the system in order to function properly. However, feedback systems are also highly sensitive to noise and rely on accurate measurement of the output. Another crucial limitation of feedback control is that it depends on the ability to track real-time changes in the system. Slow chemical reactions, neural computation, physical inertia in the system—these and other factors introduce delays and response lags in the feedback loop, with the result that the performance of feedback control deteriorates. Beyond a certain threshold, delays in the feedback loop may destabilize the system and lead to erratic, uncontrolled behavior ( Bechhoefer 2005 ; Albertos and Mareels 2010 ; Frank 2018a ).

While feedback controllers can flexibly respond to disturbances and changes in the system after they have occurred, they are intrinsically unable to anticipate them. When disturbances can be anticipated (or ignored altogether), feedforward or open-loop control becomes an effective option, allowing for improved robustness and the reduction or elimination of response delay. The term “open-loop” highlights the fact that the system output is not used to determine control actions (i.e., there is no feedback channel closing the loop between input and output). The simplest forms of open-loop control make no attempt to predict the future state of the system, and produce fixed actions that follow an inflexible course once initiated. Such “ballistic” responses are often optimal in the context of rapid defensive mechanisms, such as protective reflexes (e.g., blinking, pain-induced limb retraction) or the initial phase of the cellular response to heat shock (Shudo et al. 2003; Albertos and Mareels 2010 ). In more complex feedforward controllers, the reference input is combined with an implicit or explicit model of the system to generate a control action (or sequence of actions) based on the predicted behavior of the system over time; if the model is correct and there are no major unforeseen disturbances, such an anticipatory response will yield the desired output without further correction. Feedforward processes may integrate information about current disturbances (obtained from sensors) as well as past states of the system (stored in some form of memory); to generate control actions, a controller may compute predictive estimates of future states of the system ( Fig. 1B ). In sum, feedforward regulation ranges from simple reflexes to complex cognitive simulations of future events that integrate preexisting knowledge about the likelihood of potential outcomes, the influence of contextual variables, and so on. For simplicity, in this paper we treat “prediction” and “anticipation” as synonyms, regardless of whether a control system actually computes estimates of future states. The advantages of feedforward controllers over their feedback counterparts include reduced sensitivity to noise (robustness), greater dynamic stability, and the fact that they do not require accurate, real-time measurement of the system’s output. At the same time, sophisticated feedforward regulation requires an accurate internal model of the system and enough information about its current state so that future disturbances can be successfully anticipated. Most crucially, feedforward controllers are unable to respond to unanticipated events that occur while the current action is unfolding.

The complementary strengths of feedback and feedforward control can be combined by integrating the two strategies within a single control system. For example, predictive estimates generated by a feedforward controller can be used to compensate for the delays introduced by feedback loops and reduce the effects of sensor noise. Conversely, the errors caused by an imperfect predictive model of the system can be corrected and smoothed out by introducing reactive feedback loops ( Bechhoefer 2005 ). Unsurprisingly, most biological regulatory systems include both anticipatory and reactive components ( Barrett and Simmons 2015 ). This is true across organismal systems and even at the cellular level: for example, the biochemical pathways that mediate responses to oxidative damage not only include nested feedback loops that respond to the concentration of the damaging molecules and their metabolites, but also feedforward processes that sense early cues of danger and proactively activate other components of the system ( Zhang et al. 2009 , 2010 ; more on this below). In allostasis and predictive homeostasis, a feedforward controller anticipates the future state of the system (e.g., changes in physical activity, food scarcity) and responds by adaptively adjusting the reference input of a homeostatic feedback controller, which in turn regulates the output variable (e.g., blood pressure, metabolic rate). The brain itself can be conceptualized as a complex controller that integrates feedback and feedforward processes ( Franklin and Wolpert 2011 ). Taking this idea one step further, proponents of active inference models argue that all of cognition and behavior can be explained as the result of predictive computations; in this perspective, what feedback pathways do is carry information about prediction errors ( Friston 2010 ; Pezzulo et al. 2015 ). Crucially, predictive computations do not necessitate a complex nervous system. Even relatively simple biochemical networks can compute mathematical functions (from addition/subtraction and multiplication/division to roots and polynomials; Buisman et al. 2009 ), implement switches and oscillators ( Miller et al. 2005 ; Novák and Tyson 2008 ), and even perform associative learning ( McGregor et al. 2012 ).

Stress as control failure

The concepts reviewed above suggest a simple but general definition of stress as control failure. Specifically, stress occurs when a biological control system detects a failure to control a fitness-critical variable. By fitness-critical we mean a variable with the potential to significantly impact the survival and/or reproductive success of the organism ( Koolhaas et al. 2011 ); depending on context, this may extend to related organisms (inclusive fitness; see West and Gardner 2013 ). The term “fitness-critical” underscores the idea that not all aspects of the world with some relevance to fitness are automatically sources of stress. Some variables have a disproportionate impact on survival and reproduction; organisms are selected to rapidly detect deviations from the desired state of those variables and to forcefully respond to control failures. Note that mild and/or short-lived deviations from the system’s goal or regulatory range are expected in any realistic control system, and do not automatically qualify as failures. However, large and/or persistent discrepancies indicate that the organism is unable to achieve control over key aspects of its internal functioning and/or external environment—in other words, that the organism’s fitness is threatened.

The state of the controlled variable is usually known only indirectly through processes of measurement and estimation (which in the most complex cases may include sensory and cognitive components, with multiple layers of inference). Incorrect estimates of the state of the system can lead the controller to detect large, persistent discrepancies when they are not present. An animal may mistake a shadow for a dangerous predator; defective baroreceptors may incorrectly sense a threatening drop in blood pressure; and so on. In all these cases, stress and stress responses occur in absence of an actual threat to fitness. Conversely, discrepancies that go undetected by the control system (e.g., failing to spot an approaching predator) do not engender stress even if they may result in damage to the organism and substantial fitness costs.

By this definition, an event or challenge becomes a stressor if it results in a failure to control a fitness-critical variable (as detected by the control system); this captures the key features of threat and uncontrollability emphasized by current models ( Koolhaas et al. 2011 ). As we detail below, unpredictability refers to a particular kind of control failure in which anticipatory (feedforward) responses are lacking or inadequate. A single control failure represents an instance of acute stress; repeated failures over time indicate the existence of difficult or even intractable problems in the organism and/or its environment (and may be described as a type of chronic stress). Fitness-critical variables can be internal or external to the organism: to a mother with dependent offspring, a predator threatening the offspring can be a tremendous stressor, and failures to control offspring health and survival can be expected to be extremely stressful. While the classic concept of homeostasis suggests an emphasis on internal variables (e.g., glucose concentration, blood pressure, oxidative damage), our definition underscores that biological control and its failures apply to multiple fitness-relevant domains, which may extend well beyond the borders of the individual organism. Depending on the nature of the control system under consideration, one may identify various categories of stress—social, energetic, cardiovascular, immune, oxidative, and so on. In this paper, we are not concerned with specific stressors and the relevant responses, but only with the general concept of stress and its invariant features across systems, organisms, and levels of analysis.

In line with the current literature, stress as a condition is distinguished from both the event that induces it (stressor) and the response enacted to resolve it (stress response). Especially when dealing with internal states, it is important to draw a clear distinction between the physiological variables that the organism is attempting to control and those that mediate the response. As an illustration drawing from vertebrate physiology, consider the case of energetic stress induced by starvation (the stressor). The fitness-critical variable that the organism is failing to control is blood glucose concentration (or, more abstractly, energy availability); the response of the organism may include a temporary elevation of glucocorticoids and other hormones, which stimulate glucose release and—if successful—eventually restore energetic homeostasis. While glucocorticoid secretion may be upregulated by changing the feedback set point of the hypothalamic–pituitary–adrenal (HPA) axis, the focal variable that defines the presence or absence of stress is the concentration of glucose, and not that of glucocorticoids (though the latter may be used as indicators to infer a state of stress). The larger system that includes both glucose and glucocorticoid regulation can be described as a feedback cascade, with glucose regulation as the outer loop (higher-order goal) and glucocorticoid regulation as the inner loop (lower-order goal). This is a crucial point that may generate confusion if not properly understood; in particular, it should be noted some models of stress (notably the reactive scope model; Romero et al. 2009 ) focus on the homeostatic regulation of mediators rather than that of fitness-critical variables per se . In contrast, the definition we propose focuses on the regulation of fitness-critical variables (e.g., blood glucose or energy availability); the regulation of specific mediators (e.g., glucocorticoids) is treated as a subproblem in the generation of appropriate responses. Of course, the nature of biological adaptation is such that, in many cases, fitness-critical variables are hierarchically nested within one another (e.g., achieving the potential for successful reproduction requires sufficient energy reserves; building up energy reserves requires sufficient day-to-day energy availability; and so on). This is not a problem for our definition, as long as the proper level(s) of analysis and the nature of the stressor(s) are correctly identified in any given case.

The concept of stress as control failure is illustrated in Fig. 2 . The figure depicts a schematic control system with both feedback and feedforward components. The controlled variable can be jointly affected by disturbances in the environment as well as the organism’s own behavior and physiology (summarized as the “state of the organism” in the figure). Of course, controllers can only modify the state of the external environment through the organism’s behavior, which is why there are no arrows pointing directly from the controllers to the environment. When the feedforward controller anticipates a disturbance, it can act directly by triggering a response against the disturbance (arrow pointing to the state of the organism) or indirectly by shifting the reference input of the feedback controller. In the latter case, the anticipatory response can be described as an instance of allostasis. In the case of energetic stress discussed above, the organism may be able to predict an impending period of scarcity (disturbance); for example, based on seasonal cues that winter is approaching or declining rates of energy intake over a certain time span. Anticipatory responses to prevent starvation may range from changes in foraging behavior (e.g., leaving the current foraging patch; increasing food intake to build up energy reserves) to allostatic changes that modify the set point of feedback-regulated systems, including the HPA axis.

An idealized biological control system with both feedback and feedforward components. For simplicity, the figure does not show reference inputs, disturbances, or sensor noise (see Fig. 1 for details). The controlled fitness-critical variable (in boldface) may be a joint function of the organism and environment. The feedback controller enacts compensatory/reactive responses to challenges that produce discrepancies between the goal (reference input) and the measured state of the variable. The feedforward controller enacts anticipatory/predictive responses to challenges; anticipatory responses that change the reference input of the feedback controller represent instances of allostasis. Note that the control system may involve complex cascades and nested control loops (not shown). Stress occurs when the control system detects a failure to keep the fitness-critical variable within the target range (uncontrollability). Unpredictability refers to failures of the feedforward component to anticipate a challenge and/or respond appropriately; such failures may or may not lead to stress, depending on whether they ultimately result in a failure to control the fitness-critical variable.

For an example at the cellular level, consider the biochemical pathways that protect the cell from oxidative damage ( Zhang et al. 2009 , 2010 ). Oxidative damage is caused by reactive oxygen species and other reactive compounds (e.g., electrophiles), which can be produced as metabolites of foreign molecules (xenobiotics). The critical controlled variable in this case is the cell’s redox environment; deviations from the set point are detected by sensor proteins and relayed to a gene regulatory network in the nucleus (the feedback controller), which in turn activates the expression of antioxidant and detoxifying enzymes (a compensatory response directed at restoring homeostasis). By our definition, a persistent failure to maintain the redox environment within acceptable limits would qualify as oxidative stress. The system is organized as a feedback cascade, with a main outer loop that controls the overall activity of the regulatory network and multiple inner loops that fine-tune the expression of specific enzymes. The feedforward component is provided by xenosensors , nuclear receptors that detect potentially dangerous xenobiotics before they are converted into reactive metabolites. Activated xenosensors trigger various anticipatory responses, both directly by inducing the expression of specific detoxifying enzymes and indirectly by upregulating the activity of the main feedback controller (an instance of allostasis; for details see Zhang et al. 2009 , 2010 ).

Because biological control systems are complex and involve the interplay of multiple components ( Fig. 2 ), control failures—and hence stress—can arise for a variety of distinct reasons. On the one hand, some environmental challenges may be intrinsically hard to predict and/or address, for example because of their intensity (e.g., wildfires, potent toxins), their stochastic nature (e.g., floods, rare predators), or their evolutionary novelty (e.g., invasive predators, novel pollutants). On the other hand, uncontrollability and unpredictability are always joint functions of the environment and the organism; challenges that are manageable for some individuals may exceed the regulatory capacity of others who lack resources, skills, and/or knowledge. As a result, previous stressors may either increase or decrease the organism’s ability to effectively deal with subsequent challenges (see Romero et al. 2009 ; Taff and Vitousek 2016 ). For example, prolonged exposure to stress may deplete an organism’s resources, thus reducing its ability to cope with similar challenges in the future. Conversely, if dealing with a stressor provides useful information and improves the organism’s predictive models, future events may become more predictable and controllable (more on this below). Dysfunctions within the organism may play the role of endogenous stressors (e.g., autoimmunity, circulatory diseases) or—more indirectly—negatively impact the control system’s ability to respond to stress, resulting in delayed, insufficient, or inappropriate responses to challenges.

The nature of unpredictability

Figure 2 helps clarify the distinction between the two defining features of a stressor, uncontrollability and unpredictability (e.g., Koolhaas et al. 2011 ; see above). While uncontrollability broadly refers to the inability to keep the variable of interest within the target range (right side of the figure), unpredictability refers to a particular kind of failure—that is, a failure of the feedforward component to anticipate a challenging event and/or respond appropriately to cues that predict its onset (left side of the figure). Predictive failures can take many different forms, each with somewhat different implications: for example, the control system may correctly predict that a challenge is going to happen but fail to predict when or how it is going to play out. In turn, uncertainty and errors may arise from a number of different sources—including incorrect models of the organism and/or environment, lack of information about the state of the system, or noise in the sensors that relay that information. When predictions are uncertain and involve a large margin of error, a feedforward controller may trigger nonspecific anticipatory responses that are likely to be useful in a broad range of conditions. Alternatively, the controller may make a precise but incorrect prediction and enact an inappropriate response. Both of these cases are distinct from complete predictive failures marked by the absence of anticipatory responses. The current literature on stress emphasizes the latter case, equating unpredictability with the lack of anticipatory responses ( Koolhaas et al. 2011 ); the approach we propose suggests a more nuanced view of unpredictability. As discussed above, feedforward controllers are especially vulnerable to the damaging effects of erroneous or incomplete predictive models. While failing to predict the onset of a stressor (false negatives) leads to the absence of anticipatory responses, erroneously predicting that a stressor will occur (false positives) may trigger unnecessary responses, including allostatic adjustments. Such unnecessary responses may be strong enough to destabilize the whole system and induce a state of stress. Setting the optimal balance between false positives and false negatives is a complex problem that depends on the frequency of different challenges, the reliability of cues, and the fitness costs of responding or failing to respond. Under many conditions, selection may favor the evolution of mechanisms that accept a relatively large rate of false positives as a safety measure (see Nesse 2001 , 2005 ; Johnson et al. 2013 ; Sheriff et al. 2018 ).

Note that, by our definition, unpredictability only leads to stress if it ultimately results in a failure to control the critical variable. When this happens, the compensatory stress responses elicited by uncontrollability may prompt revisions of the predictive model employed by the feedforward controller. This idea is consistent with active inference models, according to which the primary role of feedback pathways in the nervous system is to carry information about prediction errors, which can be used to update the brain’s feedforward models (see Pezzulo et al. 2015 ). It also dovetails with the recent hypothesis that acute stress triggered by unpredictability functions as a “teaching signal” for the brain—by boosting memory for the stressful event, enhancing bottom-up information processing (i.e., increasing the weight of feedback signals), and facilitating rapid learning through mechanisms such as dopamine release ( Trapp et al. 2018 ). In organisms without a nervous system or even single cells, simple forms of revision can take place at the molecular level. In the oxidative stress example, a hypothetical revision mechanism could be as simple as the upregulated expression of xenosensors following a sustained failure to restore redox homeostasis (i.e., oxidative stress). As a result, future exposure to similar amounts of xenobiotics would trigger the expression of larger amounts of detoxifying enzymes. This general pattern has been empirically demonstrated in yeast cells exposed to oxidative stress, which respond to subsequent stressors with increased transcription rates ( Guan et al. 2012 ).

It is noteworthy that, in the approach we have outlined, prediction is treated as an integral component of physiological and behavioral control; as such, it applies equally to long-term adjustments and rapid responses to immediate challenges. For example, agonistic encounters and other social stressors seem to prime inflammatory mechanisms even before any physical damage occurs (see Takahashi et al. 2018 ). This broad view of prediction must be distinguished from the concept of predictive homeostasis in the reactive scope model ( Romero et al. 2009 ), which is explicitly restricted to highly predictable changes on a seasonal, circadian, or life history scale. In the same model, anticipatory responses in the context of acute challenges are regarded as instances of reactive homeostasis ( Romero et al. 2009 , 380). This terminological difference should be kept in mind to avoid confusion.

Hormesis and conditioning

In a variety of domains, empirical findings indicate that prior exposure to low-intensity challenges can have protective effects against later, more severe stressors of the same kind ( Fig. 3A ). Such conditioning effects have been documented in relation to toxins, hypoxia, cardiovascular and thermal stress, and other types of challenges ( Calabrese et al. 2007 ; Calabrese 2016 ). Conditioning is regarded by many as a special case of hormesis , a broad class of biphasic responses in which exposure to low versus high levels of a certain agent (e.g., a toxin) has opposite effects on physiological responses and/or outcomes (typically beneficial at low levels and harmful at high levels; Calabrese and Baldwin 2003 ; Costantini et al. 2010 ; Fig. 3B ). While there is some debate about the generality and evolutionary implications of hormesis ( Forbes 2000 ; Thayer et al. 2005 ; Mushak 2009 , 2013 , 2016 ; Costantini et al. 2010 ), these effects are both theoretically and practically interesting. For example, conditioning is relevant to understanding the interacting effects of multiple challenges and stressors over time—a scenario that is likely common in natural populations ( Romero et al. 2009 ). This is a major focus in the study of endocrine flexibility ( Taff and Vitousek 2016 ), defined as reversible phenotypic plasticity of endocrine traits (e.g., glucocorticoid levels) in response to environmental stimuli. Multiple challenges over time can result in various possible patterns, both beneficial and detrimental to fitness; for example, exposure to stressors may not only impair future flexibility, but also enable a faster response to subsequent stressors (see Taff and Vitousek 2016 ). While conditioning effects likely contribute to determine the shape of such patterns, the literature on endocrine flexibility has remained largely disconnected from that on hormesis. Conversely, biomedical research on hormesis has often ignored the potential fitness costs of ostensibly beneficial conditioning effects (e.g., Costantini et al. 2014 ), which are of primary interest to evolutionary biologists who study plasticity.

( A ) Schematic representation of conditioning effects. Prior exposure to a low-intensity challenge (solid line) has a protective effect against a later, more severe challenge. Protective effects are indicated by less intense responses and/or reduced damage following the high-intensity challenge, compared with the condition in which the organism is not exposed to the low-intensity challenge (dashed line). ( B ) Schematic representation of hormesis in a classic dose–response framework. The shape of the dose–response curve is biphasic, with beneficial effects at low doses (“hormetic zone”) and harmful effects beyond a critical threshold.

From a mechanistic perspective, hormesis is easy to explain as a manifestation or byproduct of adaptive homeostatic control, consistent with the approach presented in this paper. Specifically, hormesis (including conditioning) may arise because low-intensity challenges induce compensatory feedback responses that lead to “overcorrection” ( Stebbing 1987 ); alternatively, low-intensity challenges may engage feedforward responses designed to anticipate future perturbations ( Stebbing 2009 ). Recent work on cellular stress has started to put these ideas in quantitative form through detailed mathematical models of the biochemical networks that mediate responses to toxins, oxidative damage, and so on ( Zhang and Andersen 2007 ; Zhang et al. 2009 , 2010 ; Goulev et al. 2017 ). These models show that various specific mechanisms may produce hormetic effects, including delayed or nonlinear compensatory responses ( Zhang and Andersen 2007 ; Zhang et al. 2009 ; Goulev et al. 2017 ) as well as high-gain anticipatory responses triggered by small perturbations ( Zhang et al. 2009 ).

We suggest that insights gathered from models of cellular stress could be usefully applied to other biological systems, including animals with complex nervous systems. For example, fairly sophisticated mathematical models of the HPA axis in humans and rodents have been developed and refined ( Stanojević et al. 2018 ). These models can be used to simulate the effect of challenges of variable intensity and that of repeated challenges over time, but—to our knowledge—have never been employed to explore the dynamics of conditioning. When feedforward control relies on cognitive processes, low-intensity challenges may contribute to calibrate or revise the predictive model by providing useful information about the environment and the organism, in line with the idea that acute stressors function as “teaching signals” for the brain ( Trapp et al. 2018 ). Interestingly, even single cells show forms of (noncognitive) memory for previous stress exposures (see Guan et al. 2012 ). This example highlights the commonalities that exist between vastly different levels of organization and the potential for cross-fertilization across disciplines.

Trade-offs in the design of stress responses

A systems perspective makes it possible to harness principles from control theory and apply them to long-standing questions about the evolved design of stress responses. One of these principles is the so-called conservation of fragility in feedback-regulated systems, an instance of the pervasive trade-offs between robustness and fragility that characterize both natural and artificial mechanisms ( Csete and Doyle 2002 ; Kitano 2007 ; Khammash 2016 ; see also Bechhoefer 2005 ). The performance of a feedback controller can be modulated by changing its feedback gain (see Fig. 1A ). Specifically, slow (low-frequency) disturbances can be eliminated more effectively by increasing gain; however, each increase in low-frequency stability (robustness) is inevitably compensated by an increase in high-frequency instability (fragility; Fig. 4 ). Above a critical frequency, disturbances are not reduced but amplified and may lead to catastrophic losses of control. A thermostat that is extremely effective at canceling out slow temperature changes (e.g., between night and day) may break into uncontrolled oscillations if exposed to high-frequency changes (e.g., if another heater in the room is turned on and off every few minutes). This phenomenon has been empirically documented in yeast cells: the biochemical pathways that respond to osmotic stress can be dysregulated by fast oscillatory inputs outside the ecological range, leading to uncontrolled hyperactivation of the system ( Mitchell et al. 2015 ). From an alternative perspective, the trade-off between performance at low versus high frequencies can be framed as a trade-off between plasticity and homeostasis ( Frank 2018b ). Specifically, controllers with enhanced ability to reject short-term disturbances (homeostasis) will generally be less effective in adapting to slower, long-term changes in the environment (plasticity), and vice versa.

Illustration of the conservation of fragility in feedback-regulated systems. Fragility is a function of the absolute effect of a disturbance on the system’s output (see Fig. 1A ). Positive fragility means that disturbances are amplified, potentially leading to uncontrolled oscillations. Negative fragility (robustness) means that disturbances are attenuated. Perfect control is obtained when disturbances are fully rejected (i.e., they have no effect on the output). By increasing the feedback gain, the system can be made more robust at low frequencies (slow disturbances); however, each increase in low-frequency robustness is matched by a corresponding increase in fragility at high frequencies (fast disturbances).

Because of robustness-fragility trade-offs, the evolution of stress responses is constrained in ways that may be not immediately intuitive. In particular, the conservation of fragility suggests that organisms may not respond to challenges and stressors as rapidly and intensely as they possibly could. By compromising performance and allowing for a certain “sloppiness” in the expression of physiological responses, they may reduce the risk of catastrophic failures when encountering challenges outside the optimal range. For example, animals are often limited in their ability to undergo rapid hormonal shifts in response to unpredictable events in the environment (“rapid endocrine flexibility”). A possible explanation is that the time lag between the event and the required phenotypic change would be too long for the response to be useful ( Taff and Vitousek 2016 ). The conservation of fragility may contribute to explain why the expression of endocrine-mediated phenotypes has not evolved to be faster and more vigorous (e.g., as a means to prevent catastrophic failures, or to favor long-term plasticity over short-term homeostasis). Of course, the limitations of pure feedback control can be partially overcome by adding feedforward components to the system ( Csete and Doyle 2002 ); however, this entails new points of fragility (e.g., sensitivity to prediction errors), as well as the additional costs of building and maintaining a more complex system. Interestingly, mathematical treatments of the HPA axis have dealt extensively with issues of dynamic stability ( Savić 2008 ; Stanojević et al. 2018 ), but have not explicitly considered the role of robustness–fragility trade-offs in the design of the system.

Novel environments and evolutionary mismatches

Finally, a systems perspective may offer valuable insights into the stresses imposed by novel environments or stimuli, including those resulting from anthropogenic global change. Anthropogenic change can shift environmental parameters outside the range organisms have previously experienced (altered temperatures, carbon dioxide levels, etc.) or give rise to conditions that focal organisms have never encountered, such as the presence of invasive species ( Sih et al. 2011 ). These novel conditions often function as stressors and may reduce fitness, by playing the role of ecological and evolutionary “traps” or engendering other evolutionary mismatches (see Schlaepfer et al. 2002 ; Somero 2012 ; Cofnas 2016 ). For example, climate change interferes with the timing of the activity-hibernation cycle of Arctic ground squirrels, which is regulated by a combination of feedforward mechanisms that anticipate the coming of spring (in both sexes) and feedback mechanisms that respond to temperature (in females; see Buck and Barnes 1999a , 1999b ). With climate change, the short reproductive windows of male and female squirrels can become desynchronized, leading to intraspecific sex-dependent mismatch in reproductive timing—a likely source of stress for this species ( Richter et al. 2017 ; Williams et al. 2017 ).

The outcomes of scenarios involving novel environmental conditions are intrinsically difficult to predict ( Sih 2013 ). The approach we have presented in this paper may provide leverage by pointing to specific vulnerabilities of the various components of biological control systems ( Fig. 2 ). Feedback components are more likely to be compromised when novel conditions exceed the range they have evolved to handle (uncontrollability), resulting in stress responses that are too weak to effectively compensate disturbances. Conditions that fall outside the evolved range may also drive a feedback controller into a zone of fragility, increasing the risk of catastrophic failure (see above; Mitchell et al. 2015 ). In most cases, however, the feedforward components of regulatory systems should be disproportionately affected by novel conditions, given their reliance on prediction and their dependence on accurate models of the environment (whether implicit or explicit). Predictive failures may occur for many different reasons. For instance, sensors may not recognize impending threats that fall outside their design limits, thus failing to activate anticipatory responses; indeed, it has been suggested that many failures to conduct appropriate behavioral responses to novel conditions stem from limited or imperfect information ( Sih 2013 ). Even if sensors detect the novel threats, the controller may rely on an outdated model of the environment or utilize inappropriate decision-making rules ( Schlaepfer et al. 2010 ). As a result, the control system may initiate maladaptive responses that fail to resolve the state of stress or even exacerbate it, with escalating costs and the possibility of sustained damage. While learning can potentially attenuate the impact of novel conditions on predictive mechanisms, learning processes are themselves constrained by past evolutionary history, and may fail to perform adaptively if conditions are sufficiently novel.

Unpacking the concept of stress in light of control theory reveals deep commonalities across levels of biological organization, and suggests a simple but general definition that is potentially amenable to formal analysis. The definition we have proposed is not meant as a replacement for existing models; rather, it is an opportunity for theoretical clarification and a stimulus to explore novel ideas and research directions. From our perspective, stress is a basic feature of all biological systems—and a truly unifying concept that will continue to inform research for decades to come.

The authors wish to thank all the participants to the Editors’ Challenge Workshop on stress at the 2018 SICB meeting in San Francisco, where this paper was conceived.

This work was supported by the National Science Foundation [1711564 to C.J.T.].

Controller: a mechanism whose function is to match the value of a target variable to that of a reference input. The value of the controlled variable is the output of a system; the controller acts on the system to modify its output so as to keep the controlled variable close to the reference input.

Disturbance: an event (not produced by the controller) that changes the state of the system.

Error signal: the discrepancy between the measured system output and the reference input at a given time.

Feedback (closed-loop) control: a mode of control in which the system output is compared with the reference input, and the resulting error signal is used by the controller to determine the control action. Feedback control is reactive and can only correct the effects of disturbances after they have occurred.

Feedback gain: the weight assigned to the error signal in determining the response of the controller. A controller with higher feedback gain will respond more strongly to the same deviation from the reference input.

Feedforward (open-loop) control: a mode of control in which a model of the system is used to determine control actions, without feedback from the system output. Feedforward control can be used to anticipate future disturbances before they occur (to the extent that they can be successfully predicted).

Reference input: the desired value of the controlled variable. The reference input can be static (set point) or dynamic, and can be viewed as the “goal” of the controller.

Robustness/fragility: robustness is the ability of a system to maintain performance in the face of perturbations (broadly defined to include noise and uncertainty). Fragility is lack of robustness, or a system’s sensitivity to perturbations. The robustness of a controller is a measure of its ability to reject disturbances and/or withstand the performance-degrading effects of noise (e.g., sensor noise) and uncertainty.

Sensors: mechanisms that measure the system output (and/or current disturbances) and relay that information to the controller. Sensors may introduce noise and delays in the control loop.

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Article contents

Work, stress, coping, and stress management.

• Sharon Glazer Sharon Glazer University of Baltimore
•  and  Cong Liu Cong Liu Hofstra University
• https://doi.org/10.1093/acrefore/9780190236557.013.30
• Published online: 26 April 2017

Work stress refers to the process of job stressors, or stimuli in the workplace, leading to strains, or negative responses or reactions. Organizational development refers to a process in which problems or opportunities in the work environment are identified, plans are made to remediate or capitalize on the stimuli, action is taken, and subsequently the results of the plans and actions are evaluated. When organizational development strategies are used to assess work stress in the workplace, the actions employed are various stress management interventions. Two key factors tying work stress and organizational development are the role of the person and the role of the environment. In order to cope with work-related stressors and manage strains, organizations must be able to identify and differentiate between factors in the environment that are potential sources of stressors and how individuals perceive those factors. Primary stress management interventions focus on preventing stressors from even presenting, such as by clearly articulating workers’ roles and providing necessary resources for employees to perform their job. Secondary stress management interventions focus on a person’s appraisal of job stressors as a threat or challenge, and the person’s ability to cope with the stressors (presuming sufficient internal resources, such as a sense of meaningfulness in life, or external resources, such as social support from a supervisor). When coping is not successful, strains may develop. Tertiary stress management interventions attempt to remediate strains, by addressing the consequence itself (e.g., diabetes management) and/or the source of the strain (e.g., reducing workload). The person and/or the organization may be the targets of the intervention. The ultimate goal of stress management interventions is to minimize problems in the work environment, intensify aspects of the work environment that create a sense of a quality work context, enable people to cope with stressors that might arise, and provide tools for employees and organizations to manage strains that might develop despite all best efforts to create a healthy workplace.

• stress management
• organization development
• organizational interventions
• stress theories and frameworks

Introduction

Work stress is a generic term that refers to work-related stimuli (aka job stressors) that may lead to physical, behavioral, or psychological consequences (i.e., strains) that affect both the health and well-being of the employee and the organization. Not all stressors lead to strains, but all strains are a result of stressors, actual or perceived. Common terms often used interchangeably with work stress are occupational stress, job stress, and work-related stress. Terms used interchangeably with job stressors include work stressors, and as the specificity of the type of stressor might include psychosocial stressor (referring to the psychological experience of work demands that have a social component, e.g., conflict between two people; Hauke, Flintrop, Brun, & Rugulies, 2011 ), hindrance stressor (i.e., a stressor that prevents goal attainment; Cavanaugh, Boswell, Roehling, & Boudreau, 2000 ), and challenge stressor (i.e., a stressor that is difficult, but attainable and possibly rewarding to attain; Cavanaugh et al., 2000 ).

Stress in the workplace continues to be a highly pervasive problem, having both direct negative effects on individuals experiencing it and companies paying for it, and indirect costs vis à vis lost productivity (Dopkeen & DuBois, 2014 ). For example, U.K. public civil servants’ work-related stress rose from 10.8% in 2006 to 22.4% in 2013 and about one-third of the workforce has taken more than 20 days of leave due to stress-related ill-health, while well over 50% are present at work when ill (French, 2015 ). These findings are consistent with a report by the International Labor Organization (ILO, 2012 ), whereby 50% to 60% of all workdays are lost due to absence attributed to factors associated with work stress.

The prevalence of work-related stress is not diminishing despite improvements in technology and employment rates. The sources of stress, such as workload, seem to exacerbate with improvements in technology (Coovert & Thompson, 2003 ). Moreover, accessibility through mobile technology and virtual computer terminals is linking people to their work more than ever before (ILO, 2012 ; Tarafdar, Tu, Ragu-Nathan, & Ragu-Nathan, 2007 ). Evidence of this kind of mobility and flexibility is further reinforced in a June 2007 survey of 4,025 email users (over 13 years of age); AOL reported that four in ten survey respondents reported planning their vacations around email accessibility and 83% checked their emails at least once a day while away (McMahon, 2007 ). Ironically, despite these mounting work-related stressors and clear financial and performance outcomes, some individuals are reporting they are less “stressed,” but only because “stress has become the new normal” (Jayson, 2012 , para. 4).

This new normal is likely the source of psychological and physiological illness. Siegrist ( 2010 ) contends that conditions in the workplace, particularly psychosocial stressors that are perceived as unfavorable relationships with others and self, and an increasingly sedentary lifestyle (reinforced with desk jobs) are increasingly contributing to cardiovascular disease. These factors together justify a need to continue on the path of helping individuals recognize and cope with deleterious stressors in the work environment and, equally important, to find ways to help organizations prevent harmful stressors over which they have control, as well as implement policies or mechanisms to help employees deal with these stressors and subsequent strains. Along with a greater focus on mitigating environmental constraints are interventions that can be used to prevent anxiety, poor attitudes toward the workplace conditions and arrangements, and subsequent cardiovascular illness, absenteeism, and poor job performance (Siegrist, 2010 ).

Even the ILO has presented guidance on how the workplace can help prevent harmful job stressors (aka hindrance stressors) or at least help workers cope with them. Consistent with the view that well-being is not the absence of stressors or strains and with the view that positive psychology offers a lens for proactively preventing stressors, the ILO promotes increasing preventative risk assessments, interventions to prevent and control stressors, transparent organizational communication, worker involvement in decision-making, networks and mechanisms for workplace social support, awareness of how working and living conditions interact, safety, health, and well-being in the organization (ILO, n.d. ). The field of industrial and organizational (IO) psychology supports the ILO’s recommendations.

IO psychology views work stress as the process of a person’s interaction with multiple aspects of the work environment, job design, and work conditions in the organization. Interventions to manage work stress, therefore, focus on the psychosocial factors of the person and his or her relationships with others and the socio-technical factors related to the work environment and work processes. Viewing work stress from the lens of the person and the environment stems from Kurt Lewin’s ( 1936 ) work that stipulates a person’s state of mental health and behaviors are a function of the person within a specific environment or situation. Aspects of the work environment that affect individuals’ mental states and behaviors include organizational hierarchy, organizational climate (including processes, policies, practices, and reward structures), resources to support a person’s ability to fulfill job duties, and management structure (including leadership). Job design refers to each contributor’s tasks and responsibilities for fulfilling goals associated with the work role. Finally, working conditions refers not only to the physical environment, but also the interpersonal relationships with other contributors.

Each of the conditions that are identified in the work environment may be perceived as potentially harmful or a threat to the person or as an opportunity. When a stressor is perceived as a threat to attaining desired goals or outcomes, the stressor may be labeled as a hindrance stressor (e.g., LePine, Podsakoff, & Lepine, 2005 ). When the stressor is perceived as an opportunity to attain a desired goal or end state, it may be labeled as a challenge stressor. According to LePine and colleagues’ ( 2005 ), both challenge (e.g., time urgency, workload) and hindrance (e.g., hassles, role ambiguity, role conflict) stressors could lead to strains (as measured by “anxiety, depersonalization, depression, emotional exhaustion, frustration, health complaints, hostility, illness, physical symptoms, and tension” [p. 767]). However, challenge stressors positively relate with motivation and performance, whereas hindrance stressors negatively relate with motivation and performance. Moreover, motivation and strains partially mediate the relationship between hindrance and challenge stressors with performance.

Figure 1. Organizational development frameworks to guide identification of work stress and interventions.

In order to (1) minimize any potential negative effects from stressors, (2) increase coping skills to deal with stressors, or (3) manage strains, organizational practitioners or consultants will devise organizational interventions geared toward prevention, coping, and/or stress management. Ultimately, toxic factors in the work environment can have deleterious effects on a person’s physical and psychological well-being, as well as on an organization’s total health. It behooves management to take stock of the organization’s health, which includes the health and well-being of its employees, if the organization wishes to thrive and be profitable. According to Page and Vella-Brodrick’s ( 2009 ) model of employee well-being, employee well-being results from subjective well-being (i.e., life satisfaction and general positive or negative affect), workplace well-being (composed of job satisfaction and work-specific positive or negative affect), and psychological well-being (e.g., self-acceptance, positive social relations, mastery, purpose in life). Job stressors that become unbearable are likely to negatively affect workplace well-being and thus overall employee well-being. Because work stress is a major organizational pain point and organizations often employ organizational consultants to help identify and remediate pain points, the focus here is on organizational development (OD) frameworks; several work stress frameworks are presented that together signal areas where organizations might focus efforts for change in employee behaviors, attitudes, and performance, as well as the organization’s performance and climate. Work stress, interventions, and several OD and stress frameworks are depicted in Figure 1 .

The goals are: (1) to conceptually define and clarify terms associated with stress and stress management, particularly focusing on organizational factors that contribute to stress and stress management, and (2) to present research that informs current knowledge and practices on workplace stress management strategies. Stressors and strains will be defined, leading OD and work stress frameworks that are used to organize and help organizations make sense of the work environment and the organization’s responsibility in stress management will be explored, and stress management will be explained as an overarching thematic label; an area of study and practice that focuses on prevention (primary) interventions, coping (secondary) interventions, and managing strains (tertiary) interventions; as well as the label typically used to denote tertiary interventions. Suggestions for future research and implications toward becoming a healthy organization are presented.

Defining Stressors and Strains

Work-related stressors or job stressors can lead to different kinds of strains individuals and organizations might experience. Various types of stress management interventions, guided by OD and work stress frameworks, may be employed to prevent or cope with job stressors and manage strains that develop(ed).

A job stressor is a stimulus external to an employee and a result of an employee’s work conditions. Example job stressors include organizational constraints, workplace mistreatments (such as abusive supervision, workplace ostracism, incivility, bullying), role stressors, workload, work-family conflicts, errors or mistakes, examinations and evaluations, and lack of structure (Jex & Beehr, 1991 ; Liu, Spector, & Shi, 2007 ; Narayanan, Menon, & Spector, 1999 ). Although stressors may be categorized as hindrances and challenges, there is not yet sufficient information to be able to propose which stress management interventions would better serve to reduce those hindrance stressors or to reduce strain-producing challenge stressors while reinforcing engagement-producing challenge stressors.

Organizational Constraints

Organizational constraints may be hindrance stressors as they prevent employees from translating their motivation and ability into high-level job performance (Peters & O’Connor, 1980 ). Peters and O’Connor ( 1988 ) defined 11 categories of organizational constraints: (1) job-related information, (2) budgetary support, (3) required support, (4) materials and supplies, (5) required services and help from others, (6) task preparation, (7) time availability, (8) the work environment, (9) scheduling of activities, (10) transportation, and (11) job-relevant authority. The inhibiting effect of organizational constraints may be due to the lack of, inadequacy of, or poor quality of these categories.

Workplace Mistreatment

Workplace mistreatment presents a cluster of interpersonal variables, such as interpersonal conflict, bullying, incivility, and workplace ostracism (Hershcovis, 2011 ; Tepper & Henle, 2011 ). Typical workplace mistreatment behaviors include gossiping, rude comments, showing favoritism, yelling, lying, and ignoring other people at work (Tepper & Henle, 2011 ). These variables relate to employees’ psychological well-being, physical well-being, work attitudes (e.g., job satisfaction and organizational commitment), and turnover intention (e.g., Hershcovis, 2011 ; Spector & Jex, 1998 ). Some researchers differentiated the source of mistreatment, such as mistreatment from one’s supervisor versus mistreatment from one’s coworker (e.g., Bruk-Lee & Spector, 2006 ; Frone, 2000 ; Liu, Liu, Spector, & Shi, 2011 ).

Role Stressors

Role stressors are demands, constraints, or opportunities a person perceives to be associated, and thus expected, with his or her work role(s) across various situations. Three commonly studied role stressors are role ambiguity, role conflict, and role overload (Glazer & Beehr, 2005 ; Kahn, Wolfe, Quinn, Snoek, & Rosenthal, 1964 ). Role ambiguity in the workplace occurs when an employee lacks clarity regarding what performance-related behaviors are expected of him or her. Role conflict refers to situations wherein an employee receives incompatible role requests from the same or different supervisors or the employee is asked to engage in work that impedes his or her performance in other work or nonwork roles or clashes with his or her values. Role overload refers to excessive demands and insufficient time (quantitative) or knowledge (qualitative) to complete the work. The construct is often used interchangeably with workload, though role overload focuses more on perceived expectations from others about one’s workload. These role stressors significantly relate to low job satisfaction, low organizational commitment, low job performance, high tension or anxiety, and high turnover intention (Abramis, 1994 ; Glazer & Beehr, 2005 ; Jackson & Schuler, 1985 ).

Excessive workload is one of the most salient stressors at work (e.g., Liu et al., 2007 ). There are two types of workload: quantitative and qualitative workload (LaRocco, Tetrick, & Meder, 1989 ; Parasuraman & Purohit, 2000 ). Quantitative workload refers to the excessive amount of work one has. In a summary of a Chartered Institute of Personnel & Development Report from 2006 , Dewe and Kompier ( 2008 ) noted that quantitative workload was one of the top three stressors workers experienced at work. Qualitative workload refers to the difficulty of work. Workload also differs by the type of the load. There are mental workload and physical workload (Dwyer & Ganster, 1991 ). Excessive physical workload may result in physical discomfort or illness. Excessive mental workload will cause psychological distress such as anxiety or frustration (Bowling & Kirkendall, 2012 ). Another factor affecting quantitative workload is interruptions (during the workday). Lin, Kain, and Fritz ( 2013 ) found that interruptions delay completion of job tasks, thus adding to the perception of workload.

Work-Family Conflict

Work-family conflict is a form of inter-role conflict in which demands from one’s work domain and one’s family domain are incompatible to some extent (Greenhaus & Beutell, 1985 ). Work can interfere with family (WIF) and/or family can interfere with work (FIW) due to time-related commitments to participating in one domain or another, incompatible behavioral expectations, or when strains in one domain carry over to the other (Greenhaus & Beutell, 1985 ). Work-family conflict significantly relates to work-related outcomes (e.g., job satisfaction, organizational commitment, turnover intention, burnout, absenteeism, job performance, job strains, career satisfaction, and organizational citizenship behaviors), family-related outcomes (e.g., marital satisfaction, family satisfaction, family-related performance, family-related strains), and domain-unspecific outcomes (e.g., life satisfaction, psychological strain, somatic or physical symptoms, depression, substance use or abuse, and anxiety; Amstad, Meier, Fasel, Elfering, & Semmer, 2011 ).

Individuals and organizations can experience work-related strains. Sometimes organizations will experience strains through the employee’s negative attitudes or strains, such as that a worker’s absence might yield lower production rates, which would roll up into an organizational metric of organizational performance. In the industrial and organizational (IO) psychology literature, organizational strains are mostly observed as macro-level indicators, such as health insurance costs, accident-free days, and pervasive problems with company morale. In contrast, individual strains, usually referred to as job strains, are internal to an employee. They are responses to work conditions and relate to health and well-being of employees. In other words, “job strains are adverse reactions employees have to job stressors” (Spector, Chen, & O’Connell, 2000 , p. 211). Job strains tend to fall into three categories: behavioral, physical, and psychological (Jex & Beehr, 1991 ).

Behavioral strains consist of actions that employees take in response to job stressors. Examples of behavioral strains include employees drinking alcohol in the workplace or intentionally calling in sick when they are not ill (Spector et al., 2000 ). Physical strains consist of health symptoms that are physiological in nature that employees contract in response to job stressors. Headaches and ulcers are examples of physical strains. Lastly, psychological strains are emotional reactions and attitudes that employees have in response to job stressors. Examples of psychological strains are job dissatisfaction, anxiety, and frustration (Spector et al., 2000 ). Interestingly, research studies that utilize self-report measures find that most job strains experienced by employees tend to be psychological strains (Spector et al., 2000 ).

Leading Frameworks

Organizations that are keen on identifying organizational pain points and remedying them through organizational campaigns or initiatives often discover the pain points are rooted in work-related stressors and strains and the initiatives have to focus on reducing workers’ stress and increasing a company’s profitability. Through organizational climate surveys, for example, companies discover that aspects of the organization’s environment, including its policies, practices, reward structures, procedures, and processes, as well as employees at all levels of the company, are contributing to the individual and organizational stress. Recent studies have even begun to examine team climates for eustress and distress assessed in terms of team members’ homogenous psychological experience of vigor, efficacy, dedication, and cynicism (e.g., Kożusznik, Rodriguez, & Peiro, 2015 ).

Each of the frameworks presented advances different aspects that need to be identified in order to understand the source and potential remedy for stressors and strains. In some models, the focus is on resources, in others on the interaction of the person and environment, and in still others on the role of the person in the workplace. Few frameworks directly examine the role of the organization, but the organization could use these frameworks to plan interventions that would minimize stressors, cope with existing stressors, and prevent and/or manage strains. One of the leading frameworks in work stress research that is used to guide organizational interventions is the person and environment (P-E) fit (French & Caplan, 1972 ). Its precursor is the University of Michigan Institute for Social Research’s (ISR) role stress model (Kahn, Wolfe, Quinn, Snoek, & Rosenthal, 1964 ) and Lewin’s Field Theory. Several other theories have since evolved from the P-E fit framework, including Karasek and Theorell’s ( 1990 ), Karasek ( 1979 ) Job Demands-Control Model (JD-C), the transactional framework (Lazarus & Folkman, 1984 ), Conservation of Resources (COR) theory (Hobfoll, 1989 ), and Siegrist’s ( 1996 ) Effort-Reward Imbalance (ERI) Model.

Field Theory

The premise of Kahn et al.’s ( 1964 ) role stress theory is Lewin’s ( 1997 ) Field Theory. Lewin purported that behavior and mental events are a dynamic function of the whole person, including a person’s beliefs, values, abilities, needs, thoughts, and feelings, within a given situation (field or environment), as well as the way a person represents his or her understanding of the field and behaves in that space. Lewin explains that work-related strains are a result of individuals’ subjective perceptions of objective factors, such as work roles, relationships with others in the workplace, as well as personality indicators, and can be used to predict people’s reactions, including illness. Thus, to make changes to an organizational system, it is necessary to understand a field and try to move that field from the current state to the desired state. Making this move necessitates identifying mechanisms influencing individuals.

Role Stress Theory

Role stress theory mostly isolates the perspective a person has about his or her work-related responsibilities and expectations to determine how those perceptions relate with a person’s work-related strains. However, those relationships have been met with somewhat varied results, which Glazer and Beehr ( 2005 ) concluded might be a function of differences in culture, an environmental factor often neglected in research. Kahn et al.’s ( 1964 ) role stress theory, coupled with Lewin’s ( 1936 ) Field Theory, serves as the foundation for the P-E fit theory. Lewin ( 1936 ) wrote, “Every psychological event depends upon the state of the person and at the same time on the environment” (p. 12). Researchers of IO psychology have narrowed the environment to the organization or work team. This narrowed view of the organizational environment is evident in French and Caplan’s ( 1972 ) P-E fit framework.

Person-Environment Fit Theory

The P-E fit framework focuses on the extent to which there is congruence between the person and a given environment, such as the organization (Caplan, 1987 ; Edwards, 2008 ). For example, does the person have the necessary skills and abilities to fulfill an organization’s demands, or does the environment support a person’s desire for autonomy (i.e., do the values align?) or fulfill a person’s needs (i.e., a person’s needs are rewarded). Theoretically and empirically, the greater the person-organization fit, the greater a person’s job satisfaction and organizational commitment, the less a person’s turnover intention and work-related stress (see meta-analyses by Assouline & Meir, 1987 ; Kristof-Brown, Zimmerman, & Johnson, 2005 ; Verquer, Beehr, & Wagner, 2003 ).

Job Demands-Control/Support (JD-C/S) and Job Demands-Resources (JD-R) Model

Focusing more closely on concrete aspects of work demands and the extent to which a person perceives he or she has control or decision latitude over those demands, Karasek ( 1979 ) developed the JD-C model. Karasek and Theorell ( 1990 ) posited that high job demands under conditions of little decision latitude or control yield high strains, which have varied implications on the health of an organization (e.g., in terms of high turnover, employee ill-health, poor organizational performance). This theory was modified slightly to address not only control, but also other resources that could protect a person from unruly job demands, including support (aka JD-C/S, Johnson & Hall, 1988 ; and JD-R, Bakker, van Veldhoven, & Xanthopoulou, 2010 ). Whether focusing on control or resources, both they and job demands are said to reflect workplace characteristics, while control and resources also represent coping strategies or tools (Siegrist, 2010 ).

Despite the glut of research testing the JD-C and JD-R, results are somewhat mixed. Testing the interaction between job demands and control, Beehr, Glaser, Canali, and Wallwey ( 2001 ) did not find empirical support for the JD-C theory. However, Dawson, O’Brien, and Beehr ( 2016 ) found that high control and high support buffered against the independent deleterious effects of interpersonal conflict, role conflict, and organizational politics (demands that were categorized as hindrance stressors) on anxiety, as well as the effects of interpersonal conflict and organizational politics on physiological symptoms, but control and support did not moderate the effects between challenge stressors and strains. Coupled with Bakker, Demerouti, and Sanz-Vergel’s ( 2014 ) note that excessive job demands are a source of strain, but increased job resources are a source of engagement, Dawson et al.’s results suggest that when an organization identifies that demands are hindrances, it can create strategies for primary (preventative) stress management interventions and attempt to remove or reduce such work demands. If the demands are challenging, though manageable, but latitude to control the challenging stressors and support are insufficient, the organization could modify practices and train employees on adopting better strategies for meeting or coping (secondary stress management intervention) with the demands. Finally, if the organization can neither afford to modify the demands or the level of control and support, it will be necessary for the organization to develop stress management (tertiary) interventions to deal with the inevitable strains.

Conservation of Resources Theory

The idea that job resources reinforce engagement in work has been propagated in Hobfoll’s ( 1989 ) Conservation of Resources (COR) theory. COR theory also draws on the foundational premise that people’s mental health is a function of the person and the environment, forwarding that how people interpret their environment (including the societal context) affects their stress levels. Hobfoll focuses on resources such as objects, personal characteristics, conditions, or energies as particularly instrumental to minimizing strains. He asserts that people do whatever they can to protect their valued resources. Thus, strains develop when resources are threatened to be taken away, actually taken away, or when additional resources are not attainable after investing in the possibility of gaining more resources (Hobfoll, 2001 ). By extension, organizations can invest in activities that would minimize resource loss and create opportunities for resource gains and thus have direct implications for devising primary and secondary stress management interventions.

Transactional Framework

Lazarus and Folkman ( 1984 ) developed the widely studied transactional framework of stress. This framework holds as a key component the cognitive appraisal process. When individuals perceive factors in the work environment as a threat (i.e., primary appraisal), they will scan the available resources (external or internal to himself or herself) to cope with the stressors (i.e., secondary appraisal). If the coping resources provide minimal relief, strains develop. Until recently, little attention has been given to the cognitive appraisal associated with different work stressors (Dewe & Kompier, 2008 ; Liu & Li, 2017 ). In a study of Polish and Spanish social care service providers, stressors appraised as a threat related positively to burnout and less engagement, but stressors perceived as challenges yielded greater engagement and less burnout (Kożusznik, Rodriguez, & Peiro, 2012 ). Similarly, Dawson et al. ( 2016 ) found that even with support and control resources, hindrance demands were more strain-producing than challenge demands, suggesting that appraisal of the stressor is important. In fact, “many people respond well to challenging work” (Beehr et al., 2001 , p. 126). Kożusznik et al. ( 2012 ) recommend training employees to change the way they view work demands in order to increase engagement, considering that part of the problem may be about how the person appraises his or her environment and, thus, copes with the stressors.

Effort-Reward Imbalance

Siegrist’s ( 1996 ) Model of Effort-Reward Imbalance (ERI) focuses on the notion of social reciprocity, such that a person fulfills required work tasks in exchange for desired rewards (Siegrist, 2010 ). ERI sheds light on how an imbalance in a person’s expectations of an organization’s rewards (e.g., pay, bonus, sense of advancement and development, job security) in exchange for a person’s efforts, that is a break in one’s work contract, leads to negative responses, including long-term ill-health (Siegrist, 2010 ; Siegrist et al., 2014 ). In fact, prolonged perception of a work contract imbalance leads to adverse health, including immunological problems and inflammation, which contribute to cardiovascular disease (Siegrist, 2010 ). The model resembles the relational and interactional psychological contract theory in that it describes an employee’s perception of the terms of the relationship between the person and the workplace, including expectations of performance, job security, training and development opportunities, career progression, salary, and bonuses (Thomas, Au, & Ravlin, 2003 ). The psychological contract, like the ERI model, focuses on social exchange. Furthermore, the psychological contract, like stress theories, are influenced by cultural factors that shape how people interpret their environments (Glazer, 2008 ; Thomas et al., 2003 ). Violations of the psychological contract will negatively affect a person’s attitudes toward the workplace and subsequent health and well-being (Siegrist, 2010 ). To remediate strain, Siegrist ( 2010 ) focuses on both the person and the environment, recognizing that the organization is particularly responsible for changing unfavorable work conditions and the person is responsible for modifying his or her reactions to such conditions.

Stress Management Interventions: Primary, Secondary, and Tertiary

Remediation of work stress and organizational development interventions are about realigning the employee’s experiences in the workplace with factors in the environment, as well as closing the gap between the current environment and the desired environment. Work stress develops when an employee perceives the work demands to exceed the person’s resources to cope and thus threatens employee well-being (Dewe & Kompier, 2008 ). Likewise, an organization’s need to change arises when forces in the environment are creating a need to change in order to survive (see Figure 1 ). Lewin’s ( 1951 ) Force Field Analysis, the foundations of which are in Field Theory, is one of the first organizational development intervention tools presented in the social science literature. The concept behind Force Field Analysis is that in order to survive, organizations must adapt to environmental forces driving a need for organizational change and remove restraining forces that create obstacles to organizational change. In order to do this, management needs to delineate the current field in which the organization is functioning, understand the driving forces for change, identify and dampen or eliminate the restraining forces against change. Several models for analyses may be applied, but most approaches are variations of organizational climate surveys.

Through organizational surveys, workers provide management with a snapshot view of how they perceive aspects of their work environment. Thus, the view of the health of an organization is a function of several factors, chief among them employees’ views (i.e., the climate) about the workplace (Lewin, 1951 ). Indeed, French and Kahn ( 1962 ) posited that well-being depends on the extent to which properties of the person and properties of the environment align in terms of what a person requires and the resources available in a given environment. Therefore, only when properties of the person and properties of the environment are sufficiently understood can plans for change be developed and implemented targeting the environment (e.g., change reporting structures to relieve, and thus prevent future, communication stressors) and/or the person (e.g., providing more autonomy, vacation days, training on new technology). In short, climate survey findings can guide consultants about the emphasis for organizational interventions: before a problem arises aka stress prevention, e.g., carefully crafting job roles), when a problem is present, but steps are taken to mitigate their consequences (aka coping, e.g., providing social support groups), and/or once strains develop (aka. stress management, e.g., healthcare management policies).

For each of the primary (prevention), secondary (coping), and tertiary (stress management) techniques the target for intervention can be the entire workforce, a subset of the workforce, or a specific person. Interventions that target the entire workforce may be considered organizational interventions, as they have direct implications on the health of all individuals and consequently the health of the organization. Several interventions categorized as primary and secondary interventions may also be implemented after strains have developed and after it has been discerned that a person or the organization did not do enough to mitigate stressors or strains (see Figure 1 ). The designation of many of the interventions as belonging to one category or another may be viewed as merely a suggestion.

Primary Interventions (Preventative Stress Management)

Before individuals begin to perceive work-related stressors, organizations engage in stress prevention strategies, such as providing people with resources (e.g., computers, printers, desk space, information about the job role, organizational reporting structures) to do their jobs. However, sometimes the institutional structures and resources are insufficient or ambiguous. Scholars and practitioners have identified several preventative stress management strategies that may be implemented.

Planning and Time Management

When employees feel quantitatively overloaded, sometimes the remedy is improving the employees’ abilities to plan and manage their time (Quick, Quick, Nelson, & Hurrell, 2003 ). Planning is a future-oriented activity that focuses on conceptual and comprehensive work goals. Time management is a behavior that focuses on organizing, prioritizing, and scheduling work activities to achieve short-term goals. Given the purpose of time management, it is considered a primary intervention, as engaging in time management helps to prevent work tasks from mounting and becoming unmanageable, which would subsequently lead to adverse outcomes. Time management comprises three fundamental components: (1) establishing goals, (2) identifying and prioritizing tasks to fulfill the goals, and (3) scheduling and monitoring progress toward goal achievement (Peeters & Rutte, 2005 ). Workers who employ time management have less role ambiguity (Macan, Shahani, Dipboye, & Philips, 1990 ), psychological stress or strain (Adams & Jex, 1999 ; Jex & Elaqua, 1999 ; Macan et al., 1990 ), and greater job satisfaction (Macan, 1994 ). However, Macan ( 1994 ) did not find a relationship between time management and performance. Still, Claessens, van Eerde, Rutte, and Roe ( 2004 ) found that perceived control of time partially mediated the relationships between planning behavior (an indicator of time management), job autonomy, and workload on one hand, and job strains, job satisfaction, and job performance on the other hand. Moreover, Peeters and Rutte ( 2005 ) observed that teachers with high work demands and low autonomy experienced more burnout when they had poor time management skills.

Person-Organization Fit

Just as it is important for organizations to find the right person for the job and organization, so is it the responsibility of a person to choose to work at the right organization—an organization that fulfills the person’s needs and upholds the values important to the individual, as much as the person fulfills the organization’s needs and adapts to its values. When people fit their employing organizations they are setting themselves up for experiencing less strain-producing stressors (Kristof-Brown et al., 2005 ). In a meta-analysis of 62 person-job fit studies and 110 person-organization fit studies, Kristof-Brown et al. ( 2005 ) found that person-job fit had a negative correlation with indicators of job strain. In fact, a primary intervention of career counseling can help to reduce stress levels (Firth-Cozens, 2003 ).

Job Redesign

The Job Demands-Control/Support (JD-C/S), Job Demands-Resources (JD-R), and transactional models all suggest that factors in the work context require modifications in order to reduce potential ill-health and poor organizational performance. Drawing on Hackman and Oldham’s ( 1980 ) Job Characteristics Model, it is possible to assess with the Job Diagnostics Survey (JDS) the current state of work characteristics related to skill variety, task identity, task significance, autonomy, and feedback. Modifying those aspects would help create a sense of meaningfulness, sense of responsibility, and feeling of knowing how one is performing, which subsequently affects a person’s well-being as identified in assessments of motivation, satisfaction, improved performance, and reduced withdrawal intentions and behaviors. Extending this argument to the stress models, it can be deduced that reducing uncertainty or perceived unfairness that may be associated with a person’s perception of these work characteristics, as well as making changes to physical characteristics of the environment (e.g., lighting, seating, desk, air quality), nature of work (e.g., job responsibilities, roles, decision-making latitude), and organizational arrangements (e.g., reporting structure and feedback mechanisms), can help mitigate against numerous ill-health consequences and reduced organizational performance. In fact, Fried et al. ( 2013 ) showed that healthy patients of a medical clinic whose jobs were excessively low (i.e., monotonous) or excessively high (i.e., overstimulating) on job enrichment (as measured by the JDS) had greater abdominal obesity than those whose jobs were optimally enriched. By taking stock of employees’ perceptions of the current work situation, managers might think about ways to enhance employees’ coping toolkit, such as training on how to deal with difficult clients or creating stimulating opportunities when jobs have low levels of enrichment.

Participatory Action Research Interventions

Participatory action research (PAR) is an intervention wherein, through group discussions, employees help to identify and define problems in organizational structure, processes, policies, practices, and reward structures, as well as help to design, implement, and evaluate success of solutions. PAR is in itself an intervention, but its goal is to design interventions to eliminate or reduce work-related factors that are impeding performance and causing people to be unwell. An example of a successful primary intervention, utilizing principles of PAR and driven by the JD-C and JD-C/S stress frameworks is Health Circles (HCs; Aust & Ducki, 2004 ).

HCs, developed in Germany in the 1980s, were popular practices in industries, such as metal, steel, and chemical, and service. Similar to other problem-solving practices, such as quality circles, HCs were based on the assumptions that employees are the experts of their jobs. For this reason, to promote employee well-being, management and administrators solicited suggestions and ideas from the employees to improve occupational health, thereby increasing employees’ job control. HCs also promoted communication between managers and employees, which had a potential to increase social support. With more control and support, employees would experience less strains and better occupational well-being.

Employing the three-steps of (1) problem analysis (i.e., diagnosis or discovery through data generated from organizational records of absenteeism length, frequency, rate, and reason and employee survey), (2) HC meetings (6 to 10 meetings held over several months to brainstorm ideas to improve occupational safety and health concerns identified in the discovery phase), and (3) HC evaluation (to determine if desired changes were accomplished and if employees’ reports of stressors and strains changed after the course of 15 months), improvements were to be expected (Aust & Ducki, 2004 ). Aust and Ducki ( 2004 ) reviewed 11 studies presenting 81 health circles in 30 different organizations. Overall study participants had high satisfaction with the HCs practices. Most companies acted upon employees’ suggestions (e.g., improving driver’s seat and cab, reducing ticket sale during drive, team restructuring and job rotation to facilitate communication, hiring more employees during summer time, and supervisor training program to improve leadership and communication skills) to improve work conditions. Thus, HCs represent a successful theory-grounded intervention to routinely improve employees’ occupational health.

Physical Setting

The physical environment or physical workspace has an enormous impact on individuals’ well-being, attitudes, and interactions with others, as well as on the implications on innovation and well-being (Oksanen & Ståhle, 2013 ; Vischer, 2007 ). In a study of 74 new product development teams (total of 437 study respondents) in Western Europe, Chong, van Eerde, Rutte, and Chai ( 2012 ) found that when teams were faced with challenge time pressures, meaning the teams had a strong interest and desire in tackling complex, but engaging tasks, when they were working proximally close with one another, team communication improved. Chong et al. assert that their finding aligns with prior studies that have shown that physical proximity promotes increased awareness of other team members, greater tendency to initiate conversations, and greater team identification. However, they also found that when faced with hindrance time pressures, physical proximity related to low levels of team communication, but when hindrance time pressure was low, team proximity had an increasingly greater positive relationship with team communication.

In addition to considering the type of work demand teams must address, other physical workspace considerations include whether people need to work collaboratively and synchronously or independently and remotely (or a combination thereof). Consideration needs to be given to how company contributors would satisfy client needs through various modes of communication, such as email vs. telephone, and whether individuals who work by a window might need shading to block bright sunlight from glaring on their computer screens. Finally, people who have to use the telephone for extensive periods of time would benefit from earphones to prevent neck strains. Most physical stressors are rather simple to rectify. However, companies are often not aware of a problem until after a problem arises, such as when a person’s back is strained from trying to move heavy equipment. Companies then implement strategies to remediate the environmental stressor. With the help of human factors, and organizational and office design consultants, many of the physical barriers to optimal performance can be prevented (Rousseau & Aubé, 2010 ). In a study of 215 French-speaking Canadian healthcare employees, Rousseau and Aubé ( 2010 ) found that although supervisor instrumental support positively related with affective commitment to the organization, the relationship was even stronger for those who reported satisfaction with the ambient environment (i.e., temperature, lighting, sound, ventilation, and cleanliness).

Secondary Interventions (Coping)

Secondary interventions, also referred to as coping, focus on resources people can use to mitigate the risk of work-related illness or workplace injury. Resources may include properties related to social resources, behaviors, and cognitive structures. Each of these resource domains may be employed to cope with stressors. Monat and Lazarus ( 1991 ) summarize the definition of coping as “an individual’s efforts to master demands (or conditions of harm, threat, or challenge) that are appraised (or perceived) as exceeding or taxing his or her resources” (p. 5). To master demands requires use of the aforementioned resources. Secondary interventions help employees become aware of the psychological, physical, and behavioral responses that may occur from the stressors presented in their working environment. Secondary interventions help a person detect and attend to stressors and identify resources for and ways of mitigating job strains. Often, coping strategies are learned skills that have a cognitive foundation and serve important functions in improving people’s management of stressors (Lazarus & Folkman, 1991 ). Coping is effortful, but with practice it becomes easier to employ. This idea is the foundation for understanding the role of resilience in coping with stressors. However, “not all adaptive processes are coping. Coping is a subset of adaptational activities that involves effort and does not include everything that we do in relating to the environment” (Lazarus & Folkman, 1991 , p. 198). Furthermore, sometimes to cope with a stressor, a person may call upon social support sources to help with tangible materials or emotional comfort. People call upon support resources because they help to restructure how a person approaches or thinks about the stressor.

Most secondary interventions are aimed at helping the individual, though companies, as a policy, might require all employees to partake in training aimed at increasing employees’ awareness of and skills aimed at handling difficult situations vis à vis company channels (e.g., reporting on sexual harassment or discrimination). Furthermore, organizations might institute mentoring programs or work groups to address various work-related matters. These programs employ awareness-raising activities, stress-education, or skills training (cf., Bhagat, Segovis, & Nelson, 2012 ), which include development of skills in problem-solving, understanding emotion-focused coping, identifying and using social support, and enhancing capacity for resilience. The aim of these programs, therefore, is to help employees proactively review their perceptions of psychological, physical, and behavioral job-related strains, thereby extending their resilience, enabling them to form a personal plan to control stressors and practice coping skills (Cooper, Dewe, & O’Driscoll, 2011 ).

Often these stress management programs are instituted after an organization has observed excessive absenteeism and work-related performance problems and, therefore, are sometimes categorized as a tertiary stress management intervention or even a primary (prevention) intervention. However, the skills developed for coping with stressors also place the programs in secondary stress management interventions. Example programs that are categorized as tertiary or primary stress management interventions may also be secondary stress management interventions (see Figure 1 ), and these include lifestyle advice and planning, stress inoculation training, simple relaxation techniques, meditation, basic trainings in time management, anger management, problem-solving skills, and cognitive-behavioral therapy. Corporate wellness programs also fall under this category. In other words, some programs could be categorized as primary, secondary, or tertiary interventions depending upon when the employee (or organization) identifies the need to implement the program. For example, time management practices could be implemented as a means of preventing some stressors, as a way to cope with mounting stressors, or as a strategy to mitigate symptoms of excessive of stressors. Furthermore, these programs can be administered at the individual level or group level. As related to secondary interventions, these programs provide participants with opportunities to develop and practice skills to cognitively reappraise the stressor(s); to modify their perspectives about stressors; to take time out to breathe, stretch, meditate, relax, and/or exercise in an attempt to support better decision-making; to articulate concerns and call upon support resources; and to know how to say “no” to onslaughts of requests to complete tasks. Participants also learn how to proactively identify coping resources and solve problems.

According to Cooper, Dewe, and O’Driscoll ( 2001 ), secondary interventions are successful in helping employees modify or strengthen their ability to cope with the experience of stressors with the goal of mitigating the potential harm the job stressors may create. Secondary interventions focus on individuals’ transactions with the work environment and emphasize the fit between a person and his or her environment. However, researchers have pointed out that the underlying assumption of secondary interventions is that the responsibility for coping with the stressors of the environment lies within individuals (Quillian-Wolever & Wolever, 2003 ). If companies cannot prevent the stressors in the first place, then they are, in part, responsible for helping individuals develop coping strategies and informing employees about programs that would help them better cope with job stressors so that they are able to fulfill work assignments.

Stress management interventions that help people learn to cope with stressors focus mainly on the goals of enabling problem-resolution or expressing one’s emotions in a healthy manner. These goals are referred to as problem-focused coping and emotion-focused coping (Folkman & Lazarus, 1980 ; Pearlin & Schooler, 1978 ), and the person experiencing the stressors as potential threat is the agent for change and the recipient of the benefits of successful coping (Hobfoll, 1998 ). In addition to problem-focused and emotion-focused coping approaches, social support and resilience may be coping resources. There are many other sources for coping than there is room to present here (see e.g., Cartwright & Cooper, 2005 ); however, the current literature has primarily focused on these resources.

Problem-Focused Coping

Problem-focused or direct coping helps employees remove or reduce stressors in order to reduce their strain experiences (Bhagat et al., 2012 ). In problem-focused coping employees are responsible for working out a strategic plan in order to remove job stressors, such as setting up a set of goals and engaging in behaviors to meet these goals. Problem-focused coping is viewed as an adaptive response, though it can also be maladaptive if it creates more problems down the road, such as procrastinating getting work done or feigning illness to take time off from work. Adaptive problem-focused coping negatively relates to long-term job strains (Higgins & Endler, 1995 ). Discussion on problem-solving coping is framed from an adaptive perspective.

Problem-focused coping is featured as an extension of control, because engaging in problem-focused coping strategies requires a series of acts to keep job stressors under control (Bhagat et al., 2012 ). In the stress literature, there are generally two ways to categorize control: internal versus external locus of control, and primary versus secondary control. Locus of control refers to the extent to which people believe they have control over their own life (Rotter, 1966 ). People high in internal locus of control believe that they can control their own fate whereas people high in external locus of control believe that outside factors determine their life experience (Rotter, 1966 ). Generally, those with an external locus of control are less inclined to engage in problem-focused coping (Strentz & Auerbach, 1988 ). Primary control is the belief that people can directly influence their environment (Alloy & Abramson, 1979 ), and thus they are more likely to engage in problem-focused coping. However, when it is not feasible to exercise primary control, people search for secondary control, with which people try to adapt themselves into the objective environment (Rothbaum, Weisz, & Snyder, 1982 ).

Emotion-Focused Coping

Emotion-focused coping, sometimes referred to as palliative coping, helps employees reduce strains without the removal of job stressors. It involves cognitive or emotional efforts, such as talking about the stressor or distracting oneself from the stressor, in order to lessen emotional distress resulting from job stressors (Bhagat et al., 2012 ). Emotion-focused coping aims to reappraise and modify the perceptions of a situation or seek emotional support from friends or family. These methods do not include efforts to change the work situation or to remove the job stressors (Lazarus & Folkman, 1991 ). People tend to adopt emotion-focused coping strategies when they believe that little or nothing can be done to remove the threatening, harmful, and challenging stressors (Bhagat et al., 2012 ), such as when they are the only individuals to have the skills to get a project done or they are given increased responsibilities because of the unexpected departure of a colleague. Emotion-focused coping strategies include (1) reappraisal of the stressful situation, (2) talking to friends and receiving reassurance from them, (3) focusing on one’s strength rather than weakness, (4) optimistic comparison—comparing one’s situation to others’ or one’s past situation, (5) selective ignoring—paying less attention to the unpleasant aspects of one’s job and being more focused on the positive aspects of the job, (6) restrictive expectations—restricting one’s expectations on job satisfaction but paying more attention to monetary rewards, (7) avoidance coping—not thinking about the problem, leaving the situation, distracting oneself, or using alcohol or drugs (e.g., Billings & Moos, 1981 ).

Some emotion-focused coping strategies are maladaptive. For example, avoidance coping may lead to increased level of job strains in the long run (e.g., Parasuraman & Cleek, 1984 ). Furthermore, a person’s ability to cope with the imbalance of performing work to meet organizational expectations can take a toll on the person’s health, leading to physiological consequences such as cardiovascular disease, sleep disorders, gastrointestinal disorders, and diabetes (Fried et al., 2013 ; Siegrist, 2010 ; Toker, Shirom, Melamed, & Armon, 2012 ; Willert, Thulstrup, Hertz, & Bonde, 2010 ).

Comparing Coping Strategies across Cultures

Most coping research is conducted in individualistic, Western cultures wherein emotional control is emphasized and both problem-solving focused coping and primary control are preferred (Bhagat et al., 2010 ). However, in collectivistic cultures, emotion-focused coping and use of secondary control may be preferred and may not necessarily carry a negative evaluation (Bhagat et al., 2010 ). For example, African Americans are more likely to use emotion-focused coping than non–African Americans (Knight, Silverstein, McCallum, & Fox, 2000 ), and among women who experienced sexual harassment, Anglo American women were less likely to employ emotion focused coping (i.e., avoidance coping) than Turkish women and Hispanic American women, while Hispanic women used more denial than the other two groups (Wasti & Cortina, 2002 ).

Thus, whereas problem-focused coping is venerated in Western societies, emotion-focused coping may be more effective in reducing strains in collectivistic cultures, such as China, Japan, and India (Bhagat et al., 2010 ; Narayanan, Menon, & Spector, 1999 ; Selmer, 2002 ). Indeed, Swedish participants reported more problem-focused coping than did Chinese participants (Xiao, Ottosson, & Carlsson, 2013 ), American college students engaged in more problem-focused coping behaviors than did their Japanese counterparts (Ogawa, 2009 ), and Indian (vs. Canadian) students reported more emotion-focused coping, such as seeking social support and positive reappraisal (Sinha, Willson, & Watson, 2000 ). Moreover, Glazer, Stetz, and Izso ( 2004 ) found that internal locus of control was more predominant in individualistic cultures (United Kingdom and United States), whereas external locus of control was more predominant in communal cultures (Italy and Hungary). Also, internal locus of control was associated with less job stress, but more so for nurses in the United Kingdom and United States than Italy and Hungary. Taken together, adoption of coping strategies and their effectiveness differ significantly across cultures. The extent to which a coping strategy is perceived favorably and thus selected or not selected is not only a function of culture, but also a person’s sociocultural beliefs toward the coping strategy (Morimoto, Shimada, & Ozaki, 2013 ).

Social Support

Social support refers to the aid an entity gives to a person. The source of the support can be a single person, such as a supervisor, coworker, subordinate, family member, friend, or stranger, or an organization as represented by upper-level management representing organizational practices. The type of support can be instrumental or emotional. Instrumental support, including informational support, refers to that which is tangible, such as data to help someone make a decision or colleagues’ sick days so one does not lose vital pay while recovering from illness. Emotional support, including esteem support, refers to the psychological boost given to a person who needs to express emotions and feel empathy from others or to have his or her perspective validated. Beehr and Glazer ( 2001 ) present an overview of the role of social support on the stressor-strain relationship and arguments regarding the role of culture in shaping the utility of different sources and types of support.

Meaningfulness and Resilience

Meaningfulness reflects the extent to which people believe their lives are significant, purposeful, goal-directed, and fulfilling (Glazer, Kożusznik, Meyers, & Ganai, 2014 ). When faced with stressors, people who have a strong sense of meaning in life will also try to make sense of the stressors. Maintaining a positive outlook on life stressors helps to manage emotions, which is helpful in reducing strains, particularly when some stressors cannot be problem-solved (Lazarus & Folkman, 1991 ). Lazarus and Folkman ( 1991 ) emphasize that being able to reframe threatening situations can be just as important in an adaptation as efforts to control the stressors. Having a sense of meaningfulness motivates people to behave in ways that help them overcome stressors. Thus, meaningfulness is often used in the same breath as resilience, because people who are resilient are often protecting that which is meaningful.

Resilience is a personality state that can be fortified and enhanced through varied experiences. People who perceive their lives are meaningful are more likely to find ways to face adversity and are therefore more prone to intensifying their resiliency. When people demonstrate resilience to cope with noxious stressors, their ability to be resilient against other stressors strengthens because through the experience, they develop more competencies (Glazer et al., 2014 ). Thus, fitting with Hobfoll’s ( 1989 , 2001 ) COR theory, meaningfulness and resilience are psychological resources people attempt to conserve and protect, and employ when necessary for making sense of or coping with stressors.

Tertiary Interventions (Stress Management)

Stress management refers to interventions employed to treat and repair harmful repercussions of stressors that were not coped with sufficiently. As Lazarus and Folkman ( 1991 ) noted, not all stressors “are amenable to mastery” (p. 205). Stressors that are unmanageable and lead to strains require interventions to reverse or slow down those effects. Workplace interventions might focus on the person, the organization, or both. Unfortunately, instead of looking at the whole system to include the person and the workplace, most companies focus on the person. Such a focus should not be a surprise given the results of van der Klink, Blonk, Schene, and van Dijk’s ( 2001 ) meta-analysis of 48 experimental studies conducted between 1977 and 1996 . They found that of four types of tertiary interventions, the effect size for cognitive-behavioral interventions and multimodal programs (e.g., the combination of assertive training and time management) was moderate and the effect size for relaxation techniques was small in reducing psychological complaints, but not turnover intention related to work stress. However, the effects of (the five studies that used) organization-focused interventions were not significant. Similarly, Richardson and Rothstein’s ( 2008 ) meta-analytic study, including 36 experimental studies with 55 interventions, showed a larger effect size for cognitive-behavioral interventions than relaxation, organizational, multimodal, or alternative. However, like with van der Klink et al. ( 2001 ), Richardson and Rothstein ( 2008 ) cautioned that there were few organizational intervention studies included and the impact of interventions were determined on the basis of psychological outcomes and not physiological or organizational outcomes. Van der Klink et al. ( 2001 ) further expressed concern that organizational interventions target the workplace and that changes in the individual may take longer to observe than individual interventions aimed directly at the individual.

The long-term benefits of individual focused interventions are not yet clear either. Per Giga, Cooper, and Faragher ( 2003 ), the benefits of person-directed stress management programs will be short-lived if organizational factors to reduce stressors are not addressed too. Indeed, LaMontagne, Keegel, Louie, Ostry, and Landsbergis ( 2007 ), in their meta-analysis of 90 studies on stress management interventions published between 1990 and 2005 , revealed that in relation to interventions targeting organizations only, and interventions targeting individuals only, interventions targeting both organizations and individuals (i.e. the systems approach) had the most favorable positive effects on both the organizations and the individuals. Furthermore, the organization-level interventions were effective at both the individual and organization levels, but the individual-level interventions were effective only at the individual level.

Individual-Focused Stress Management

Individual-focused interventions concentrate on improving conditions for the individual, though counseling programs emphasize that the worker is in charge of reducing “stress,” whereas role-focused interventions emphasize activities that organizations can guide to actually reduce unnecessary noxious environmental factors.

Individual-Focused Stress Management: Employee Assistance Programs

When stress become sufficiently problematic (which is individually gauged or attended to by supportive others) in a worker’s life, employees may utilize the short-term counseling services or referral services Employee Assistance Programs (EAPs) provide. People who utilize the counseling services may engage in cognitive behavioral therapy aimed at changing the way people think about the stressors (e.g., as challenge opportunity over threat) and manage strains. Example topics that may be covered in these therapy sessions include time management and goal setting (prioritization), career planning and development, cognitive restructuring and mindfulness, relaxation, and anger management. In a study of healthcare workers and teachers who participated in a 2-day to 2.5-day comprehensive stress management training program (including 26 topics on identifying, coping with, and managing stressors and strains), Siu, Cooper, and Phillips ( 2013 ) found psychological and physical improvements were self-reported among the healthcare workers (for which there was no control group). However, comparing an intervention group of teachers to a control group of teachers, the extent of change was not as visible, though teachers in the intervention group engaged in more mastery recovery experiences (i.e., they purposefully chose to engage in challenging activities after work).

Individual-Focused Stress Management: Mindfulness

A popular therapy today is to train people to be more mindful, which involves helping people live in the present, reduce negative judgement of current and past experiences, and practicing patience (Birnie, Speca, & Carlson, 2010 ). Mindfulness programs usually include training on relaxation exercises, gentle yoga, and awareness of the body’s senses. In one study offered through the continuing education program at a Canadian university, 104 study participants took part in an 8-week, 90 minute per group (15–20 participants per) session mindfulness program (Birnie et al., 2010 ). In addition to body scanning, they also listened to lectures on incorporating mindfulness into one’s daily life and received a take-home booklet and compact discs that guided participants through the exercises studied in person. Two weeks after completing the program, participants’ mindfulness attendance and general positive moods increased, while physical, psychological, and behavioral strains decreased. In another study on a sample of U.K. government employees, study participants receiving three sessions of 2.5 to 3 hours each training on mindfulness, with the first two sessions occurring in consecutive weeks and the third occurring about three months later, Flaxman and Bond ( 2010 ) found that compared to the control group, the intervention group showed a decrease in distress levels from Time 1 (baseline) to Time 2 (three months after first two training sessions) and Time 1 to Time 3 (after final training session). Moreover, of the mindfulness intervention study participants who were clinically distressed, 69% experienced clinical improvement in their psychological health.

Individual-Focused Stress Management: Biofeedback/Imagery/Meditation/Deep Breathing

Biofeedback uses electronic equipment to inform users about how their body is responding to tension. With guidance from a therapist, individuals then learn to change their physiological responses so that their pulse normalizes and muscles relax (Norris, Fahrion, & Oikawa, 2007 ). The therapist’s guidance might include reminders for imagery, meditation, body scan relaxation, and deep breathing. Saunders, Driskell, Johnston, and Salas’s ( 1996 ) meta-analysis of 37 studies found that imagery helped reduce state and performance anxiety. Once people have been trained to relax, reminder triggers may be sent through smartphone push notifications (Villani et al., 2013 ).

Smartphone technology can also be used to support weight loss programs, smoking cessation programs, and medication or disease (e.g., diabetes) management compliance (Heron & Smyth, 2010 ; Kannampallil, Waicekauskas, Morrow, Kopren, & Fu, 2013 ). For example, smartphones could remind a person to take medications or test blood sugar levels or send messages about healthy behaviors and positive affirmations.

Individual-Focused Stress Management: Sleep/Rest/Respite

Workers today sleep less per night than adults did nearly 30 years ago (Luckhaupt, Tak, & Calvert, 2010 ; National Sleep Foundation, 2005 , 2013 ). In order to combat problems, such as increased anxiety and cardiovascular artery disease, associated with sleep deprivation and insufficient rest, it is imperative that people disconnect from their work at least one day per week or preferably for several weeks so that they are able to restore psychological health (Etzion, Eden, & Lapidot, 1998 ; Ragsdale, Beehr, Grebner, & Han, 2011 ). When college students engaged in relaxation-type activities, such as reading or watching television, over the weekend, they experienced less emotional exhaustion and greater general well-being than students who engaged in resources-consuming activities, such as house cleaning (Ragsdale et al., 2011 ). Additional research and future directions for research are reviewed and identified in the work of Sonnentag ( 2012 ). For example, she asks whether lack of ability to detach from work is problematic for people who find their work meaningful. In other words, are negative health consequences only among those who do not take pleasure in their work? Sonnetag also asks how teleworkers detach from their work when engaging in work from the home. Ironically, one of the ways that companies are trying to help with the challenges of high workload or increased need to be available to colleagues, clients, or vendors around the globe is by offering flexible work arrangements, whereby employees who can work from home are given the opportunity to do so. Companies that require global interactions 24-hours per day often employ this strategy, but is the solution also a source of strain (Glazer, Kożusznik, & Shargo, 2012 )?

Individual-Focused Stress Management: Role Analysis

Role analysis or role clarification aims to redefine, expressly identify, and align employees’ roles and responsibilities with their work goals. Through role negotiation, involved parties begin to develop a new formal or informal contract about expectations and define resources needed to fulfill those expectations. Glazer has used this approach in organizational consulting and, with one memorable client engagement, found that not only were the individuals whose roles required deeper re-evaluation happier at work (six months later), but so were their subordinates. Subordinates who once characterized the two partners as hostile and akin to a couple going through a bad divorce, later referred to them as a blissful pair. Schaubroeck, Ganster, Sime, and Ditman ( 1993 ) also found in a three-wave study over a two-year period that university employees’ reports of role clarity and greater satisfaction with their supervisor increased after a role clarification exercise of top managers’ roles and subordinates’ roles. However, the intervention did not have any impact on reported physical symptoms, absenteeism, or psychological well-being. Role analysis is categorized under individual-focused stress management intervention because it is usually implemented after individuals or teams begin to demonstrate poor performance and because the intervention typically focuses on a few individuals rather than an entire organization or group. In other words, the intervention treats the person’s symptoms by redefining the role so as to eliminate the stimulant causing the problem.

Organization-Focused Stress Management

At the organizational level, companies that face major declines in productivity and profitability or increased costs related to healthcare and disability might be motivated to reassess organizational factors that might be impinging on employees’ health and well-being. After all, without healthy workers, it is not possible to have a healthy organization. Companies may choose to implement practices and policies that are expected to help not only the employees, but also the organization with reduced costs associated with employee ill-health, such as medical insurance, disability payments, and unused office space. Example practices and policies that may be implemented include flexible work arrangements to ensure that employees are not on the streets in the middle of the night for work that can be done from anywhere (such as the home), diversity programs to reduce stress-induced animosity and prejudice toward others, providing only healthy food choices in cafeterias, mandating that all employees have physicals in order to receive reduced prices for insurance, company-wide closures or mandatory paid time off, and changes in organizational visioning.

Organization-Focused Stress Management: Organizational-Level Occupational Health Interventions

As with job design interventions that are implemented to remediate work characteristics that were a source of unnecessary or excessive stressors, so are organizational-level occupational health (OLOH) interventions. As with many of the interventions, its placement as a primary or tertiary stress management intervention may seem arbitrary, but when considering the goal and target of change, it is clear that the intervention is implemented in response to some ailing organizational issues that need to be reversed or stopped, and because it brings in the entire organization’s workforce to address the problems, it has been placed in this category. There are several more case studies than empirical studies on the topic of whole system organizational change efforts (see example case studies presented by the United Kingdom’s Health and Safety Executive). It is possible that lack of published empirical work is not so much due to lack of attempting to gather and evaluate the data for publication, but rather because the OLOH interventions themselves never made it to the intervention stage, the interventions failed (Biron, Gatrell, & Cooper, 2010 ), or the level of evaluation was not rigorous enough to get into empirical peer-review journals. Fortunately, case studies provide some indication of the opportunities and problems associated with OLOH interventions.

One case study regarding Cardiff and Value University Health Board revealed that through focus group meetings with members of a steering group (including high-level managers and supported by top management) and facilitated by a neutral, non-judgemental organizational health consultant, ideas for change were posted on newsprint, discussed, and areas in the organization needing change were identified. The intervention for giving voice to people who initially had little already had a positive effect on the organization, as absence decreased by 2.09% and 6.9% merely 12 and 18 months, respectively, after the intervention. Translated in financial terms, the 6.9% change was equivalent to a quarterly savings of £80,000 (Health & Safety Executive, n.d. ). Thus, focusing on the context of change and how people will be involved in the change process probably helped the organization realize improvements (Biron et al., 2010 ). In a recent and rare empirical study, employing both qualitative and quantitative data collection methods, Sørensen and Holman ( 2014 ) utilized PAR in order to plan and implement an OLOH intervention over the course of 14 months. Their study aimed to examine the effectiveness of the PAR process in reducing workers’ work-related and social or interpersonal-related stressors that derive from the workplace and improving psychological, behavioral, and physiological well-being across six Danish organizations. Based on group dialogue, 30 proposals for change were proposed, all of which could be categorized as either interventions to focus on relational factors (e.g., management feedback improvement, engagement) or work processes (e.g., reduced interruptions, workload, reinforcing creativity). Of the interventions that were implemented, results showed improvements on manager relationship quality and reduced burnout, but no changes with respect to work processes (i.e., workload and work pace) perhaps because the employees already had sufficient task control and variety. These findings support Dewe and Kompier’s ( 2008 ) position that occupational health can be reinforced through organizational policies that reinforce quality jobs and work experiences.

Organization-Focused Stress Management: Flexible Work Arrangements

Dewe and Kompier ( 2008 ), citing the work of Isles ( 2005 ), noted that concern over losing one’s job is a reason for why 40% of survey respondents indicated they work more hours than formally required. In an attempt to create balance and perceived fairness in one’s compensation for putting in extra work hours, employees will sometimes be legitimately or illegitimately absent. As companies become increasingly global, many people with desk jobs are finding themselves communicating with colleagues who are halfway around the globe and at all hours of the day or night (Glazer et al., 2012 ). To help minimize the strains associated with these stressors, companies might devise flexible work arrangements (FWA), though the type of FWA needs to be tailored to the cultural environment (Masuda et al., 2012 ). FWAs give employees some leverage to decide what would be the optimal work arrangement for them (e.g., part-time, flexible work hours, compressed work week, telecommuting). In other words, FWA provides employees with the choice of when to work, where to work (on-site or off-site), and how many hours to work in a day, week, or pay period (Kossek, Thompson, & Lautsch, 2015 ). However, not all employees of an organization have equal access to or equitable use of FWAs; workers in low-wage, hourly jobs are often beholden to being physically present during specific hours (Swanberg McKechnie, Ojha, & James, 2011 ). In a study of over 1,300 full-time hourly retail employees in the United States, Swanberg et al. ( 2011 ) showed that employees who have control over their work schedules and over their work hours were satisfied with their work schedules, perceived support from the supervisor, and work engagement.

Unfortunately, not all FWAs yield successful results for the individual or the organization. Being able to work from home or part-time can have problems too, as a person finds himself or herself working more hours from home than required. Sometimes telecommuting creates work-family conflict too as a person struggles to balance work and family obligations while working from home. Other drawbacks include reduced face-to-face contact between work colleagues and stakeholders, challenges shaping one’s career growth due to limited contact, perceived inequity if some have more flexibility than others, and ambiguity about work role processes for interacting with employees utilizing the FWA (Kossek et al., 2015 ). Organizations that institute FWAs must carefully weigh the benefits and drawbacks the flexibility may have on the employees using it or the employees affected by others using it, as well as the implications on the organization, including the vendors who are serving and clients served by the organization.

Organization-Focused Stress Management: Diversity Programs

Employees in the workplace might experience strain due to feelings of discrimination or prejudice. Organizational climates that do not promote diversity (in terms of age, religion, physical abilities, ethnicity, nationality, sex, and other characteristics) are breeding grounds for undesirable attitudes toward the workplace, lower performance, and greater turnover intention (Bergman, Palmieri, Drasgow, & Ormerod, 2012 ; Velez, Moradi, & Brewster, 2013 ). Management is thus advised to implement programs that reinforce the value and importance of diversity, as well as manage diversity to reduce conflict and feelings of prejudice. In fact, managers who attended a leadership training program reported higher multicultural competence in dealing with stressful situations (Chrobot-Mason & Leslie, 2012 ), and managers who persevered through challenges were more dedicated to coping with difficult diversity issues (Cilliers, 2011 ). Thus, diversity programs can help to reduce strains by directly reducing stressors associated with conflict linked to diversity in the workplace and by building managers’ resilience.

Organization-Focused Stress Management: Healthcare Management Policies

Over the past few years, organizations have adopted insurance plans that implement wellness programs for the sake of managing the increasing cost of healthcare that is believed to be a result of individuals’ not managing their own health, with regular check-ups and treatment. The wellness programs require all insured employees to visit a primary care provider, complete a health risk assessment, and engage in disease management activities as specified by a physician (e.g., see frequently asked questions regarding the State of Maryland’s Wellness Program). Companies believe that requiring compliance will reduce health problems, although there is no proof that such programs save money or that people would comply. One study that does, however, boast success, was a 12-week workplace health promotion program aimed at reducing Houston airport workers’ weight (Ebunlomo, Hare-Everline, Weber, & Rich, 2015 ). The program, which included 235 volunteer participants, was deemed a success, as there was a total weight loss of 345 pounds (or 1.5 lbs per person). Given such results in Houston, it is clear why some people are also skeptical over the likely success of wellness programs, particularly as there is no clear method for evaluating their efficacy (Sinnott & Vatz, 2015 ).

Moreover, for some, such a program is too paternalistic and intrusive, as well as punishes anyone who chooses not to actively participate in disease management programs (Sinnott & Vatz, 2015 ). The programs put the onus of change on the person, though it is a response to the high costs of ill-health. The programs neglect to consider the role of the organization in reducing the barriers to healthy lifestyle, such as cloaking exempt employment as simply needing to get the work done, when it usually means working significantly more hours than a standard workweek. In fact, workplace health promotion programs did not reduce presenteeism (i.e., people going to work while unwell thereby reducing their job performance) among those who suffered from physical pain (Cancelliere, Cassidy, Ammendolia, & Côte, 2011 ). However, supervisor education, worksite exercise, lifestyle intervention through email, midday respite from repetitive work, a global stress management program, changes in lighting, and telephone interventions helped to reduce presenteeism. Thus, emphasis needs to be placed on psychosocial aspects of the organization’s structure, including managers and overall organizational climate for on-site presence, that reinforces such behavior (Cancelliere et al., 2011 ). Moreover, wellness programs are only as good as the interventions to reduce work-related stressors and improve organizational resources to enable workers to improve their overall psychological and physical health.

Concluding Remarks

Future research.

One of the areas requiring more theoretical and practical attention is that of the utility of stress frameworks to guide organizational development change interventions. Although it has been proposed that the foundation for work stress management interventions is in organizational development, and even though scholars and practitioners of organization development were also founders of research programs that focused on employee health and well-being or work stress, there are few studies or other theoretical works that link the two bodies of literature.

A second area that requires additional attention is the efficacy of stress management interventions across cultures. In examining secondary stress management interventions (i.e., coping), some cross-cultural differences in findings were described; however, there is still a dearth of literature from different countries on the utility of different prevention, coping, and stress management strategies.

A third area that has been blossoming since the start of the 21st century is the topic of hindrance and challenge stressors and the implications of both on workers’ well-being and performance. More research is needed on this topic in several areas. First, there is little consistency by which researchers label a stressor as a hindrance or a challenge. Researchers sometimes take liberties with labels, but it is not the researchers who should label a stressor but the study participants themselves who should indicate if a stressor is a source of strain. Rodríguez, Kozusznik, and Peiró ( 2013 ) developed a measure in which respondents indicate whether a stressor is a challenge or a hindrance. Just as some people may perceive demands to be challenges that they savor and that result in a psychological state of eustress (Nelson & Simmons, 2003 ), others find them to be constraints that impede goal fulfillment and thus might experience distress. Likewise, some people might perceive ambiguity as a challenge that can be overcome and others as a constraint over which he or she has little control and few or no resources with which to cope. More research on validating the measurement of challenge vs. hindrance stressors, as well as eustress vs. distress, and savoring vs. coping, is warranted. Second, at what point are challenge stressors harmful? Just because people experiencing challenge stressors continue to perform well, it does not necessarily mean that they are healthy people. A great deal of stressors are intellectually stimulating, but excessive stimulation can also take a toll on one’s physiological well-being, as evident by the droves of professionals experiencing different kinds of diseases not experienced as much a few decades ago, such as obesity (Fried et al., 2013 ). Third, which stress management interventions would better serve to reduce hindrance stressors or to reduce strain that may result from challenge stressors while reinforcing engagement-producing challenge stressors?

A fourth area that requires additional attention is that of the flexible work arrangements (FWAs). One of the reasons companies have been willing to permit employees to work from home is not so much out of concern for the employee, but out of the company’s need for the focal person to be able to communicate with a colleague working from a geographic region when it is night or early morning for the focal person. Glazer, Kożusznik, and Shargo ( 2012 ) presented several areas for future research on this topic, noting that by participating on global virtual teams, workers face additional stressors, even while given flexibility of workplace and work time. As noted earlier, more research needs to be done on the extent to which people who take advantage of FWAs are advantaged in terms of detachment from work. Can people working from home detach? Are those who find their work invigorating also likely to experience ill-health by not detaching from work?

A fifth area worthy of further research attention is workplace wellness programing. According to Page and Vella-Brodrick ( 2009 ), “subjective and psychological well-being [are] key criteria for employee mental health” (p. 442), whereby mental health focuses on wellness, rather than the absence of illness. They assert that by fostering employee mental health, organizations are supporting performance and retention. Employee well-being can be supported by ensuring that jobs are interesting and meaningful, goals are achievable, employees have control over their work, and skills are used to support organizational and individual goals (Dewe & Kompier, 2008 ). However, just as mental health is not the absence of illness, work stress is not indicative of an absence of psychological well-being. Given the perspective that employee well-being is a state of mind (Page & Vella-Brodrick, 2009 ), we suggest that employee well-being can be negatively affected by noxious job stressors that cannot be remediated, but when job stressors are preventable, employee well-being can serve to protect an employee who faces job stressors. Thus, wellness programs ought to focus on providing positive experiences by enhancing and promoting health, as well as building individual resources. These programs are termed “green cape” interventions (Pawelski, 2016 ). For example, with the growing interests in positive psychology, researchers and practitioners have suggested employing several positive psychology interventions, such as expressing gratitude, savoring experiences, and identifying one’s strengths (Tetrick & Winslow, 2015 ). Another stream of positive psychology is psychological capital, which includes four malleable functions of self-efficacy, optimism, hope, and resilience (Luthans, Youssef, & Avolio, 2007 ). Workplace interventions should include both “red cape” interventions (i.e., interventions to reduce negative experiences) and “green cape” interventions (i.e., workplace wellness programs; Polly, 2014 ).

A Healthy Organization’s Pledge

A healthy workplace requires healthy workers. Period. Among all organizations’ missions should be the focus on a healthy workforce. To maintain a healthy workforce, the company must routinely examine its own contributions in terms of how it structures itself; reinforces communications among employees, vendors, and clients; how it rewards and cares for its people (e.g., ensuring they get sufficient rest and can detach from work); and the extent to which people at the upper levels are truly connected with the people at the lower levels. As a matter of practice, management must recognize when employees are overworked, unwell, and poorly engaged. Management must also take stock of when it is doing well and right by its contributors’ and maintain and reinforce the good practices, norms, and procedures. People in the workplace make the rules; people in the workplace can change the rules. How management sees its employees and values their contribution will have a huge role in how a company takes stock of its own pain points. Providing employees with tools to manage their own reactions to work-related stressors and consequent strains is fine, but wouldn’t it be grand if organizations took better notice about what they could do to mitigate the strain-producing stressors in the first place and take ownership over how employees are treated?

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Psychological Theories of Stress

The psychological theories of stress gradually evolved from the Theory of Emotion (James-Lange), The Emergency Theory (Cannon-Bard), and to the Theory of Emotion (Schachter-Singer).

This article is a part of the guide:

• Stress and Cognitive Appraisal
• General Adaptation Syndrome
• Three Different Kinds of Stress
• Coping Mechanisms
• How does Stress Affect Performance?

Browse Full Outline

• 1 What is Stress?
• 2.1 Physiological Stress Response
• 2.2 Nature of Emotions
• 3.1 James-Lange Theory of Emotion
• 3.2 Cannon-Bard Theory of Emotion
• 3.3 Schachter-Singer Theory of Emotion
• 3.4 Stress and Cognitive Appraisal
• 4.1 Social Support
• 4.2 Gender and Culture
• 5.1 Theories of Coping
• 5.2 Stress Management
• 5.3 Stress Therapies
• 5.4 How does Stress Affect Performance?
• 6.1 Knowing Your Stressors
• 7.1 Stress and Cancer
• 7.2 Warning Signs - Burnout
• 7.3 Stress in Children
• 8 Two-Factor Theory of Motivation

Because stress is one of the most interesting and mysterious subjects we have since the beginning of time, its study is not only limited to what happens to the body during a stressful situation, but also to what occurs in the psyche of an individual. In this article, we will discuss the different psychological theories of stress proposed by James & Lange, Cannon & Brad, and Schachter & Singer.

James-Lange: Theory of Emotion

In 1884 and in 1885, theorists William James and Carl Lange might have separately proposed their respective theories on the correlation of stress and emotion, but they had a unified idea on this relationship - emotions do not immediately succeed the perception of the stressor or the stressful event; they become present after the body’s response to the stress. For instance, when you see a growling dog, your heart starts to race, your breath begins to go faster, then your eyes become wide open. According to James and Lange, the feeling of fear or any other emotion only begins after you experience these bodily changes. This means that the emotional behavior is not possible to occur unless it is connected to one’s brain.

See the full article: The James-Lange Theory of Emotion

Cannon-Bard: The Emergency Theory

This theory is quite the opposite of what James and Lange proposed. According to theorist Walter Cannon, emotion in response to stress can actually occur even when the bodily changes are not present. Cannon said that the visceral or internal physiologic response of one’s body is more slowly recognized by the brain as compared with its function to release emotional response. He attempted to prove his theory by means of creating the so-called “decorticated cats”, wherein the neural connections of the body are separated from the cortex in the brain of the cats. When faced with a stressful response, the decorticated cats showed emotional behavior which meant feelings of aggression and rage. This emotion was then manifested by bodily changes such as baring of teeth, growling and erect hair.

To further enhance Cannon’s theory, theorist Philip Bard expanded the ideals of Cannon by arguing that a lower brain stem structure called the thalamus is important in the production of emotional responses. According to Bard, the emotional response is released first, and then sent as signals by the thalamus to the brain cortex for the interpretation alongside with the sending of signals to the sympathetic nervous system or SNS to begin the physiologic response to stress. Therefore, this theory argues that emotional response to stress is not a product of the physiologic response; rather, they occur simultaneously.

See the full article: Cannon-Bard Theory of Emotion

The Schachter-Singer Theory

Theorists Stanley Schachter and Jerome Singer argued that the appropriate identification of the emotion requires both cognitive activity and emotional arousal in order to experience an emotion. Attribution, or the process wherein the brain can identify the stress stimulus producing an emotion is also proposed by Schachter and Singer . The theory explains that we become aware of the reason behind the emotional response, and when we the reason is not obvious, we start to look for environmental clues for the proper interpretation of the emotion to occur.

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How to Write a Great Hypothesis

Hypothesis Definition, Format, Examples, and Tips

Verywell / Alex Dos Diaz

• The Scientific Method

Hypothesis Format

Falsifiability of a hypothesis.

• Operationalization

Hypothesis Types

Hypotheses examples.

• Collecting Data

A hypothesis is a tentative statement about the relationship between two or more variables. It is a specific, testable prediction about what you expect to happen in a study. It is a preliminary answer to your question that helps guide the research process.

Consider a study designed to examine the relationship between sleep deprivation and test performance. The hypothesis might be: "This study is designed to assess the hypothesis that sleep-deprived people will perform worse on a test than individuals who are not sleep-deprived."

At a Glance

A hypothesis is crucial to scientific research because it offers a clear direction for what the researchers are looking to find. This allows them to design experiments to test their predictions and add to our scientific knowledge about the world. This article explores how a hypothesis is used in psychology research, how to write a good hypothesis, and the different types of hypotheses you might use.

The Hypothesis in the Scientific Method

In the scientific method , whether it involves research in psychology, biology, or some other area, a hypothesis represents what the researchers think will happen in an experiment. The scientific method involves the following steps:

• Forming a question
• Performing background research
• Creating a hypothesis
• Designing an experiment
• Collecting data
• Analyzing the results
• Drawing conclusions
• Communicating the results

The hypothesis is a prediction, but it involves more than a guess. Most of the time, the hypothesis begins with a question which is then explored through background research. At this point, researchers then begin to develop a testable hypothesis.

Unless you are creating an exploratory study, your hypothesis should always explain what you  expect  to happen.

In a study exploring the effects of a particular drug, the hypothesis might be that researchers expect the drug to have some type of effect on the symptoms of a specific illness. In psychology, the hypothesis might focus on how a certain aspect of the environment might influence a particular behavior.

Remember, a hypothesis does not have to be correct. While the hypothesis predicts what the researchers expect to see, the goal of the research is to determine whether this guess is right or wrong. When conducting an experiment, researchers might explore numerous factors to determine which ones might contribute to the ultimate outcome.

In many cases, researchers may find that the results of an experiment  do not  support the original hypothesis. When writing up these results, the researchers might suggest other options that should be explored in future studies.

In many cases, researchers might draw a hypothesis from a specific theory or build on previous research. For example, prior research has shown that stress can impact the immune system. So a researcher might hypothesize: "People with high-stress levels will be more likely to contract a common cold after being exposed to the virus than people who have low-stress levels."

In other instances, researchers might look at commonly held beliefs or folk wisdom. "Birds of a feather flock together" is one example of folk adage that a psychologist might try to investigate. The researcher might pose a specific hypothesis that "People tend to select romantic partners who are similar to them in interests and educational level."

Elements of a Good Hypothesis

So how do you write a good hypothesis? When trying to come up with a hypothesis for your research or experiments, ask yourself the following questions:

• Is your hypothesis based on your research on a topic?
• Can your hypothesis be tested?
• Does your hypothesis include independent and dependent variables?

Before you come up with a specific hypothesis, spend some time doing background research. Once you have completed a literature review, start thinking about potential questions you still have. Pay attention to the discussion section in the  journal articles you read . Many authors will suggest questions that still need to be explored.

How to Formulate a Good Hypothesis

To form a hypothesis, you should take these steps:

• Collect as many observations about a topic or problem as you can.
• Evaluate these observations and look for possible causes of the problem.
• Create a list of possible explanations that you might want to explore.
• After you have developed some possible hypotheses, think of ways that you could confirm or disprove each hypothesis through experimentation. This is known as falsifiability.

In the scientific method ,  falsifiability is an important part of any valid hypothesis. In order to test a claim scientifically, it must be possible that the claim could be proven false.

Students sometimes confuse the idea of falsifiability with the idea that it means that something is false, which is not the case. What falsifiability means is that  if  something was false, then it is possible to demonstrate that it is false.

One of the hallmarks of pseudoscience is that it makes claims that cannot be refuted or proven false.

The Importance of Operational Definitions

A variable is a factor or element that can be changed and manipulated in ways that are observable and measurable. However, the researcher must also define how the variable will be manipulated and measured in the study.

Operational definitions are specific definitions for all relevant factors in a study. This process helps make vague or ambiguous concepts detailed and measurable.

For example, a researcher might operationally define the variable " test anxiety " as the results of a self-report measure of anxiety experienced during an exam. A "study habits" variable might be defined by the amount of studying that actually occurs as measured by time.

These precise descriptions are important because many things can be measured in various ways. Clearly defining these variables and how they are measured helps ensure that other researchers can replicate your results.

Replicability

One of the basic principles of any type of scientific research is that the results must be replicable.

Replication means repeating an experiment in the same way to produce the same results. By clearly detailing the specifics of how the variables were measured and manipulated, other researchers can better understand the results and repeat the study if needed.

Some variables are more difficult than others to define. For example, how would you operationally define a variable such as aggression ? For obvious ethical reasons, researchers cannot create a situation in which a person behaves aggressively toward others.

To measure this variable, the researcher must devise a measurement that assesses aggressive behavior without harming others. The researcher might utilize a simulated task to measure aggressiveness in this situation.

Hypothesis Checklist

• Does your hypothesis focus on something that you can actually test?
• Does your hypothesis include both an independent and dependent variable?
• Can you manipulate the variables?
• Can your hypothesis be tested without violating ethical standards?

The hypothesis you use will depend on what you are investigating and hoping to find. Some of the main types of hypotheses that you might use include:

• Simple hypothesis : This type of hypothesis suggests there is a relationship between one independent variable and one dependent variable.
• Complex hypothesis : This type suggests a relationship between three or more variables, such as two independent and dependent variables.
• Null hypothesis : This hypothesis suggests no relationship exists between two or more variables.
• Alternative hypothesis : This hypothesis states the opposite of the null hypothesis.
• Statistical hypothesis : This hypothesis uses statistical analysis to evaluate a representative population sample and then generalizes the findings to the larger group.
• Logical hypothesis : This hypothesis assumes a relationship between variables without collecting data or evidence.

A hypothesis often follows a basic format of "If {this happens} then {this will happen}." One way to structure your hypothesis is to describe what will happen to the  dependent variable  if you change the  independent variable .

The basic format might be: "If {these changes are made to a certain independent variable}, then we will observe {a change in a specific dependent variable}."

A few examples of simple hypotheses:

• "Students who eat breakfast will perform better on a math exam than students who do not eat breakfast."
• "Students who experience test anxiety before an English exam will get lower scores than students who do not experience test anxiety."​
• "Motorists who talk on the phone while driving will be more likely to make errors on a driving course than those who do not talk on the phone."
• "Children who receive a new reading intervention will have higher reading scores than students who do not receive the intervention."

Examples of a complex hypothesis include:

• "People with high-sugar diets and sedentary activity levels are more likely to develop depression."
• "Younger people who are regularly exposed to green, outdoor areas have better subjective well-being than older adults who have limited exposure to green spaces."

Examples of a null hypothesis include:

• "There is no difference in anxiety levels between people who take St. John's wort supplements and those who do not."
• "There is no difference in scores on a memory recall task between children and adults."
• "There is no difference in aggression levels between children who play first-person shooter games and those who do not."

Examples of an alternative hypothesis:

• "People who take St. John's wort supplements will have less anxiety than those who do not."
• "Adults will perform better on a memory task than children."
• "Children who play first-person shooter games will show higher levels of aggression than children who do not." 

Collecting Data on Your Hypothesis

Once a researcher has formed a testable hypothesis, the next step is to select a research design and start collecting data. The research method depends largely on exactly what they are studying. There are two basic types of research methods: descriptive research and experimental research.

Descriptive Research Methods

Descriptive research such as  case studies ,  naturalistic observations , and surveys are often used when  conducting an experiment is difficult or impossible. These methods are best used to describe different aspects of a behavior or psychological phenomenon.

Once a researcher has collected data using descriptive methods, a  correlational study  can examine how the variables are related. This research method might be used to investigate a hypothesis that is difficult to test experimentally.

Experimental Research Methods

Experimental methods  are used to demonstrate causal relationships between variables. In an experiment, the researcher systematically manipulates a variable of interest (known as the independent variable) and measures the effect on another variable (known as the dependent variable).

Unlike correlational studies, which can only be used to determine if there is a relationship between two variables, experimental methods can be used to determine the actual nature of the relationship—whether changes in one variable actually  cause  another to change.

The hypothesis is a critical part of any scientific exploration. It represents what researchers expect to find in a study or experiment. In situations where the hypothesis is unsupported by the research, the research still has value. Such research helps us better understand how different aspects of the natural world relate to one another. It also helps us develop new hypotheses that can then be tested in the future.

Thompson WH, Skau S. On the scope of scientific hypotheses .  R Soc Open Sci . 2023;10(8):230607. doi:10.1098/rsos.230607

Taran S, Adhikari NKJ, Fan E. Falsifiability in medicine: what clinicians can learn from Karl Popper [published correction appears in Intensive Care Med. 2021 Jun 17;:].  Intensive Care Med . 2021;47(9):1054-1056. doi:10.1007/s00134-021-06432-z

Eyler AA. Research Methods for Public Health . 1st ed. Springer Publishing Company; 2020. doi:10.1891/9780826182067.0004

Nosek BA, Errington TM. What is replication ?  PLoS Biol . 2020;18(3):e3000691. doi:10.1371/journal.pbio.3000691

Aggarwal R, Ranganathan P. Study designs: Part 2 - Descriptive studies .  Perspect Clin Res . 2019;10(1):34-36. doi:10.4103/picr.PICR_154_18

Nevid J. Psychology: Concepts and Applications. Wadworth, 2013.

By Kendra Cherry, MSEd Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

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Stress sensitivity analysis of vuggy porous media based on two-scale fractal theory

• Zhaoqin Huang 1 , 2 ,
• Xu Zhou 1 , 2 ,
• Hao Wang 1 , 2 ,
• Qi Wang 3 &
• Yu-Shu Wu 4  

Scientific Reports volume  14 , Article number:  20710 ( 2024 ) Cite this article

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• Energy science and technology
• Engineering
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Interparticle pore space and vugs are two different scales of pore space in vuggy porous media. Vuggy porous media widely exists in carbonate reservoirs, and the permeability of this porous media plays an important role in many engineering fields. It has been shown that the change of effective stress has important effects on the permeability of vuggy porous media. In this work, a fractal permeability model for vuggy porous media is developed based on the fractal theory and elastic mechanics. Besides, a Monte Carlo simulation is also implemented to obtain feasible values of permeability. The proposed model can predict the elastic deformation of the fractal vuggy porous media under loading stress, which plays a crucial role in the variations of permeability. The predicted permeability data based on the present fractal model are compared with experimental data, which verifies the validity of the present fractal permeability model for vuggy porous media. The parameter sensitivity analysis indicates that the permeability of stress-sensitivity vuggy porous media is related to the capillary fractal dimension, capillary fractal tortuosity dimension, Young’s modulus, and Poisson’s ratio.

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Experimental and digital investigations of heterogeneity in lower cretaceous carbonate reservoir using fractal and multifractal concepts

Stress-Dependent Pore Deformation Effects on Multiphase Flow Properties of Porous Media

Introduction.

Carbonate reservoirs hold a significant position among the reservoirs discovered worldwide 1 , 2 . The carbonate reservoir deposition process is complex, and at the same time by the stripping effect and other influences, the carbonate reservoir pore space is rich and non-homogeneous, which leads to the carbonate reservoir being very complex 3 . Permeability can directly reflect the seepage characteristics of a reservoir and is a crucial parameter for predicting its oil and gas production. The decrease in permeability caused by an increase in effective stress significantly impacts reservoir development. Thus, studying the stress sensitivity characteristics of permeability is essential.

During the development of oil and gas reservoirs, with the continuous output of fluids in the reservoir, the formation pressure gradually decreases and the effective stress on the rock skeleton increases. The increasing effective stress compresses the rock, which leads to a decrease in pore connectivity and a decrease in reservoir permeability 4 . The phenomenon that reservoir permeability decreases with increasing effective stress is called permeability stress sensitivity 5 , 6 , 7 . This phenomenon is widespread in both natural and man-made materials 8 , 9 . The study of stress sensitivity of permeability in porous media spans a wide range of scientific and engineering fields, including hydraulics 10 , physics 11 , and petroleum engineering 12 . There are many factors affecting permeability stress sensitivity, and stress sensitivity has a significant impact on the development of oil and gas reservoirs 3 . Many scholars have investigated the effect of stress sensitivity on reservoir permeability through experiments, theoretical models, and numerical simulations.

Numerical methods play an important role in the analysis of flow in porous media considering stress sensitivity. Faisal et al. 13 numerically predicted the variation of elastic properties of carbonate rocks as a function of stress and improved the accuracy of the numerical prediction using a multiscale imaging method and an "up-scaling" framework. Civan 14 established a mathematical model to express the preferential flow paths in heterogeneous porous rocks by a bundle of tortuous cylindrical elastic tubes, this model can depict the stress dependency of the porosity and permeability of porous rocks, and he introduced the Biot–Willis poroelastic coefficient to construct the equation of net confining pressure and make the analysis results more accurate. Al Balushi et al. 15 used micro-computed Tomography images to simulate the stress-induced deformation of rocks and used the lattice Boltzmann method to simulate the fluid flow in the deformed medium. Ahmed et al. 16 established a rock mechanics model combined with geomechanical modeling and performed reservoir geomechanical simulations of a carbonate gas reservoir to analyze the change of reservoir permeability with effective stress. Quevedo et al. 17 predicted the change of reservoir permeability around a carbonate fault by numerical simulation based on the finite element method, combined with an elastic–plastic model and fault damage data. Fu et al. 18 digitally imaged the pressurization and depressurization processes of pore, pore–pore, and pore–pore cavities in carbonate rocks by using X-ray tomography, and simulated and predicted the permeability under different peritectic pressures by using the lattice Boltzmann method and pore network model. However, the actual rock pore structure is complex, and the numerical method requires more cumbersome calculations and accurate modeling, which limits its ability to analyze the permeability of highly inhomogeneous reservoirs.

Numerous scholars have conducted indoor experiments to study the relationship between reservoir permeability and effective stress 19 , 20 , 21 , 22 , 23 , 24 . However, obtaining permeability data of seam-and-hole carbonate reservoirs through experimental methods has its limitations. The cores used in indoor experiments are usually ordinary core samples with a diameter of 1.5 inches, and the core samples only cover a small portion of the reservoir section, which makes it difficult to restore the actual situation of pore structure distribution in carbonate reservoirs. Therefore, it is of great practical significance to study the stress-related permeability of porous media using theoretical methods. The microstructure of porous media is disordered and extremely complex, and it is more difficult to consider its stress sensitivity, so fractal theory can be introduced to analyze the stress sensitivity of flow and permeability in porous media 25 , 26 , 27 , 28 , 29 , 30 , 31 . Luo et al. 32 established a dual permeability calculation model considering stress-induced fracture closure by introducing the fractal dimension of the rock matrix and the curvature of the aperture surface of the fracture network. Miao et al. 33 predicted the change of permeability and porosity of fractured rock with stress based on fractal theory and Hooke's model. Ge et al. 34 proposed a new permeability model based on micro- and nano-scale discrete pore structures based on fractal theory and analyzed the effect of effective stress permeability. Tian et al. 35 proposed a bi-fractal permeability model to quantitatively study the effect of coal internal structure on permeability and considered the effect of effective stress and matrix shrinkage evolution on permeability. Jin et al. 36 constructed a bound water saturation model, a permeability model, and a relative permeability model based on the capillary bundle model and the fractal theory while considering the effects of water film and stress sensitivity. Currently, some progress has been made in the study of permeability stress sensitivity based on fractal theory, but most of the studies focus on conventional reservoirs. The permeability stress sensitivity characteristics of vuggy porous media lack comprehensive research and analysis.

In this paper, a two-scale fractal permeability model for vuggy porous media is established, which considers the elastotic deformation of vuggy porous media under stress sensitivity conditions. The proposed fractal model, based on the two-scale fractal theory, takes into account both interparticle pores and vugs. Different matching relations between capillary tubes and vugs are examined to predict the permeability of a vuggy porous medium. Additionally, using a set of random match relations, the most likely predicted permeability of an actual vuggy rock core is calculated based on the Monte Carlo method. The model’s accuracy is verified by real experimental data. And the influence of Young’s modulus, Poisson’s ratio, capillary fractal tortuosity dimension, capillary fractal dimension, and vug fractal dimensions on the models are analyzed.

The conceptual two-scale fractal model

Vuggy carbonate rock is a special type of carbonate rock, and when analyzing this type of carbonate rock, the influence of the vug system and matrix system on their permeability is mainly considered. As shown in Fig.  1 a, The core image of this type of carbonate rock reveals vugs of varying sizes caused by dissolution. The matrix is relatively dense, exhibiting certain levels of porosity and permeability.

Conceptual model schematic diagram: ( a ) Dissolution vuggy reservoirs outcrop ( b ) Simplified vuggy porous model.

The storage and seepage spaces in vuggy carbonate rocks are highly complex, making it difficult to accurately describe their microstructural details using traditional methods. Based on these characteristics, a two-scale fractal conceptual model of vuggy porous media is established, as shown in Fig.  1 b. For matrix pores, there are two main fractal structural features: the fractal distribution of pore diameters and the fractal tortuosity of fluid flow paths within the pores. Both structural features can be described by fractal theory. For vugs, the size distribution follows the fractal scaling law. Although the sizes of capillaries and vugs are not on the same scale, their size distributions both conform to the fractal scaling law.

To consider the effect of stress on the permeability of vuggy porous media, this paper reasonably simplifies the actual problem and makes the following reasonable assumptions on the above conceptual model:

For the capillary bundle: (1) The fluid channels in the matrix of porous medium can be seen as curved capillaries with different radii. (2) When the porous medium sample is under pressure, the internal capillary flow channel is uniformly stressed. (3) The total number of the capillary of the porous media remains the same after deformation. (4) The stress–strain and the fluid flow of the porous medium are steady state. (5) A porous medium is an ideal elastic body. Based on this assumption, the thick-walled cylinder model can be used to analyze the deformation of the single capillary caused by stress. As shown in Fig.  2 , where λ is the inner radius of the capillary, and tλ is the outer radius, the pressure of the fluid on the inside of the capillary is referred to as P i , and the outside pressure is subjected to the P o .

Force on a single capillary under elastic deformation: ( a ) Single capillary ( b ) Single capillary cross-section.

In the capillary model, the stress-induced change in the permeability of a porous medium can be characterized by the elastic deformation of the capillary cross-sectional area. According to the theory of mechanics of materials 37 , for the thick-walled cylinder model, the displacement at any radius can be expressed as:

where E is the Young’s modulus, ν is the Poisson’s ratio.

Therefore, the deformations of the inner surface of the capillary can be expressed as,

Under stress elastic deformation conditions, the radius of the inner surface of the capillary considering the stress can be expressed as,

where λ 0 is the radius of the inner surface of the capillary when the stress equals 0.

For the vugs: (1) The vugs of the porous medium can be modeled as hollow spheres with varying radii. (2) When the porous medium sample is under pressure, the internal vugs experience uniform stress. (3) The total number of the vugs of the porous media remains unchanged after deformation. (4) The stress–strain relationship and the fluid flow of the porous medium are steady state. (5) The porous medium is assumed to be an ideal elastic body. Based on this assumption, the thick-walled hollow sphere model is employed to analyze the deformation of a single vug under stress. As shown in Fig.  3 , where a is the inner radius of the capillary, and ta is the outer radius, the pressure of the fluid inside of the vug is denoted as P i , and the external pressure is P o .

Force on a single vug under elastic deformation: ( a ) Single vug ( b ) Single vug cross-section.

According to material mechanics 36 , the displacement at hollow sphere radius u ( r h ) can be expressed as

Therefore, the deformations of the inner surface of the vug can be expressed as

Under stress elastic deformation conditions, the radius of the inner surface of the vug considering the stress can be expressed as,

where a 0 is the radius of the inner surface of the vug when the stress equals 0.

The stress-sensitive permeability model of fractal vuggy porous media

According to the fractal theory 38 , the fractal scaling law of the capillary can be rewritten as,

where N λ is the number of capillaries, l is a certain length of the capillary, λ is a determined radius of the capillary, λ σ max is the maximum pore radius in the porous media sample, and D f is the number of fractal dimensions. When it is a two-dimensional space, 0 <  D f  < 2, and when it is a three-dimensional space,0 <  D f  < 3.

Equation ( 9 ) can be regarded as a continuous and differentiable function. The number of capillaries between the λ and d λ can be obtained by differentiating,

Based on the fractal scaling law, the capillary length when considering the tortuosity can be expressed as,

where L pσ is the length of the capillary, D T is the capillary tortuosity fractal dimension, and L σ is the characteristic length, whose value is the same as the core sample’s length in this study.

The same, the fractal scaling law of the vugs can be rewritten as,

where N a is the number of vugs, a is the determined radius of the vug, a σ max is the maximum vug radius in the porous media sample, and D a is the vug fractal dimension.

In the study of fluid flow in vuggy carbonate rocks, the flow of fluids in the matrix system and the vug system is mainly considered. In the fractal conceptual model, the matrix system is regarded as capillary tubes with different radii, and the vug system is simplified as spheres with different radii. Existing research results show that in capillary vuggy porous media, the vugs connected with the capillary can be regarded as an equipotential volume, which means the influence of vugs on the capillary can be seen as the vugs reduce the length of the capillary.

As shown in Fig.  4 , in the vuggy carbonate reservoir, one vug may equally affect many capillaries, and each capillary is not only affected by one vug, so it is necessary to add parameters to consider the influence of different numbers of dissolution pores on the capillaries. In addition, when considering the effect of stress on the permeability of the vuggy porous media, to simplify the problem more, this paper considers the vug and capillary separately and studies the deformation of the capillary model and the spherical shell model when they are subjected to stress, respectively, with the outer pressure of the model being the external pressure exerted on the core, and the inner pressure of the model being the fluid pressure inside the core.

The connection between capillaries and vugs: ( a ) One vug connects with many capillaries ( b ) One capillary connects with many vugs.

Therefore, the capillary length considering the effect of vugs can be expressed as:

where λ σ is the radius of the capillary; a is the radius of the vug, L σ is the length of the capillary, D T is the tortuosity fractal dimension of the capillary; and n is the number of vugs that affect the capillary. β indicates the degree of influence of vugs on capillary length, if the vug is a regular sphere and the diameter of the vug just coincides with the capillary, the impact of the vug on the capillary reaches the maximum value, and at this time, β  = 1.

The fluid flow through a curved capillary can be described according to the Hagen-Poisenille equation:

where λ σ is the radius of the capillary, L p σ is the length of the capillary, μ is the viscosity of the fluid, Δ p is the pressure difference between the two ends of the capillary.

Therefore, the total flow of the entire fractal porous medium can be obtained through integrating Eq. ( 14 )

The permeability of porous media can be expressed by Darcy’s law,

According to Hooke’s Law, the radius of the porous media sample considering the stress can be expressed as:

where σ is the stress, E is Young’s modulus, and R 0 is the radius of the porous media sample when the stress equals 0.

The area of the porous media sample considering the cross-section stress can be expressed as,

The sample length considering the stress can be expressed as,

Substituting Eq. ( 15 ) into Eq. ( 16 ), the expression of permeability of capillary vuggy porous media can be obtained.

Vuggy porous media exhibit a certain degree of heterogeneity, and the spatial relationship between vugs and matrix capillaries is complex, making accurate description challenging. However, through theoretical analysis, the theoretical maximum and minimum permeability of vuggy porous media can be determined by idealizing the relationship between the vugs and matrix capillaries.

The maximum permeability model

Under the condition that the total number of vugs and capillaries in the vuggy porous media is constant, if the vug has the greatest influence on the fluid flow in the porous medium, the vug with the largest radius should have an influence on the n capillaries with the largest radius and the vug with the smallest radius affects the n capillaries with the smallest radius.

Equation ( 9 ) also means sorting the capillary from largest to smallest. the capillary whose radius is closest to λ and also is greater than λ ranked n th. The same relationship of vugs can be obtained from Eq. ( 12 ).

Therefore, the relationship that the largest vug impacts the n largest aperture capillary and that the smallest vug impacts the n smallest aperture capillary can be expressed as,

Substituting Eqs. ( 9 ) and ( 12 ) into Eq. ( 21 ), the relationship of capillary aperture λ and vug radius a can be obtained.

Substituting Eq. ( 22 ) into Eq. ( 20 ), we can get the expression of permeability of porous media

The minimum permeability model

Conversely, if the vug has the least effect on the fluid flow in the medium, the cave with the largest radius should have an effect on the n capillaries with the smallest radius, and the vug with the smallest radius should have an effect on the n capillaries with the largest radius.

The relationship between capillary aperture λ and vug radius can be expressed as:

Substituting Eqs. ( 9 ) and ( 12 ) into Eq. ( 24 ), the relationship of capillary radius λ and vug radius a can be obtained.

Substituting Eq. ( 25 ) into Eq. ( 20 ), we can get the expression of permeability of porous media,

Monte Carlo simulation based on fractal theory

The Monte Carlo simulation method is a kind of random sampling calculation method with probability theory and statistical theory as the basic theory, between the theoretical method and the real reality, which can simulate the actual physical process more realistically and effectively, and has a wide range of cross-applications in the fields of physics, chemistry, economics, and engineering technology. The basic idea is to establish a stochastic process to describe the randomness of the variables in the actual model and to predict the statistical characteristics of the required parameters by random sampling tests on the model to give an approximate solution of the required parameters. Since the pore distribution in porous media is random and proven to satisfy the fractal scalar law, fractal theory and Monte Carlo simulation methods are naturally combined.

In this paper, the prediction of permeability of vuggy porous media considering the stress case is analyzed by the Monte Carlo simulation method based on the previous studies and combined with the above proposed fractal model.

Monte Carlo characterization of the matrix and vugs

The probability density function of the vug \(f\left( a \right)\) satisfies the normalization condition

The vug fractal dimension D a is always greater than one: D a  > 1, which means the second equal sign in Eq. ( 27 ) exists only when the condition a min  <  <  a max is satisfied. Generally, the actual vug satisfied the condition \(\frac{{a_{\min } }}{{a_{\max } }} < 10^{ - 2}\) , So Eq. ( 27 ) is correct in the actual application.

According to Eq. ( 27 ), The cumulative probability of vug size within the range of any vug can be expressed as

It can be seen from Eqs. ( 27 ) and ( 28 ) that when the vug radius a infinitely approaching the a min , W ( a )≈0 when the vug radius a infinitely approaching the a max , W ( a )≈1, which means the value of the W ( a ) is a random number from 0 to 1.

The Eq. ( 28 ) can be also written as,

Therefore, the value of \(\frac{{a_{\min } }}{a}\) is also a random number from 0 to 1. The expression of the vug diameter can be expressed as

The vug radius a can be replaced by a i in the probabilistic model of random vug radius:

where i  = (1, 2, 3, …, N ), N is the total number of Monte Carlo simulations.

The capillary radius λ in the probabilistic model of random capillary radius can be obtained in the same way:

where W i ( λ ) is the cumulative probability of capillary radius within the range of any capillary in the i th Monte Carlo simulation. λ min is the minimum capillary radius, λ max is the maximum capillary radius, D f is the capillary fractal number.

Monte Carlo algorithm workflow

Based on the fractal permeability model illustrated in Sect. " The conceptual two-scale fractal model " the permeability of vuggy porous media with fractal Monte Carlo method can be determined. As shown in Fig.  5 , the algorithm for the Fractal-Monte Carlo method is summarized as follows.

Fractal-Monte Carlo algorithm flow chart.

Results and discussions

In this part, the validity of the proposed fractal model is verified by the experimental data. Then, the effect of the key parameters of the vuggy porous media is analyzed.

Experimental validation

The correctness of the fractal model proposed in this paper to predict the elastic deformation and permeability change of vuggy porous media under stress conditions is verified. In this paper, two groups of representative dissolution pore-type carbonate rock cores are selected, they are shown in Figs.  6 a and 8 a. The cores are scanned by CT, and mechanical experiments are conducted to obtain the relevant parameters required by the model, permeability stress sensitivity experiments are conducted on the two groups of cores respectively, and the experimental results are compared with the model prediction results (Fig.  7 and Fig. 9 ).

Outcrop core and CT scan image, Example 1: ( a ) Sample 1 ( b ) Three-dimensional CT scan image ( c ) Processed CT image.

A comparison between model predictions and experimental data, Example 1: ( a ) Fractal-Monte Carlo simulation results of first data ( b ) Comparison between model and experimental.

Figures  6 b and 8 b represent three-dimensional CT scan images. Figures  6 c and 8 c are corresponding processed CT images of samples. To be more consistent with the actual pore structure of the core, the fractal dimensions in multiple CT scans are averaged. From the CT image of the sample, the number of the vug fractal dimension D a can measured as 1.65 and 1.75, respectively, the measurement method is the box dimension method. From the CT image of the matrix of samples, the number of fractal dimensions D f can measured as 1.35 and 1.3, respectively. Figures  7 a and 9 a show the simulated results of 1000 times the permeability of the vuggy porous media simulated by the Monte Carlo simulation results of the first data. The final experimental results are shown in Figs.  7 b and 9 b. The experimental data of the permeability of the carbonate rock medium are represented by the red remark. In Figs.  7 c and 9 c, the maximum permeability model K max is represented by a blue solid line, and the minimum permeability model K min is represented by a black solid line. Monte Carlo simulation results based on these experimental data are represented by an orange solid line. It can be seen from these two pictures that our Fractal-Monte Carlo method of vuggy porous media shows a great agreement with the experiment data.

Outcrop core and CT scan image, Example 2: ( a ) Sample 2 ( b ) Three-dimensional CT scan image ( c ) Processed CT image.

A comparison between model predictions and experimental data, Example 2: ( a ) Fractal-Monte Carlo simulation results of first data ( b ) Comparison between model and experimental.

Parameter sensitivity analysis

In the following, the effect of the structural parameters (Young’s modulus E and Poisson’s ratio v ) on the normalized permeability is analyzed. The relationships between the permeability and the effective stress are shown in Figs.  10 and 11 .

The predicted permeability vs effective stress with the different Young’s modulus: ( a ) Fractal theory ( b ) Fractal-Monte Carlo method.

The predicted permeability vs effective stress with the different Poisson's ratio: ( a ) Fractal theory ( b ) Fractal-Monte Carlo method.

It shows from Figs.  10 and 11 , that with the effective stress increasing gradually, the permeability decreases rapidly. This is because the increase of the effective stress implies the cross-sectional area of the pore and throat decreasing, leading to the decrease of flowing space and the increase of flowing distance. Figure  10 also shows the permeability varies with the effective stress at different Young’s modulus E . Figure  10 depicts that the permeability increased with the higher value of Young’s modulus E . Figure  10 depicts that the permeability increased with the higher value of Young’s modulus E , and this can be interpreted as that the higher Young’s modulus E brings the higher resistance to the capillary bundles. Figure  11 reveals that the higher Poisson’s ratio ν, the higher permeability at the same effective stress condition. This phenomenon attributed to the higher Poisson’s ratio ν leads to a smaller increase in the flowing distance.

Figures  12 and 13 show the permeability of the porous media is affected by the capillary fractal dimension D f and capillary fractal tortuosity dimension D T . It can be seen from Fig.  13 that both the max permeability model K max and the minimum permeability model K min increase with the increase of the capillary fractal dimension D f . This can be explained by that the capillary fractal dimension is related to the cross-sectional distribution of the capillary in porous media, the increase of the capillary fractal dimension means an increase in the number of the capillary. Under the condition of constant cross-sectional area, the increase in capillary number will lead to an increase in the conductivity of the capillary network, which increases the permeability of the porous media.

The predicted vs effective stress with the different capillary fractal tortuosity dimensions D T : ( a ) Fractal theory ( b ) Fractal-Monte Carlo method.

The predicted permeability vs effective stress with the different capillary fractal dimensions D f : ( a ) Fractal theory ( b ) Fractal-Monte Carlo method.

Figure  12 reveals the effect of the capillary fractal tortuosity dimension D T on the vuggy porous media. It can be seen from Fig.  12 that with the increase of tortuosity fractal dimension of the capillary, the prediction value of the maximum and minimum permeability prediction model decreases rapidly: under the same other conditions, the value of max permeability model K max when the tortuosity fractal dimension D T  = 1.2 is even lower than the permeability of the minimum permeability model K min when the tortuosity fractal dimension D T  = 1.1.

It can be seen from Fig.  14 that under the same effective stress conditions, a larger fractal dimension of dissolution pores corresponds to higher permeability. This is because a larger fractal dimension indicates a greater number of dissolved pores, which results in less tortuosity of the capillaries within the porous medium and shorter capillary paths. Consequently, the fluid flow path through the capillaries is reduced, leading to an increase in permeability.

The predicted permeability vs effective stress with the different vug fractal dimensions D a : ( a ) Fractal theory ( b ) Fractal Monte Carlo method.

Conclusions

A novel fractal predictive model has been developed for the permeability of vuggy porous media considering the stress. Compared with the other available stress sensitivity permeability models, this work shows better accuracy in highly effective stress conditions and can be able to predict permeability change due to the elastic deformation of the fractal vuggy porous media under loading stress. Each parameter in the models has a clear physical meaning. The models are verified by experimental data. The sensitivity analysis of the influencing factors of the models has also been done and the results show that Young’s modulus E and Poisson’s ratio v play significant roles in stress-depend permeability. The Parameter sensitivity analysis shows that the permeability of vuggy porous media increased with the higher value of Young’s modulus, Poisson’s ratio, capillary fractal tortuosity dimensions, capillary fractal dimensions, and vug fractal dimensions. However, the model also has limitations. For example, it ignores the plastic deformation of the fractal vuggy porous. Besides, the model also neglects the change in the number of the capillary and vug of the vuggy porous media. More work can be done in this aspect in the future.

Data availability

The data that support the findings of this study is provided within the manuscript.

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Acknowledgements

The authors would like to thank the support of the National Nature Science Foundation of China (52074336, 52034010) and CNPC Science and Technology Major Project (RIPED-2022-JS-1563, ZD2019-183-008-001).

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Zhaoqin Huang, Xu Zhou & Hao Wang

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Huang, Z., Zhou, X., Wang, H. et al. Stress sensitivity analysis of vuggy porous media based on two-scale fractal theory. Sci Rep 14 , 20710 (2024). https://doi.org/10.1038/s41598-024-71171-2

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5.5 Introduction to Hypothesis Tests

One job of a statistician is to make statistical inferences about populations based on samples taken from the population. Confidence intervals are one way to estimate a population parameter.

Another way to make a statistical inference is to make a decision about a parameter. For instance, a car dealership advertises that its new small truck gets 35 miles per gallon on average. A tutoring service claims that its method of tutoring helps 90% of its students get an A or a B. A company says that female managers in their company earn an average of $60,000 per year. A statistician may want to make a decision about or evaluate these claims. A hypothesis test can be used to do this.

A hypothesis test involves collecting data from a sample and evaluating the data. Then the statistician makes a decision as to whether or not there is sufficient evidence to reject the null hypothesis based upon analyses of the data.

In this section, you will conduct hypothesis tests on single means when the population standard deviation is known.

Hypothesis testing consists of two contradictory hypotheses or statements, a decision based on the data, and a conclusion. To perform a hypothesis test, a statistician will perform some variation of these steps:

• Define hypotheses.
• Collect and/or use the sample data to determine the correct distribution to use.
• Calculate test statistic.
• Make a decision.
• Write a conclusion.

Defining your hypotheses

The actual test begins by considering two hypotheses: the null hypothesis and the alternative hypothesis. These hypotheses contain opposing viewpoints.

The null hypothesis ( H 0 ) is often a statement of the accepted historical value or norm. This is your starting point that you must assume from the beginning in order to show an effect exists.

The alternative hypothesis ( H a ) is a claim about the population that is contradictory to H 0 and what we conclude when we reject H 0 .

Since the null and alternative hypotheses are contradictory, you must examine evidence to decide if you have enough evidence to reject the null hypothesis or not. The evidence is in the form of sample data.

After you have determined which hypothesis the sample supports, you make a decision . There are two options for a decision. They are “reject H 0 ” if the sample information favors the alternative hypothesis or “do not reject H 0 ” or “decline to reject H 0 ” if the sample information is insufficient to reject the null hypothesis.

The following table shows mathematical symbols used in H 0 and H a :

NOTE: H 0 always has a symbol with an equal in it. H a never has a symbol with an equal in it. The choice of symbol in the alternative hypothesis depends on the wording of the hypothesis test. Despite this, many researchers may use =, ≤, or ≥ in the null hypothesis. This practice is acceptable because our only decision is to reject or not reject the null hypothesis.

We want to test whether the mean GPA of students in American colleges is 2.0 (out of 4.0). The null hypothesis is: H 0 : μ = 2.0. What is the alternative hypothesis?

A medical trial is conducted to test whether or not a new medicine reduces cholesterol by 25%. State the null and alternative hypotheses.

Using the Sample to Test the Null Hypothesis

Once you have defined your hypotheses, the next step in the process is to collect sample data. In a classroom context, the data or summary statistics will usually be given to you.

Then you will have to determine the correct distribution to perform the hypothesis test, given the assumptions you are able to make about the situation. Right now, we are demonstrating these ideas in a test for a mean when the population standard deviation is known using the z distribution. We will see other scenarios in the future.

Calculating a Test Statistic

Next you will start evaluating the data. This begins with calculating your test statistic , which is a measure of the distance between what you observed and what you are assuming to be true. In this context, your test statistic, z ο , quantifies the number of standard deviations between the sample mean, x, and the population mean, µ . Calculating the test statistic is analogous to the previously discussed process of standardizing observations with z -scores:

where µ o   is the value assumed to be true in the null hypothesis.

Making a Decision

Once you have your test statistic, there are two methods to use it to make your decision:

• Critical value method (discussed further in later chapters)
• p -value method (our current focus)

p -Value Method

To find a p -value , we use the test statistic to calculate the actual probability of getting the test result. Formally, the p -value is the probability that, if the null hypothesis is true, the results from another randomly selected sample will be as extreme or more extreme as the results obtained from the given sample.

A large p -value calculated from the data indicates that we should not reject the null hypothesis. The smaller the p -value, the more unlikely the outcome and the stronger the evidence is against the null hypothesis. We would reject the null hypothesis if the evidence is strongly against it.

Draw a graph that shows the p -value. The hypothesis test is easier to perform if you use a graph because you see the problem more clearly.

Suppose a baker claims that his bread height is more than 15 cm on average. Several of his customers do not believe him. To persuade his customers that he is right, the baker decides to do a hypothesis test. He bakes ten loaves of bread. The mean height of the sample loaves is 17 cm. The baker knows from baking hundreds of loaves of bread that the standard deviation for the height is 0.5 cm and the distribution of heights is normal.

The null hypothesis could be H 0 : μ ≤ 15.

The alternate hypothesis is H a : μ > 15.

The words “is more than” calls for the use of the > symbol, so “ μ > 15″ goes into the alternate hypothesis. The null hypothesis must contradict the alternate hypothesis.

Suppose the null hypothesis is true (the mean height of the loaves is no more than 15 cm). Then, is the mean height (17 cm) calculated from the sample unexpectedly large? The hypothesis test works by asking how unlikely the sample mean would be if the null hypothesis were true. The graph shows how far out the sample mean is on the normal curve. The p -value is the probability that, if we were to take other samples, any other sample mean would fall at least as far out as 17 cm.

This means that the p -value is the probability that a sample mean is the same or greater than 17 cm when the population mean is, in fact, 15 cm. We can calculate this probability using the normal distribution for means.

A p -value of approximately zero tells us that it is highly unlikely that a loaf of bread rises no more than 15 cm on average. That is, almost 0% of all loaves of bread would be at least as high as 17 cm purely by CHANCE had the population mean height really been 15 cm. Because the outcome of 17 cm is so unlikely (meaning it is happening NOT by chance alone), we conclude that the evidence is strongly against the null hypothesis that the mean height would be at most 15 cm. There is sufficient evidence that the true mean height for the population of the baker’s loaves of bread is greater than 15 cm.

A normal distribution has a standard deviation of one. We want to verify a claim that the mean is greater than 12. A sample of 36 is taken with a sample mean of 12.5.

Find the p -value.

Decision and Conclusion

A systematic way to decide whether to reject or not reject the null hypothesis is to compare the p -value and a preset or preconceived α (also called a significance level ). A preset α is the probability of a type I error (rejecting the null hypothesis when the null hypothesis is true). It may or may not be given to you at the beginning of the problem. If there is no given preconceived α , then use α = 0.05.

When you make a decision to reject or not reject H 0 , do as follows:

• If α > p -value, reject H 0 . The results of the sample data are statistically significant . You can say there is sufficient evidence to conclude that H 0 is an incorrect belief and that the alternative hypothesis, H a , may be correct.
• If α ≤ p -value, fail to reject H 0 . The results of the sample data are not significant. There is not sufficient evidence to conclude that the alternative hypothesis, H a , may be correct.

After you make your decision, write a thoughtful conclusion in the context of the scenario incorporating the hypotheses.

NOTE: When you “do not reject H 0 ,” it does not mean that you should believe that H 0 is true. It simply means that the sample data have failed to provide sufficient evidence to cast serious doubt about the truthfulness of H o .

When using the p -value to evaluate a hypothesis test, the following rhymes can come in handy:

If the p -value is low, the null must go.

If the p -value is high, the null must fly.

This memory aid relates a p -value less than the established alpha (“the p -value is low”) as rejecting the null hypothesis and, likewise, relates a p -value higher than the established alpha (“the p -value is high”) as not rejecting the null hypothesis.

Fill in the blanks:

• Reject the null hypothesis when              .
• The results of the sample data             .
• Do not reject the null when hypothesis when             .

It’s a Boy Genetics Labs claim their procedures improve the chances of a boy being born. The results for a test of a single population proportion are as follows:

• H 0 : p = 0.50, H a : p > 0.50
• p -value = 0.025

Interpret the results and state a conclusion in simple, non-technical terms.

Click here for more multimedia resources, including podcasts, videos, lecture notes, and worked examples.

Figure References

Figure 5.11: Alora Griffiths (2019). dalmatian puppy near man in blue shorts kneeling. Unsplash license. https://unsplash.com/photos/7aRQZtLsvqw

Figure 5.13: Kindred Grey (2020). Bread height probability. CC BY-SA 4.0.

A decision-making procedure for determining whether sample evidence supports a hypothesis

The claim that is assumed to be true and is tested in a hypothesis test

A working hypothesis that is contradictory to the null hypothesis

A measure of the difference between observations and the hypothesized (or claimed) value

The probability that an event will occur, assuming the null hypothesis is true

Probability that a true null hypothesis will be rejected, also known as type I error and denoted by α

Finding sufficient evidence that the observed effect is not just due to variability, often from rejecting the null hypothesis

Significant Statistics Copyright © 2024 by John Morgan Russell, OpenStaxCollege, OpenIntro is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License , except where otherwise noted.

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Stress, coping, and depression: testing new hypotheses in a prospectively studied general population sample of U.S. born Whites and Blacks

1 Department of Epidemiology, Columbia University, New York, NY

The scarcity of empirically supported explanations for the Black/White prevalence difference in depression in the U.S. is a conspicuous gap in the literature. Recent evidence suggests that the paradoxical observation of decreased risk of depression but elevated rates of physical illness among Blacks in the U.S. compared with Whites may be accounted for by the use of coping behaviors (e.g., alcohol and nicotine consumption, overeating) among Blacks exposed to high stress levels. Such coping behaviors may mitigate deleterious effects of stressful exposures on mental health while increasing the risk of physical ailments. The racial patterning in mental and physical health outcomes could therefore be explained by this mechanism if a) these behaviors were more prevalent among Blacks than Whites and/or b) the effect of these behavioral responses to stress was differential by race. The present study challenges this hypothesis using longitudinal, nationally-representative data with comprehensive DSM-IV diagnoses. Data are drawn from 34,653 individuals sampled in Waves 1 (2001-2002) and 2 (2004-2005) as part of the US National Epidemiologic Survey on Alcohol and Related Conditions. Results showed that a) Blacks were less likely to engage in alcohol or nicotine consumption at low, moderate, and high levels of stress compared to Whites, and b) there was a significant three-way interaction between race, stress, and coping behavior for BMI only (F=2.11, df=12, p=0.03), but, contrary to the hypothesis, elevated BMI was protective against depression in Blacks at low, not high, levels of stress. Further, engagement in unhealthy behaviors, especially at pathological levels, did not protect against depression in Blacks or in Whites. In sum, the impact of stress and coping processes on depression do not appear to operate differently in Blacks versus Whites. Further research testing innovative hypotheses that would explain the difference in Black/White depression prevalence is warranted.

Introduction

Epidemiologic studies have consistently documented that Blacks living in the United States have higher rates of physical illness such as hypertension and diabetes, and higher rates of mortality, compared with non-Hispanic Whites controlling for indicators of socio-economic position (SEP) ( Heckler 1985 ; McCord and Freeman 1990 ; Williams and Jackson 2005 ). Conversely, major psychiatric epidemiologic household surveys have reported that Blacks have equal or lower rates of most psychiatric disorders, including major depression ( Kessler, McGonagle et al. 1994 ; Hasin, Goodwin et al. 2005 ; Breslau, Aguilar-Gaxiola et al. 2006 ; Williams, Gonzalez et al. 2007 ). These divergent patterns for mental and physical health outcomes have been termed a ‘paradox’ ( Williams 2001 ). Blacks in the U.S. face historic and contemporary institutionalized discrimination which exposes them to disadvantaged SEP, worse living conditions, and greater stress and adversity due to marginalized social status ( Kessler, Mickelson et al. 1999 ; Kreiger 2000 ; Williams and Williams-Morris 2000 ), all of which seemingly place Blacks at greater risk for depression compared with Whites ( Dohrenwend 2000 ). Indeed, among Blacks in the U.S., perception of discrimination and adversity due to race is associated with greater psychological distress and depressive symptoms ( Kessler, Mickelson et al. 1999 ; Williams and Williams-Morris 2000 ). However, absolute rates of depression remain lower among Blacks compared with Whites.

Many pathways have been posited to explain the elevated rates of physical health problems among Blacks in the U.S. compared with Whites. One well-studied mechanism is stress associated with disadvantaged social status. The physiologic responses to stress via allostatic load have been hypothesized to influence health by a process of ‘wear and tear’ whereby the body can no longer effectively regulate itself ( McEwen 2000 ; McEwen 2004 ). “Weathering” ( Geronimus 1994 ; Geronimus 1996 ), which describes a process of accelerated aging as an effect of the cumulative experience of stress and adversity, has been hypothesized to explain why Blacks have lower birthweights as well as higher mortality at younger ages than Whites after controlling for SEP. Further, interpersonal discrimination appraised by the individual as negative can result in fear, anger, and denial, thereby inducing injurious physiologic responses in cardiovascular, endocrine, neurologic and immune systems ( Krieger 1990 ; Krieger and Sidney 1996 ; Kreiger 2000 ). Adverse neighborhood conditions, to which Blacks have greater exposure than Whites, can influence health through inadequate access to social and health services, exposures to health hazards, and reduction in social cohesion and connectedness ( Massey 1985 ; Massey 2004 ). Greater stress, worse bodily wear and tear, reduced access to medical services, and greater exposure to deleterious neighborhood conditions are all risk factors for depression ( Leonard 2000 ; McEwen 2003 ; Stansfeld 2005 ), and yet Blacks consistently generate estimates of depression below those of Whites; this poses a perplexing, unresolved issue for social and psychiatric epidemiology.

Two methodological hypotheses advanced to explain this mental/physical health paradox posit that rates of depression among Blacks are underestimated in major psychiatric epidemiologic studies due to selection bias and measurement error. The selection bias hypothesis reflects the fact that all major psychiatric epidemiologic surveys conducted in the U.S. exclude institutionalized populations. Young Black men in the U.S. are overrepresented in prison and jail populations ( Petit and Western 2004 ), where depression is more prevalent compared with household populations ( Teplin 1990 ; Teplin, Abram et al. 1996 ). Thus, the underestimation of depression prevalence in household samples could affect Blacks to a greater extent compared with Whites, though the effect of this bias would primarily be age- and gender-specific. The measurement error hypothesis suggests potential diagnostic bias in the major survey instruments used to capture depression. Given the same symptom presentation, Blacks interviewed by clinicians in unstructured or semi-structured formats are more likely to be diagnosed as having a disorder in the psychotic spectrum and Whites as having a disorder in the mood spectrum ( Neighbors, Trierweiler et al. 1999 ; Neighbors, Trierweiler et al. 2003 ; Strakowski, Keck et al. 2003 ). Additionally, some argue that depression may manifest differently in Blacks compared with Whites, and current diagnostic nosology more appropriately captures depression in Whites compared with Blacks ( Rogler 1999 ; Baker 2001 ; Brown 2003 ; Kleinman 2004 ). Available data suggest that while these hypotheses may explain some of the Black/White difference in depression, methodological issues cannot account for the all of the difference ( Williams, Gonzalez et al. 2007 ; Breslau, Javaras et al. 2008 ). Thus, hypotheses exploring alternative mechanisms through which Blacks may have a lower prevalence of depression compared with Whites remain necessary.

In contrast to methodological hypotheses explaining the mental/physical health ‘paradox’, a recently advanced alternative hypothesis is that the patterning in physical and mental health outcomes in Blacks versus Whites arises from mechanisms for coping with stressors that on average operate differently for Black and White Americans ( Jackson and Knight 2006 ; Jackson, Knight et al. 2009 ). Jackson and colleagues have argued that Blacks in the U.S. face greater, and unique, stressors compared with Whites, and that strategies deployed to cope emotionally with this increased stress may protect mental health while having deleterious consequences for physical health. Recently, Jackson and colleagues reported that at high levels of stress, Blacks with elevated body mass index (BMI) and/or who smoke cigarettes and/or drink alcohol (collectively termed ‘unhealthy behaviors’ or ‘UHBs’ ( Jackson, Knight et al. 2009 )) were less likely than Blacks not engaging in these behaviors to develop depression, whereas the pattern trended in the opposite direction for Whites ( Jackson, Knight et al. 2009 ). Further empirical support for this hypothesis was recently reported using data from the Baltimore Epidemiologic Catchment Area Study ( Mezuk, Rafferty et al. 2010 ). Evidence indicates that UHBs can ameliorate immediate anxiety and depressive symptoms in response to stressful experiences by regulating corticotropin-releasing factor in the hypothalamic-pituitary-adrenalcortical (HPA) axis ( Benowitz 1988 ; Koob, Roberts et al. 1998 ; Dallman, Pecoraro et al. 2003 ). However, long-term heavy alcohol consumption, smoking, and high BMI can lead to a cascade of physical health consequences. This hypothesis suggests that, in the context of chronic stress, Blacks’ engagement in UHBs may serve to buffer the deleterious consequences of stress on depression through the HPA pathway, leading to a lower prevalence of depression but a greater prevalence of physical health problems than would have otherwise occurred. This hypothesis also suggests that the same processes operate differently or with different consequences in Whites. In the interest of brevity, we refer to these potentially differential patterns in the relationships between stress, coping, and depression between Blacks and Whites as “group-specific,” meaning that they arise from the unequal distribution of exposures and coping resources engendered by a racialized environment, rather than differences embedded in the individual.

Differences in stress and coping processes between Blacks and Whites could account for the mental/physical health ‘paradox’ under two scenarios. (1) UHBs are indeed protective against depression, among both Blacks and Whites, but Blacks are much more likely to engage in them compared with Whites at a given level of stress. This is unlikely in light of previous epidemiologic evidence suggesting that a) substance disorders and obesity are comorbid with depression ( Reiger, Farmer et al. 1990 ; Kessler, Crum et al. 1997 ; Hasin, Goodwin et al. 2005 ) and b) Blacks are less likely than Whites to engage in alcohol and nicotine consumption ( Grant, Hasin et al. 2004 ; Hasin, Stinson et al. 2007 ). However, patterns of comorbidity and Black/White differences in depression at all levels of stress have not been investigated systematically. (2) UHBs operate differentially by race, whereby they protect against depression to a greater extent among Blacks compared with Whites (either overall or variably by level of stress). This hypothesis is supported by data from the Americans’ Changing Lives Survey ( Jackson, Knight et al. 2009 ) and the Baltimore Epidemiologic Catchment Area Study ( Mezuk, Rafferty et al. 2010 ), as described above.

We propose to comprehensively investigate each of the above scenarios in a large nationally representative prospective study of U.S. adults. The present study is intended to both replicate and extend the analyses presented in Jackson et al. (2009) to provide a comprehensive test of the underlying theory. Using the National Epidemiologic Survey on Alcohol and Related Conditions (NESARC) we accomplish five main aims. First, we construct as exact a replication as possible of Jackson et al. (2009) in order to provide a baseline for comparison and from which to broaden the analyses. The remaining four aims systematically test the theory underlying the two scenarios outlined above. We examine whether alcohol consumption, nicotine consumption, and body mass index (as a proxy for overeating, consistent with Jackson et al., (2009) ) are prospectively protective against depression; we examine whether Blacks engage in more of these behaviors than Whites at low, moderate, and/or high levels of stress; and we test the hypothesis that Blacks exposed to high levels of stress are protected against depression if engaged in UHBs at the time of the stressors and, simultaneously, that Whites are not similarly conferred such protection from these behaviors. Finally, the hypothesis outlined by Jackson et al. (2009) suggests that the stress exposure of Blacks is qualitatively different compared to that of Whites. The NESARC data allows us to examine a measure of perceived racial discrimination in order to test whether Blacks who report high levels of discrimination and engage in UHBs have less depression than Blacks who report high levels of discrimination and do not engage in UHBs.

The data used in the present study have distinct advantages over those in ( Jackson, Knight et al. 2009 ): namely a larger sample size, DSM-IV diagnoses of major depression at two time points, DSM-IV diagnoses of nicotine dependence and alcohol use disorders, and comprehensive measures of nicotine, alcohol consumption, and stressful life events. Extending the analyses of Jackson et al, (2009) to include pathological alcohol and nicotine consumption is important in testing the hypothesis, as high and chronic levels of nicotine and alcohol use are behaviors most associated with poor physical health outcomes; if the Black/White “paradox” can be attributed to discrepant mental and physical health consequences of unhealthy behaviors, the nature and degree of engagement in those behaviors most implicated in poor somatic health should be considered.

Data are drawn from the National Epidemiologic Survey on Alcohol and Related Conditions (NESARC), a two-wave longitudinal survey of adults in the United States residing in households and group quarters. Wave 1 was conducted in 2001-2002 (N=43,093); young adults, Hispanics and Blacks were oversampled, with an overall response rate of 81%. Respondents were re-interviewed for Wave 2 approximately three years after Wave 1, with 34,653 (80.4%) successfully re-interviewed. More information on the study methods is found elsewhere ( Grant, Goldstein et al. 2009 ). The research protocol, including written informed consent procedures, received full ethical review and approval from the U.S. Census Bureau and the U.S. Office of Management and Budget.

All measures were assessed using the Alcohol Use Disorder and Associated Disabilities Interview Schedule-DSM-IV Version (AUDADIS-IV). We used measures of race/ethnicity, UHBs, and stressful life events ascertained at Wave 1 and measures of the outcomes, major depression and physical illness, from Wave 2. This design established the temporality of the exposures as occurring prior to the outcome; we controlled for major depression at Wave 1 in all analyses for which depression at Wave 2 was an outcome to further establish temporal sequence.

Race/ethnicity

We included self-identified non-Hispanic Whites (N=19,216) and non-Hispanic Blacks (N=6,065) who reported being born in the U.S. Foreign-born Blacks (N=664) and Whites (N=1,264) were excluded from the present analysis because patterns of substance use, depression and stressful life events differ between foreign- and non-foreign born individuals.

‘Unhealthy behaviors’ (UHBs)

We considered three types of ‘UHBs’: alcohol consumption, nicotine consumption, and body mass index (BMI). While a compelling argument can be made regarding the validity of terming alcohol consumption, nicotine consumption, and BMI collectively as ‘UHBs’ (e.g., moderate consumption of alcohol may be cardioprotective ( Klatsky 2009 )), we have used this terminology to remain consistent with the prior empirical support for the hypothesis we are testing ( Jackson, Knight et al. 2009 ). For our replication analysis, we use definitions exactly consistent with Jackson, Knight et al. (2009) , namely a UHB count measure (0-3) indicating if the individual ever consumed at least one alcoholic beverage in their lifetime, ever smoked at least 100+ cigarettes in their lifetime, and whether they currently have a BMI≥30. For our extended test of the overall theory, we used the following definitions:

• Alcohol consumption in the past 12 -months at Wave 1 was operationalized as a three-level variable: no consumption (N=2,293); non-pathological consumption (i.e., any level of consumption but no alcohol abuse/dependence diagnosis) at levels less than weekly binge (>4 drinks for men or >3 drinks per women on at least one occasion in the past year) (N=13,765); and DSM-IV alcohol abuse/dependence or at least weekly binge drinking (N=8,593). Measurement of alcohol consumption and diagnoses is a particular strength of the AUDADIS-IV instrument; diagnoses are made based on assessment of over 40 symptom items, and the excellent reliability and validity of alcohol diagnosis in the AUDADIS-IV have been extensively documented both the United States and internationally (see Hasin et al., 2007 ). Limited differential item functioning by race/ethnicity has been noted for alcohol disorder criteria in Item Response Theory analysis ( Saha, Chou et al. 2006 ).
• Nicotine consumption in the past 12 -months at Wave 1 was operationalized as a three-level variable: no nicotine use (N=18,601); non-pathological use (any level of use but no DSM-IV-defined nicotine dependence diagnosis) (N=3,358); and DSM-IV nicotine dependence (N=3,313). The good reliability and validity of nicotine dependence in the AUDADIS-IV have been well-documented ( Grant, Hasin et al. 2004 ). Limited differential item functioning by race/ethnicity has been noted for nicotine dependence criteria in Item Response Theory analysis ( Saha, Compton et al. 2010 ).
• Unhealthy eating in the past 12 -months at Wave 1 was operationalized using current BMI based on respondent’s self-reported height and weight. BMI an imperfect proxy for unhealthy eating; BMI is known to be determined by more than simply caloric intake, including exercise patterns and genetic vulnerability ( Hetherington and Cecil 2010 ). However, empirical studies have documented a robust correlation between unhealthy eating and BMI (e.g., ( Haimoto, Iwata et al. 2008 ; Kent and Worsley 2009 )). Three categories were created: BMI<25 (N=10,252), BMI greater than or equal to 25 but less than 35 (N=12,615), and BMI≥35 (N=2,414). While conventional cut-points define overweight as BMI between 25 and <30 and obese as ≥30 ( Centers for Disease Control and Prevention 2010 ), we chose more conservative cut points due to known error in the measurement BMI ( Rothman 2008 ), often overestimating an individual’s true body size.
• UHB count . The three measures described above were combined to create an overall measure of UHBs, comparable to that in Jackson et al. (2009) . Respondents were given a score of 0 for the least severe level of each behavior (i.e., no alcohol consumption, no nicotine consumption, or BMI<25), one point for the moderate level, and two points for the most severe level (i.e., DSM-IV alcohol abuse/dependence or at-least weekly binge drinking, DSM-IV nicotine dependence, or BMI≥35) within each unhealthy behavior category. Based on this summary score, we created a three level variable indicating no unhealthy behaviors (count was equal to zero) (N=2,539), low levels of unhealthy behavior (count was 1, 2, or 3) (N=20,077), and high levels of unhealthy behaviors (count of 4 or more) (N=2,656).

Stressful life events in the past 12-months

Twelve stressful life events were assessed at Wave 1 using a checklist with dichotomous response options: family member or close friend had a serious illness (38.4%), family member or close friend died (32.1%), respondent changed jobs/job responsibilities/work hours (23.8%), moved or someone new came to live with respondent (15.8%), major financial crisis/unable to pay bills/bankruptcy (10.6%), trouble with a boss or co-worker (8.7%), unemployed and looking for work >1 month (7.7%), respondent or family member was the victim of a crime (6.7%), fired or laid off (5.9%), problems with neighbor/friend/relative (5.8%), separated/divorced/broke up (5.4%), and respondent or a family member had trouble with police/got arrested/sent to jail (5.1%).

Figure 1 shows the relationship between number of past year stressful life events, race, and depression. As shown, the number of stressful life events at Wave 1 was not linearly related to depression at Wave 2 among Blacks, though the difference in prevalence between Blacks and Whites was not statistically significantly different at any level of stressful life events save for among those with one stressful life event (p=0.04). Also shown in Figure 1 , the confidence intervals for the proportions substantially overlap, indicative of the small sample sizes among those with high levels of stress. Therefore, we created a categorical measure of the number of stressful life events reported by the respondent. We extensively evaluated the appropriate threshold for ‘high stress’, and found that the direction and magnitude of the results were not dependent on the upper cutpoint used. We also evaluated whether the data would fit a quadratic term for past year stressful life events; the results did not change when a quadratic term was used. Therefore, to maximize statistical power and to provide the best fit to these data, we used the following cut points: no stressful life events in the past-year (N=7,274), one or two stressful life events (N=11,832), and three or more (N=6,175). Finer categorizations could not be utilized due to the minimum cell sizes required to conduct large-sample statistics.

Prevalence of depression at Wave 2 by number of past year stressor among non-Hispanic U.S.-born Whites (N=19,216) and non-Hispanic U.S.-born Blacks (N=6,065) in the general population

Perceived discrimination

Respondents self-reporting Black race were asked at the Wave 2 interview, “How often have you experienced discrimination, been prevented from doing something, or been hassled or made to feel inferior in any of the following situations because of your race?” The frequencies of seven discrimination experiences in the past 12 months were assessed (e.g., obtaining health care or health insurance coverage, obtaining a job or while on the job, or being called a racist name) ( Krieger, Smith et al. 2005 ). The scale showed good internal consistency reliability (α=0.76) ( Ruan, Goldstein et al. 2008 ). Responses were summed and a three-level variable was created indicating: no discriminatory experiences reported (N=3,708), a low level of discriminatory experiences (more than zero but less than the 75 th percentile on the scale, N=1,753), and a high level of discriminatory experiences (75 th percentile or greater, N=604).

Major Depressive Episode (MDE)

The good reliability and validity of DSM-IV major depression diagnosis in the AUDADIS-IV have been well-documented ( Hasin, Goodwin et al. 2005 ). At Wave 1, major depression in the past 12-months or prior to the past 12-months was assessed; we combined these timeframes to create a W1 lifetime depression diagnosis, and used this variable as a control in all analyses predicting major depression at Wave 2. At Wave 2, major depression was assessed in the past 12-months, and since the last interview but prior to the past 12-months. We combined these times frames to create a W2 depression diagnosis.

Physical illness

We examined Black/White differences in fourteen physical illnesses (e.g., arteriosclerosis, hypertension, diabetes, heart attack, high cholesterol, ulcer) assessed at Wave 2. Physical illness status was based on respondent self-report of a physician diagnosis.

Control variables

In all analyses we also controlled for age, sex, past-year personal income, education, and region of residence as assessed at Wave 1. We also controlled for major depression at prior to the past-year or the past-year Wave 1; Blacks had a lower prevalence of past year (OR=0.80, 95% C.I. 0.66-0.96) and lifetime depression (OR=0.56, 95% C.I. 0.49-0.64) at Wave 1.

Statistical analysis

Prevalence estimates by race, stressful life events, and UHBs were generated using cross-tabulations. Odds ratios and 95% confidence intervals were generated using logistic regression. All interaction tests are on the multiplicative scale. All analyses were conducted using SUDAAN software to adjust standard errors for the non-random probability of selection into the sample. All prevalence estimates and odds ratios are sample weighted to be representative of the U.S. population based on the year 2000 census.

Overall Black/White differences in the NESARC data

Consistent with prior literature, Blacks were less likely to have Wave 2 major depression (OR=0.80, 95% C.I. 0.70-0.91) and more likely to have a Wave 2 physical illness (OR=1.20, 95% C.I. 1.08-1.35) compared with Whites (data not shown).

Results of the Jackson et al. (2009) replication attempt

Our findings did not replicate those of Jackson et al. (2009) . Figures 2a and 2b show the predicted probability of depression based on the results of a logistic regression model categorizing UHB consumption (any lifetime smoking, any lifetime drinking, and/or current obesity) and past-year stressful life events, and controlling for age, sex, past-year personal income, education, region of residence, and major depression at Wave 1. Among Whites, the figures indicate a higher predicted probability of depression with each increasing level of UHB consumption and each increasing level of stressful life events. Among Blacks, the pattern is less consistent, but no evidence emerges suggesting that those who engage in more UHB consumption have less depression. There were no significant interactions between stressful life events and UHBs predicting depression among Blacks (F=1.20, df=6, p=0.32) or Whites (F=0.43, df=6, p=0.86), and no significant three-way interaction between stressful life events, UHBs, and race (F=1.05, df=17, p=0.42).

Predicted probability of depression at Wave 2 based on unhealthy behaviors as defined by Jackson et al. (2009) * and past-year stressful life events at Wave 1, by race, among non-Hispanic U.S.-born Whites (Figure 2a, N=19,216) and non-Hispanic U.S.-born Blacks Figure 2b, N=6,065) in the general population

* UHBs defined to be consistent with Jackson et al. (2009) : any consumption of at least one alcoholic beverage in lifetime, any consumption of 100+ cigarettes in lifetime, and/or current BMI≥30.

As part of our replication attempt, we also conducted an analysis with a mean centered, continuous stress variable in order to more closely approximate Jackson et al. (2009) and Mezuk et al. (2010) , despite the evident violation of the linearity assumption among Blacks (shown in Figure 1 ). Among Blacks at high levels of mean-centered stress, those with 0 UHBs have a higher predicted probability of depression compared to those with 1 UHB, and those with 1 UHB have a higher predicted probability of depression compared to those with 2 or 3 UHBs (consistent with Jackson et al. (2009) and Mezuk et al. (2010) ). The same pattern is not evident among Whites (results not shown). However, this result arises entirely from the misspecification of the regression model by entering stress as a continuous variable among Blacks. Further, none of the interactions were significant when using the mean centered, continuous stress variable (interaction of stress and UHBs among Blacks: F=0.89, df=3, p=0.45; interaction of stress and UHBs among Whites: F=1.46, df=3, p=0.23; three way interaction of stress, UHBs, and race: F=1.37, df=7, p=0.23).

Results of the extended test of the Jackson et al hypothesis

Are uhbs protective against depression and is stress associated with more depression.

We found that Wave 1 UHBs, at any level, are not protective against Wave 2 depression. Stress, however, is prospectively predictive of Wave 2 depression. Table 1 shows the odds of Wave 2 depression given Wave 1 UHBs among the whole sample, and for Blacks and Whites separately. Among Whites, greater Wave 1 alcohol, nicotine, BMI severity, and overall UHB score predicted higher odds of depression at Wave 2. Among Blacks, no significant odds ratios were observed for the relation between Wave 1 UHBs and Wave 2 depression. However, all four odds ratios for the highest UHB category were in the direction consistent with high levels of UHB predicting greater odds of depression. Among both Whites and Blacks, more stressful life events at Wave 1 predicted greater odds of depression at Wave 2 (see Table 1 ).

Alcohol consumption, nicotine consumption, BMI, and stressful life events prospectively predicting major depression three years later among non-Hispanic U.S.-Born Whites (N=19,216) and non-Hispanic U.S-born Blacks (N=6,065)

Bold text indicates statistical significance at p<0.05

AOR = odds ratio adjusted for age, sex, past-year personal income, education, region of residence, and major depression at Wave 1

Do Blacks report higher levels of UHBs?

Blacks had lower odds of Wave 1 alcohol consumption, nicotine consumption, and any UHBs compared with Whites, but a higher proportion of Blacks were in high Wave 1 BMI categories compared with Whites. This finding held in every level of Wave 1 stressful life events (see Table 2 ) save the lowest level. Among those with no stressful life events, there was no significant relationship between UHBs and race. The magnitude and strength of the relationship between UHB and race increased with each level of stressful life event category.

Odds of alcohol consumption, nicotine consumption, high BMI, and ‘unhealthy behaviors’ in non-Hispanic U.S.-born Blacks (N=6, 065) compared to non-Hispanic U.S.-born Whites (N=19,216) at low, moderate, and high levels of stress

AOR = odds ratio adjusted for age, sex, past-year personal income, education, and region of residence

Do UHBs have a differential effect on depression among Blacks and Whites at certain stress levels?

Little support was found for the hypothesis that UHBs have a differential effect on Blacks and Whites at high levels of stress. We examined whether the effect of Wave 1 UHBs on Wave 2 depression differed by race and Wave 1 stressful life event status ( Table 3 ). Results indicated that a low level of unhealthy behaviors is protective against depression in Blacks (OR=0.06, 95% C.I. 0.01-0.24) but not Whites (OR=2.14, 95% C.I. 0.71-6.48) among those at low levels of stress. However, the three-way interaction test was not significant, limiting the conclusions that can be drawn from this association. We did find a significant three-way interaction between race, Wave 1 stress, and Wave 1 BMI (F=2.11, df=12, p=0.03). Based on the patterns of odds ratios shown in Table 3 , we conclude that there is evidence to suggest a protective effect of Wave 1 BMI 25-34 on Wave 2 depression in Blacks but not Whites, but only at very low levels of stress.

Odds of depression at Wave 2 based on unhealthy behaviors and past-year stressful life events at Wave 1, by race and sex, among non-Hispanic U.S.-born Blacks (N=6,065) and non-Hispanic U.S.-born Whites (N=19,216) in the general population

We also examined these patterns by sex (results not shown). UHBs significantly interacted with race among men only (F=6.07, df=2, p=0.004), whereby Black men reporting a low level of unhealthy behaviors had significantly lower odds of depression compared to White men (OR=0.06, 95% C.I. 0.01-0.24). Similar to the aggregated analysis, a three way interaction between Wave 1 BMI, race, and Wave 1 stress was statistically significant in men (F=2.28, df=12, p=0.02). This interaction was significant at the trend level among women (F=1.7, df=12, p=0.09).

Are UHBs protective against depression among Blacks reporting more race-specific stress?

Wave 1 UHBs did not moderate the effect of perceived discrimination reported at Wave 2 among Blacks. The observed prevalence of Wave 2 depression by UHB consumption and discrimination experiences are shown in Figure 3 . In unadjusted analyses, Wave 1 non-pathological nicotine use was associated with a lower odds of depression at Wave 2 compared to no nicotine use (OR=0.48, 95% C.I. 0.24-0.96) (data not shown). However, the effect was no longer significant when lifetime depression at Wave 1 was controlled (OR=0.52, 95% C.I. 0.26, 1.05) (data not shown). No other odds ratios were significant in unadjusted or adjusted analyses. We also replicated these analyses using UHBs defined at Wave 2 (concurrent to measurement of discrimination): results were unchanged.

Prevalence of depression at Wave 2 based on unhealthy behaviors and lifetime perceived discrimination exposure among non-Hispanic U.S.-born Blacks (N=6,065) in the general population

The present study did not find support for the hypothesis that engaging in unhealthy behaviors ameliorates major depression among Blacks in the U.S. exposed to high levels of stress, or that a differential effect of UHBs on depression among Blacks compared with Whites accounts for the mental/physical health paradox. First, we showed that the results presented in Jackson et al. (2009) and Mezuk et al (2010) do not replicate in a nationally-representative sample using model specification to account for the non-linear association between stress and depression among Blacks that we observed in these data. Next, as part of a more in-depth investigation of the hypothesis, we demonstrated that the relationship between depression and alcohol consumption, nicotine consumption, and BMI among Blacks is not statistically significant and, in fact, the direction of association between UHBs and depression is positive, not negative. Third, we documented that Blacks are less likely to engage in alcohol and nicotine consumption but have higher BMI than Whites at all levels of stress. We note, however, that an overall count of UHBs was not associated with race among those with no stressful life events. This suggests a complex patterning of unhealthy behaviors and race across stress levels that should be more comprehensively examined in these and other data in future analyses.

Finally, we showed that while race, stress, and BMI did interact significantly to predict depression in this sample, being overweight was protective against depression among Blacks only at very low levels of stress . Similarly, among those with no stressful life events, we found that low levels of UHBs were associated with less depression in Blacks but not Whites, though this result was significant among men only and a three-way interaction test was not significant. Furthermore, examination of perceived discrimination as a measure of stress in Blacks revealed no significant effects of unhealthy behaviors on depression at any exposure level. Taken together, these results indicate that engagement in unhealthy behaviors, especially at pathological levels, does not protect against depression, and that stress pathways do not operate differently in Blacks compared with Whites in the U.S. Thus, our confidence in the group-specific stress and coping hypothesis proposed by Jackson and colleagues ( Jackson and Knight 2006 ; Jackson, Knight et al. 2009 ; Mezuk et al. 2010 ) is diminished. Although UHBs may have immediate positive psychological effects via the HPA axis, the evidence presented here suggests these effects are not robust enough to prevent the clinical manifestation of major depression.

We did find evidence that some measures of unhealthy behaviors were significant predictors of depression in Whites but not Blacks. For example, at high levels of stress, Whites with high BMI, nicotine dependence, and a high unhealthy behavior count were more likely to evidence depression compared with Whites without these unhealthy behaviors, but the same predictors were not significant among Blacks. However, we caution against over-interpretation of these findings; as noted by Gelman and Stern: “The Difference Between ‘Significant’ and ‘Not Significant’ is not Itself Statistically Significant” ( Gelman and Stern 2006 ). There were no significant interactions between race and unhealthy behaviors at high levels of stress, indicating that the odds ratios across race categories were not statistically distinguishable. Further, ignoring significance levels, thirty-two of forty-eight odds ratios calculated (67%) in the total sample were in the same direction for Whites and Blacks. Thus, the most appropriate conclusion from these data is the pathway through which unhealthy behaviors and stress impact depression does not differ in Blacks compared with Whites in the U.S., and that in general, UHBs increase the risk for depression at all levels of stress.

In the present analysis we predicted major depression during a three-year follow-up based on stressful events and UHBs assessed at baseline. While this strategy is most appropriate to establish temporality, it may overlook a key component of the hypothesis, namely, that UHBs in response to stress are active coping strategies for the suppression of immediate depressive symptoms ( Benowitz 1988 ; Koob, Roberts et al. 1998 ; Dallman, Pecoraro et al. 2003 ; Jackson and Knight 2006 ; Jackson, Knight et al. 2009 ). Thus, we may have failed to capture protective effects because we did not examine major depressive episodes concurrent with stressors and unhealthy behaviors. To explore this possibility, we re-analyzed our data using stress, UHBs and depression diagnoses all measured concurrently, at both baseline and follow-up. Neither analysis suggested different conclusions; results were generally consistent with those presented in our main analyses. Thus, we conclude that these data, analyzed multiple ways at multiple time points, do not provide sufficient evidence for either a protective effect of UHBs on depression, or a differential pathway through which unhealthy behaviors affect depression in Blacks compared with Whites, regardless of the exposure to stress.

These results decrease confidence in the validity of the hypothesis that group-specific stress processes explain the depression difference in Blacks and Whites, leaving open other theories to be tested. Measurement and selection bias hypotheses are unlikely to fully explain the “paradox” ( Breslau, Javaras et al. 2008 ), suggesting the need for both new theories and more direct tests of existing theories based on the premise that the lower prevalence of depression in Blacks is not artefactual. Studies suggest that Blacks develop different coping strategies when faced with life stress compared with Whites ( Smith 1985 ; Wilson 1989 ; Maton, Teti et al. 1996 ), which, given the extraordinary nature and degree of stress to which Blacks are exposed starting at a young age, are hypothesized to develop over the life course. Compared with Whites, Blacks are more likely to find emotional strength and support in religious communities ( Taylor, Chatters et al. 1996 ; Gibson and Hendricks 2006 ; Giger, Appel et al. 2008 ), and develop racial self-esteem and strong ethnic identity ( Nagel 1994 ). Further, extensive research has documented the ‘John Henryism’ effect among Blacks in the U.S., the personality trait characterized by active coping with stressful and negative experiences and associated with worse health outcomes for Blacks at high levels of socio-economic position ( James, Strogatz et al. 1987 ; James 1994 ). Alternatively, the present DSM nosology may not accurately tap Black psychological responses to their unique stress exposures, and therefore DSM-IV depression as currently defined may not be the appropriate outcome to fully understand racial differences in depressive mood states ( Brown 2003 ; Kendrick, Anderson et al. 2007 ). Support for this theory can be drawn from the multiple studies showing that Blacks report lower levels of well-being, higher levels of distress, and higher depressive scores when measured on non-DSM instruments ( Brown 2003 ; Mabry and Kiecolt 2005 ). Taken together, the results from the present study should serve as a catalyst to promote the advancement of innovative and alternative theories to explain the Black/White paradox in mental and physical health. Few studies are conducted with the primary aim of untangling this paradox, a situation that should be redressed. Such research should include rich measurement of the social and political context, and conduct in-depth examination of the role of ethnic identity, religion, and responses to group-specific stressor, such as racial discrimination.

Several limitations should be noted. First, our measure of stressful life events is a checklist of experiences susceptible to respondent subjectivity and appraisal processes, and without regard to salience, severity, or context of experience. Substantial evidence indicates that objective measures of stressful experiences as well as information on the context of the experience is necessary to fully analyze and interpret stress in mental health research ( Dohrenwend 1998 ; Dohrenwend 2006 ). Additionally, the stressful events experienced by Blacks in the U.S. may be more chronic and race-specific than what is captured in the scale of past-year stressors ( Jones 2000 ; Kreiger 2000 ). We attempted to mitigate this limitation by also using a measure of perceived racial/ethnic discrimination. Further, we evaluated whether results changed if higher cut-offs of past-year stressful experiences were used to define the ‘high stress’ exposure group; higher cut-offs did not change the results. Thus, the conclusions from these data are limited by the available stress measure.

In conclusion, the persistent differences in health outcomes between White and Black adults remain one of the most challenging public health issues in the U.S. As theories regarding the etiology of these differences continue to develop, the mental health ‘paradox’ will be increasingly important to explain as part of a robust etiologic pathway. Substantive etiologic hypotheses that simultaneously explain why Blacks in the U.S. have higher rates of physical illness and lower rates of mood disorders need to be tested directly in order to resolve the ‘paradox’ and progress toward intervention and prevention efforts.

Hypothesis that Black-White depression paradox is due to protective effects of unhealthy behaviors at high stress unsupported.

Blacks less likely to engage in alcohol consumption or cigarette smoking compared with Whites, but have higher average BMI.

Engaging in unhealthy behaviors is not protective against depression at any stress level in either Blacks or Whites.

Acknowledgments

This research was supported in part by a fellowship from the National Institute of Mental Health (T32MH013043-36, Barnes) and a fellowship from the National Institute of Drug Abuse (F31-DA026689, K. Keyes).

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Stress sensitivity analysis of vuggy porous media based on two-scale fractal theory

Affiliations.

• 1 State Key Laboratory of Deep Oil and Gas, China University of Petroleum (East China), Qingdao, 266580, China. [email protected].
• 2 School of Petroleum Engineering, China University of Petroleum (East China), Qingdao, 266580, China. [email protected].
• 3 State Key Laboratory of Deep Oil and Gas, China University of Petroleum (East China), Qingdao, 266580, China.
• 4 School of Petroleum Engineering, China University of Petroleum (East China), Qingdao, 266580, China.
• 5 Research Institute of Petroleum Exploration and Development, CNPC, Beijing, 100007, China.
• 6 Department of Petroleum Engineering, Colorado School of Mines, Golden, CO, 80401, USA.
• PMID: 39237641
• DOI: 10.1038/s41598-024-71171-2

Interparticle pore space and vugs are two different scales of pore space in vuggy porous media. Vuggy porous media widely exists in carbonate reservoirs, and the permeability of this porous media plays an important role in many engineering fields. It has been shown that the change of effective stress has important effects on the permeability of vuggy porous media. In this work, a fractal permeability model for vuggy porous media is developed based on the fractal theory and elastic mechanics. Besides, a Monte Carlo simulation is also implemented to obtain feasible values of permeability. The proposed model can predict the elastic deformation of the fractal vuggy porous media under loading stress, which plays a crucial role in the variations of permeability. The predicted permeability data based on the present fractal model are compared with experimental data, which verifies the validity of the present fractal permeability model for vuggy porous media. The parameter sensitivity analysis indicates that the permeability of stress-sensitivity vuggy porous media is related to the capillary fractal dimension, capillary fractal tortuosity dimension, Young's modulus, and Poisson's ratio.

Keywords: Fractal; Monte Carlo simulation; Permeability; Stress sensitivity analysis; Vuggy porous media.

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