University of Groningen A Dynamical Approach to Psychological Resilience Hill, Yannick

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A Dynamical Approach to Psychological Resilience

Hill, Yannick

DOI:

10.33612/diss.144252644

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Publication date: 2020

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Hill, Y. (2020). A Dynamical Approach to Psychological Resilience. University of Groningen. https://doi.org/10.33612/diss.144252644

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548915-L-bw-Hill 548915-L-bw-Hill 548915-L-bw-Hill 548915-L-bw-Hill Processed on: 30-9-2020 Processed on: 30-9-2020 Processed on: 30-9-2020

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Resilience in Sports from

a Dynamical Perspective

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This chapter consists of three parts that form a discussion.

First, our target article:

Hill, Y., Den Hartigh, R. J. R., Meijer, R. R., De Jonge, P., & Van Yperen, N. W. (2018a). Resilience in sports from a dynamical perspective. Sport, Exercise, and Performance

Psychology, 7, 333-341. doi: 10.1037/spy0000118

Second, the abstracts of three commentaries:

Bryan, C., O’Shea, D., & MacIntyre, T. (2018). The What, How, Where, and When of Resilience as a dynamic, episodic, self-regulating system: A response to Hill et al. (2018).

Sport, Exercise, and Performance Psychology 7, 355-362. doi: 10.1037/spy0000133.

Galli, N. & Pagano, K. (2018). Comment on “Resilience in sports from a Dynamical Perspective” by Hill, den Hartigh, Meijer, de Jonge, and Van Yperen (2018). Sport,

Exercise, and Performance Psychology 7, 351-354. doi: 10.1037/spy0000128.

Kiefer, A. W., Silva, P. L., Harrison, H. S., & Araújo, D. (2018). Antifragility in sport: Leveraging adversity to enhance performance. Sport, Exercise, and Performance

Psychology, 7, 342-350. doi: 10.1037/spy0000130

Third, our response:

Hill, Y., Den Hartigh, R. J. R., Meijer, R. R., De Jonge, P., & Van Yperen, N. W. (2018b). The temporal process of resilience. Sport, Exercise, and Performance Psychology, 7, 363-370. doi: 10.1037/spy0000143

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PART I Abstract

On the road to excellence, it is essential to develop resilience, that is, to be able to positi-vely adapt within the context of significant adversity. Researchers tend to agree that resilience is a complex process with a multitude of underlying variables. To stimulate research on the process of resilience, we propose the dynamical system approach that provides a theoretical perspective on mapping out and understanding how resilience unfolds over time. Furthermore, we will demonstrate how the findings of previous research on resilience in sports fit with several dynamical properties, including com-plexity, iterativity, and the formation of attractor states. New findings on the dynamic properties of resilience will result in in-depth knowledge about, and understanding of, the process of how individuals adapt to adverse events. Practitioners might benefit from this approach by being able to detect early warning signals of critical transitions (e.g., critical slowing down) and take preventive actions before breakdowns in performance occur.

Keywords: Adversity, Complexity, Critical Slowing Down, Dynamical Systems,

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1 | Introduction

On the road to excellent performance, athletes unavoidably encounter stressful events, which they have to overcome to become successful. These events can be either sports-related or non-sports-sports-related and range from short time scales (e.g., losing a point in a match) to long time scales (e.g., a serious injury or parental divorce, Fletcher & Hanton, 2003; Gould et al., 1993; Rees et al., 2016; Sarkar & Fletcher, 2014). In the sports literature, the process of positive adaptation within the context of significant adversity is defined as resilience (see Fletcher & Sarkar, 2012, 2013; Galli & Gonzalez, 2015). A definition of resilience that is commonly used in sports emphasizes “the role of mental processes and behavior in promoting personal assets and protecting an individual from the potential effect of negative stressors” (Fletcher & Sarkar, 2012, p. 675, 2013, p. 16). This definition acknowledges both the underlying trait-like protective factors and (mental) processes, which define how one adapts to adversity (Fletcher & Sarkar, 2012, 2013). In addition, the speed of the resilience process can vary across different setbacks and people over time (Carver, 1998; see also Egeland et al., 1993; Fletcher & Sarkar, 2012). Although resilience in sports and in other contexts, such as the organizational and personal domain, is generally considered as a process (Fletcher & Sarkar, 2012), there are few studies in sports on the characteristics of the resilience process. Sports researchers have primarily focused on identifying protective factors, such as personality traits and psychosocial variables, in order to explain individual differences in resilience (see Sarkar & Fletcher, 2014).

In line with the view that resilience is a complex process (Fletcher & Sarkar, 2012; Galli & Vealey, 2008), we draw upon the dynamical systems approach (e.g., Kelso, 1995; Nowak & Vallacher, 1998; Van Geert, 2009), which provides tools that allow researchers to capture the properties of the resilience process. A dynamical system can be defined as a set of elements, which are in constant dynamic interactions and undergo change over time (e.g., Kelso, 1995; Nowak & Vallacher, 1998; Vallacher & Nowak, 1997; Van Geert, 1994). In the next section, we will demonstrate how the findings of previous research on resilience in sports provide a logical fit with several dynamical properties, including complexity, iterativity, and the formation of attractor states.

2 | The Complexity of Resilience

The property of complexity entails that the explanation of a system state cannot be reduced to its constituent elements. In other words, the system is interaction dominant, meaning that the state of the system emerges through dynamic interactions between multiple components (e.g., Van Orden et al., 2003; Den Hartigh et al., 2017). In terms of resilience, this would entail that a state of resilience develops through an interaction

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between various factors (cf. Fletcher & Sarkar, 2012; Galli & Vealey, 2008), and cannot be reduced to specific contributions of isolated explanatory components. Indications for the complexity of resilience can be derived from studies focusing on protective factors, that is, the resources protecting an individual from setbacks or helping in responding positively to adverse events. In these studies, a large number of variables have been identified that protect athletes or help them to be resilient, such as perceived social support, positive personality, motivation, confidence, and focus (see Fletcher & Sarkar, 2012; Sarkar & Fletcher, 2014). For example, a sport-specific study of psychosocial determinants found that swimmers who recovered from a negative performance differed from swimmers who failed to recover from a setback in perceived level of endurance, coping styles, self-concept, and social support (Mummery et al., 2004).

However, so far, no single factor or set of factors has been identified to give rise to resilience across contexts, settings, or individuals (Galli & Gonzalez, 2015; Rutter, 1981). For some variables even opposite effects have been found. For example, whereas Fletcher and Sarkar (2012) found that high levels of perceived social support were positively related to resilience, Mummery and colleagues (2004) observed that resilient athletes demonstrated lower levels of perceived social support than their non-resilient counterparts.

Another indication for the complexity of the resilience process comes from the pre-sumption that resilience is determined by the person-environment interaction (Egeland et al., 1993). Different situational demands may require different processes and facilitative responses from athletes in order to adapt well to a given situation (Fletcher & Sarkar, 2012). For example, responses that promote positive adaptation to personal stressor (i.e., stressors related to the non-sporting, personal life domain) might not be applicable to competitive stressors (i.e., stressors directly related to the competitive performance context), and vice versa (Sarkar & Fletcher, 2014). Therefore, scholars concluded that resilience is strongly coupled to the situational demands of the adverse event (Fletcher & Sarkar, 2013; Rutter, 1981). In other words, resilience is a function of person- and environment-related explanatory variables, among which complex interactions likely exist (Egeland et al., 1993; Fletcher & Sarkar, 2012, 2013, 2016; Galli & Vealey, 2008; Luthar et al., 2000). Indeed, sports researchers tend to agree that resilience is a complex process with a multitude of underlying variables rather than a component-driven ability. It seems to be a process that emerges from the constant interactions of the various components within the person and the environment over time (cf. Fletcher & Sarkar, 2013; Sarkar et al., 2015).

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3 | The Iterativity of Resilience

The property of iterativity implies that a given state of the system develops out of the system’s previous state, and hence that any future state depends on the system’s history of preceding states (e.g., Den Hartigh, Van Dijk et al., 2016; Gernigon et al., 2015; Nowak & Vallacher, 1998; Vallacher et al., 2015; Van Geert, 1991). Therefore, a given variable can act as an effect in the one moment and as a cause in the next (Vallacher & Nowak, 1997). Translated to resilience, the complex interactions among the protective factors and the environmental demands over time form an ongoing process, which determines an athlete’s state of resilience through iterative steps (cf. Egeland et al., 1993; Fletcher & Sarkar, 2012, 2013, 2016; Fletcher & Scott, 2010; Seery, 2011; Seery et al., 2010). To the best of our knowledge, there are currently two sport-specific studies providing clues for such an iterative process, which are based on interviews with athletes who successfully overcame adversity during their careers (Fletcher & Sarkar, 2012; Galli & Vealey, 2008). For example, the findings of Fletcher and Sarkar (2012) indicate that the protective factors influence challenge appraisals and meta-cognitions, which in turn yield facilitative responses. More specifically, all protective factors aid the facilitative interpretation of emotions, effective decision-making, reflecting, and task engagement. This, in turn, leads to increases in effort and commitment (Fletcher & Sarkar, 2012). Therefore, no factor can be singled out as the main determinant for the process of adapting well to adversity and no protective factor can be neglected. Rather, the complex interactions among all elements form the process, from which successively resilience emerges (Fletcher & Sarkar, 2012, 2013; Galli & Vealey, 2008).

The complex, iterative process of resilience is also likely to occur on the time scale of single matches. For example, in a tennis match, the person (the player), the environment (the opponent), and the task (i.e., playing/scoring points, the situational demands) are in constant interaction. The behaviors of players and their opponents constantly influence each other as they adapt to the changing circumstances. This means that the player and the opponent build a match history together that includes (among many other things) successes and setbacks (i.e., adverse events in the performance context). Thereby the situational demands and the protective factors constantly alter each other and adapt to the changing circumstances. Therefore, the displayable level of resilience changes in accordance with the history of these setbacks and successes. For instance, it might be easier for an athlete to demonstrate resilience when a first adverse event is encountered than if several adverse events have preceded this particular event. In accordance with this idea, the role of the history of performance patterns has been demonstrated repeatedly in studies on psychological momentum (PM, see also the next sub-section). Positive PM describes an individual’s perception of moving towards a desired goal, whereas negative PM describes an individual’s perception of moving away from a desired goal (Adler, 1981,

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Briki et al., 2013, Den Hartigh et al., 2014; Den Hartigh, Van Geert, et al., 2016; Vallerand et al., 1988). These studies showed that the impact of an adverse event, such as losing points or seconds on the opponent, is embedded in the process, that is, the athlete’s performance history (Briki et al., 2013; Den Hartigh et al., 2014; Den Hartigh, Van Geert et al., 2016; Gernigon et al., 2010).

4 | Resilience as Defining Attractor States

Attractors emerge from the iterative process of the system’s underlying components, as the components adjust to each other in a self-organizing process (Nowak & Vallacher, 1998; Vallacher & Nowak, 1997; Vallacher et al., 2015). A fixed-point attractor is a relatively stable state of the system, towards which it develops over time and returns to after being perturbed (Gernigon et al., 2015; Vallacher et al., 2015). This state is characterized by a recurring pattern of affect, behavior, and cognition. A metaphoric conceptualization of

Figure 3 | Hypothetical time-series of an athlete’s performance trajectory. The dotted circles mark the occurrence of an adverse event. Critical slowing down occurs as the athlete requires increasingly more time to recover from an adverse event, which signals a change in the attractor landscape (1, 2, and 3). The current state is represented by the ball rolling over the landscape and the arrows indicate the direction of the perturbation. With repeated adverse events the attractor for the high performance level becomes weaker while the attractor for the low performance level becomes stronger (2), ultimately leading to a qualitative shift in performance (3).

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different attractor states usually depicts a hilly landscape over which a ball is rolling (see

Figure 3). Under the forces of gravity, the ball will roll into a valley (i.e., attractor state) and remains there, unless an external force sets the ball into motion (i.e., a perturbation). The depth of the valley indicates the strength of the attractor. The deeper the valley, the stronger the perturbation (i.e., incidents that shake the stability of a system) needs to be in order to push the ball out of the valley. However, the attractor landscape may not remain stable over time (see Figure 3). Repeated perturbations may cause the strength of an attractor state to decrease while simultaneously increasing the strength of another attractor state, thereby changing the landscape of the attractor states (for an example in sport psychology, see Den Hartigh, Van Geert et al., 2016).

Although never explicitly studied, indications for the existence of attractor states in resilience research comes from studies that have operationalized resilience as adapting well after experience a worse-than-expected performance (for examples, see Mummery et al, 2004; Seligman et al., 1990). Resilient individuals were able to return to their previous level of performance after encountering the perturbation, whereas non-resilient athletes’ negative performance was followed by another negative performance. In terms of attractor states, some individuals were able to return to their (prior) attractor state, whereas for others a critical transition occurred to a lower performance level (cf. Dai et al., 2012; Kelso, 1995; Scheffer et al., 2012; Schöner & Kelso, 1988; Van de Leemput et al., 2014). Following such a transition, it is typically difficult for the athlete to recover his or her previous performance level (Bonanno, 2004; Den Hartigh, Van Geert et al., 2016; Gernigon et al., 2010; Gernigon et al., 2015). Furthermore, the commonly applied definition of resilience in sports also points to the protection of potential negative consequences of stressors (Fletcher & Sarkar, 2012, 2013). According to Sarkar and Fletcher (2014), this definition implies that resilience is defined by an equilibrium in the level of functioning when facing an adversity (cf. Bonanno, 2004; Mancini & Bonanno, 2009; Holling 1973).

Research on PM in sports provides additional support for the link between resilience and attractor formation (e.g., Briki et al., 2013; Den Hartigh et al., 2014; Den Hartigh, Van Geert et al., 2016; Gernigon et al., 2010). For example, Briki et al. (2013), Den Hartigh et al. (2014), and Gernigon, Briki, and Eykens (2010) found that negative PM is a relatively strong attractor state, meaning that it is relatively easily entered and difficult to escape from. Den Hartigh, Van Geert, et al. (2016) recently provided deeper insights into PM attractor dynamics. In a study in which participants took part in an ergometer rowing tournament spanning four weeks, the athletes who had lost the first three races (i.e., successive adverse events) entered negative PM more rapidly in the fourth race (i.e., decline in effort and self-efficacy), when they started losing seconds to their opponent, than the athletes who had won the previous races (Den Hartigh, Van Geert, et al.,

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2016). This line of research suggests that (a) adapting well to adversity (i.e., resilience) is embedded in the performance history both on a short timescale (within a single performance) as well as over the course of several weeks, and (b) the attractor landscape may change.

In summary, various findings across different domains of sports research point to the dynamic properties of resilience. The dynamical systems approach seems to be an appropriate framework for understanding resilience. However, this approach is not limited to descriptive support; it also yields practical implications for future research, which will be discussed later.

5 | Measuring Resilience in the Context

of Athletic Performance

A key question with regard to measuring the process of resilience in sports is: What should we measure (Sarkar & Fletcher, 2013)? Concrete recommendations in this regard can be derived from research on resilience outside the field of sport psychology. A recent article on resilience on the domain of clinical psychology has described the history-dependence and the change in the attractor landscape that arises from an iterative process, based on time-serial data (Van De Leemput et al., 2014). These authors demonstrated the effect of encountering several subsequent stressors on the development of a depressive episode. More specifically, the exposure to several adverse events after another can lead to a period in which a system takes increasingly more time to demonstrate resilience, called “critical slowing down” (see also Dai et al., 2012; Scheffer et al., 2012). This means that the system requires increasing amounts of time to positively adapt to perturbations. A series of setbacks within a short time can reduce the displayable level of resilience so much that a single stressor (even if it has a low magnitude) can cause a person to develop a depressive episode (Van de Leemput et al., 2014). Therefore, a critical transition of the stability of a system is anteceded by a period of reduced resilience (i.e., critical slowing down, Dai et al., 2012; Kelso, 1995; Scheffer et al., 2012; Schöner & Kelso, 1988; Van de Leemput et al., 2014). As this line of research provides insight into the dynamic properties of resilience, we suggest transferring it to the domain of sports.

Since the proposed complex interplay of underlying components (i.e., protective factors and environmental demands) manifests itself in the actual behavior that an athlete displays in a performance context (cf. Luthar & Cicchetti, 2000), the state of the system can be defined as the athlete’s current performance level. Whereas adjustment to parental divorce may take several months or years and is meaningful in the time scale

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of an athlete’s career, adapting well to a lost point in a tennis match occupies merely a

few seconds and is meaningful in the time scale of a single match. Therefore, the type of adversity and the positive must occur in a meaningful timeframe (Den Hartigh, Van Geert et al., 2016).

Following the dynamical systems approach, to map out how the resilience process unfolds, individual time-series (dense repeated measurements) need to be established (e.g., Araujo et al., 2015; Den Hartigh et al., 2017). Assessing multiple measurement points allows insight to be gained into how the trajectory of resilience is formed for any given adverse event or series of adverse events (cf. Fletcher & Sarkar, 2013; Sarkar & Fletcher, 2013). When the aim is to investigate the resilience process on a short time scale, during actual performance, a future research agenda should address the following issues and considerations. First, relevant measures of athletic performance should be defined, which can be measured repeatedly (preferably as continuously as possible) in order to compile a time-series (Araujo et al., 2015). For example, for cyclists, their pace can be continuously tracked and measured. Second, the behavior of participants should stay close to their behavior in the usual sports setting, thereby optimally capturing the dynamics underlying athletic performance (see Araujo et al., 2015; Davids & Araujo, 2010; Davids et al., 2003, 2013; Pinder et al., 2011).

When conducting experimental studies on resilience, researchers could use, for instance, stationary bikes or rowing ergometers which can continuously collect measures of power output and allow for controlled manipulations of adverse events (e.g., Den Hartigh et al., 2014; Den Hartigh, Van Geert et al., 2016). This could be accomplished by using software in which adverse events during performance can be manipulated. As an illustration, in studies on cycling (Briki et al., 2013) and rowing (Den Hartigh et al., 2014; Den Hartigh, Van Geert et al., 2016), athletes were performing on ergometers. In one of the conditions they took a comfortable lead, but then, at repeated intervals (e.g., 1 minute), the athletes lost their advantage. In this way, adverse events (here, losing the lead) were systematically manipulated in a controlled experimental setting. For data collection in naturalistic settings, new technological advancements, such as local position measurement systems, can be used to gather continuous performance data of naturalistic behavior (e.g., Frencken et al., 2010). Third, and most importantly, in order to measure resilience, the duration and shape of the trajectory following an adverse event with a decline in performance must be assessed (Bonanno, 2004; Carver, 1998; Van de Leemput et al., 2014). Increases in the duration of time required for the resilience process after experiencing a series of adverse events (i.e., critical slowing down) can signal a critical shift in performance toward another attractor state (see Figure 1). Such patterns can be detected in time-series data by using techniques, such as auto-correlation or running correlations (Araújo et al., 2015). Therefore, based on intra-individual

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formance processes over time following several adversities, future breakdowns in resilience can be predicted (cf. Van de Leemput et al., 2014).

To investigate resilience on a long time scale, longitudinal studies based on an integration of physical sensor data from wearables (such as a smartwatch) and self-report data may be employed. For instance, Blaauw et al. (2016) coupled self-reported mental health variables (diary data over a period of 30 days) with physical measures (such as heart rate) collected via wearable sensors in smartwatches over the same period of time. Together, the accumulated data offered insight into the intra-individual variability of the assessed variables over time, as well as the dynamic relationships between them. Translated to an example of athletic resilience, cyclists could report a certain practice route they take every day with stable environmental conditions, which refrain inferences that can influence the performance (Araujo et al., 2015). During this activity, sensors in wearables can collect and report various physical measures, positional measures, and completion times. This would yield objective measures of athletic performance over a longer period of time. In addition to the physical measures, self-report questionnaires on cognitions, behaviors, emotions, as well as the type of adversity and protective factors (Sarkar & Fletcher, 2013) over the same period of time, could be integrated in order to provide insight into the dynamical interactions of behavioral and psychological processes. Again, researchers can then specifically focus on periods of critical slowing down that may precede a breakdown in resilience (cf. Van de Leemput et al., 2014).

6 | Conclusion

Research on resilience in sports has increasingly focused on investigating the process that defines resilience (Fletcher & Sarkar, 2012, 2013; Galli & Vealey, 2008). To improve our understanding of this crucial concept for athletic performance, we call for using dynamical systems approach to understand resilience as an iterative process that is driven by ongoing interactions among a multitude of variables. New research designs should be tailored to measure adequate performance behavior and capture how the resilience process unfolds over time (Galli & Gonzalez, 2015). Specifically, researchers need to demonstrate the dynamic properties of resilience in individual time-series in realistic performance contexts and throughout athletes’ careers. We expect this research agenda to result in in-depth knowledge about, and understanding of, the process of how individuals adapt to adverse events. Furthermore, practitioners might benefit from the dynamical systems approach by being able to detect early warning signals of critical transitions (e.g., critical slowing down, Scheffer et al., 2012) and take preventive actions before breakdowns in performance occur.

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PART II

The What, How, Where and When of Resilience as a Dynamic, Episodic, Self-Regulating System: A Response to Hill et al. (2018)

Christopher Bryan, Deirdre O’Shea, and Tadhg E. MacIntyre

Resilience research is undergoing a shift away from trait approaches, acknowledging the inherent process and dynamism of stress interactions. Hill et al. (2018) suggest that to understand the iterative nature of the multifactorial resilience process, a dynamical systems approach needs to be used. We suggest that explaining resilience through Whetten’s (1989) what, how, where and when of theory building will elucidate our under-standing of both the disruptive and reintegrative pathways of resilience. Adopting this approach to resilience, we clarify (a) self-regulatory and episodic pathways to positive adaptation in the face of a broader range of stressors, and (b) we use conservation of resources theory to explain the fluctuation and developable capacity of resilience. Researchers and practitioners are encouraged to develop resilience interventions for specific predictable adversities in sport. Building strategies around the dual pathway model will promote preventive and reintegrative resilience approaches, optimizing performance episodes and well-being in ongoing sporting endeavors.

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Furthering the Discussion on the Use of Dynamical Systems Theory for Investigating Resilience in Sport

Nick Galli and Katherine Pagano

In this commentary, we offer a critique of Hill, Den Hartigh, Meijer, De Jonge, and Van Yperen’s (2018) article, “Resilience in Sports From a Dynamical Perspective,” in which they recommended the dynamical systems theory as a framework for the study of resilience in sport. Specifically, we rely on our research and practical experiences to call into question some of the author’s assertions. We suggest further clarification on what constitutes an interaction in the sport environment, more emphasis on precompetition athlete history in determining performance following failure, and further consideration of the role of athlete cognition. Recommendations for future research in sport resilience include examining the interactions in resilience through moderation-based statistical techniques and the potential for successive sport failures to promote personal growth.

Keywords: stress, adversity, growth

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Antifragility in Sport: Leveraging Adversity to Enhance Performance

Adam W. Kiefer, Paula L. Silva, Henry S. Harrison, and Duarte Araújo

This commentary focuses on a complementary theoretical–experimental approach to the target article by Hill, Den Hartigh, Meijer, De Jonge, and Van Yperen (2018). In the target article, the authors develop an initial roadmap for identifying persistent behavioral patterns (i.e., athletic resilience) through measurements to identify specific attractor states and/or the attractor landscape. The goal of this approach is to promote a more complete understanding of the underlying attractor dynamics that give rise to resilient behavior. We extend the thesis of the target article via the concept of metastability. Metastable dynamics are the result of the system remaining poised on the edge of criticality. We argue that metastability is key for positively adapted behavior and, ultimately, successful athletic performance. When considered in this light, positive adaptations to adversity (i.e., resilience) are the minimum outcome, with performance enhancement in the face of adversity as the true performance goal. Such growth from adversity is termed antifragility. We next couch this concept in the context of evolutionary biology to leverage biological hormesis as a stress-response model for athletic performance. This allows for biology-inspired fitness profiles that provide a quantifiable measure of stress response relative to environmental change. From there, phenotypic plasticity can be calculated to further elucidate the relation between adversity and performance responses as a quantifiable index of antifragility. Finally, this approach is discussed in the context of personalized training interventions that facilitate the emergence of metastable dynamics that underlie phenotypic plasticity, with critical training windows introduced as opportunities to increase athletic antifragility.

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PART III Abstract

In our target article, we proposed the application of the dynamical systems approach to studying how the dynamic process of resilience unfolds over time. Sparked by the commentaries by Bryan and colleagues, Galli and Pagano, and Kiefer and colleagues, we aim to provide clarifications of the dynamical systems approach as well as possible extensions of the framework. Specifically, we discuss more elaborately the basic assumption of the dynamical systems approach that behavior emerges from ongoing, bidirectional interactions among a multitude of components over time. Given current knowledge of resilience in sports, the next logical step is to focus on understanding the temporal process of resilience rather than untangling its underlying components. Inspired by the commentaries, we further discuss the changing magnitude of stressors’ impact over time, the issue of interconnected timescales, and resilience versus growth. We conclude by discussing practical- and data analytical implications of examining the process of resilience.

Keywords: Adversity, Complexity, Coping, Critical Slowing Down, Growth, Mental

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7 | Introduction

In the target article (Hill, et al., 2018a), we pointed out that scholars typically consider resilience (i.e., positively adapting to adversity) as a process. However, the current literature is still lacking insight into how this process unfolds over time. To fill this void, we proposed the application of a dynamical systems approach which is marked by ongoing dynamic interactions among multiple components1 _{over time (e.g., Kelso, 1995; Nowak}

& Vallacher, 1998; Van Geert, 2009). We are grateful to the authors who provided well thought-through commentaries to our article. We believe a discussion on the theoretical underpinnings of resilience is necessary to move forward with our understanding of, and interventions on, this important concept.

The idea that resilience research will profit from focusing on the process that defines resilience has reached consensus among researchers and is reinforced throughout the commentary articles (Bryan et al., 2018; Galli & Pagano, 2018; Kiefer et al., 2018). However, there seem to be two different conceptualizations of the term “process”, namely the causal chain process (e.g., Bryan et al., 2018; Galli & Pagano, 2018) and the temporal process (e.g., Hill et al., 2018a; Kiefer et al., 2018). This key difference in conceptualizing the process, which consequently leads to the application of different theoretical as well as different methodological foci, distinguishes the theoretical framework of the dynamical systems approach and main stream approaches to resilience in psychology. At the same time, we believe that all commentaries provided interesting comments and suggestions that can be integrated into the dynamical systems approach to resilience. Therefore, this response is structured as follows. First, we will clarify our theoretical approach of dynamical systems and how it may differ from mainstream approaches in psychology. Second, we will demonstrate how suggestions from the authors of the commentary articles may be integrated into the dynamical systems framework. We will end this paper by discussing challenges of the dynamical systems approach and future avenues for research.

8 | The Dynamical Systems Approach as the next

Logical Step

Researchers often aim to detect causal relationships between the different variables that they study. For instance, in a standard psychological experiment, we systematically

1_{Note that throughout the article the term “component” refers to any psychological, physiological, or}

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manipulate an independent variable, which we assume to have a direct impact on the dependent variable, while keeping all other aspects of the situation constant. When we observe a change in the dependent variable, we conclude that this change has been

caused by the independent variable. The basic assumption of this causal chain approach

is that there are directional causal processes that determine behavior. In line with this reasoning, the last decade of research suggests that resilience in athletes is determined by a multitude of underlying components (Bryan et al., 2018; Galli & Pagano, 2018; see for sport-specific reviews, Galli & Gonzalez, 2015; Fletcher & Sarkar, 2013). Such an approach does not exclude the possibility that components can also interact with each other in order to determine the behavioral outcome. For example, Galli and Pagano (2018) pointed to the use of moderation-effects to pinpoint the specific effects of the components. The authors used the example of the personality trait hardiness that could influence the perceived stress on recovering from injury. Furthermore, the different components can also have reciprocal influences on each other (i.e., bidirectional causality). This means that a given component A causes changes in component B, which in turn causes changes in component A, probably as a function of moderators. Therefore, researchers who embrace a causal chain process, aim at identifying the specific components, their interactions, and their bidirectional causal order.

When assuming that the components and their interactions remain stable over time, a suitable approach to understand resilience would indeed be to examine the independent variable(s) of interest and their interactions at a single, and thus representative, point in time. However, as acknowledged by the commentary articles, the components can change over time (Bryan et al., 2018; Galli & Pagano, 2018). Importantly, the interactions between components, as well as the causal directions, are also undergoing change (Kiefer et al., 2018). Therefore, obtaining a snapshot of the state of the components at a given moment may be misleading due to their inherent dynamics that characterize the process of resilience (cf. Hill et al., 2018a). Therefore, the next logical step for researchers is to develop a theoretical framework that is explicitly built on the notion that the observable behavior is the result of the ongoing, temporal changes in the underlying interacting components. Based on this core principle, we propose the dynamical system approach which focuses on how a dynamic process such as resilience, unfolds over time. It provides the tools to demonstrate, for example, whether an athlete is able to quickly adapt to a stressor or when an athlete is not be able to adapt at all (Den Hartigh, Hill et al., 2018). Thereby, the main focus of researchers shifts from identifying the components that determine resilience in a causal chain to how the process unfolds over time (i.e., the temporal process of resilience).

In the target article, we outlined that the hallmark of a dynamical system is its complexity. Complexity means that the underlying components are constantly interacting and are

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changing over time (Beek et al., 1997; Den Hartigh et al., 2017). These ongoing changes

and interactions manifest themselves in the behavior that a system generates (Hill et al., 2018a). In accordance with this idea, literature on resilience also maintains that the process is determined by the (dynamic) interactions between the person and the environment, rather than being driven by a steady (set of) component(s) (e.g., Egeland et al., 1993). This dynamic coupling between the person and the environment to determine resilience is further supported by the fact that, so far, no single (set of) component(s) has been identified as reliable predictors of resilience across individuals, time, and contexts. For some components even opposite effects were reported (see Hill et al., 2018a). Therefore, we propose that resilience is driven by the functional way the different components interact with each other (i.e., interaction-dominance, e.g., Den Hartigh et al., 2017; Den Hartigh, Hill et al., 2018; Van Orden et al., 2003).

In their commentary, Kiefer and colleagues (2018) further elaborated on this notion of interaction-dominance by showing that a dynamical system can make use of structurally different components in order to achieve the same functional output. Thus, in a dynamical system, the same behavior may result from different interacting components or underlying processes (Davids et al., 2006; Edelman & Gally, 2001; Kiefer et al., 2018). Because the interactions among all of the underlying components are essential in understanding the behavior of a dynamical system, the system needs to be kept intact in order to be studied (Hill et al., 2018a). Deconstructing the system and studying its components in isolation likely disrupts the dynamic interactions between the components.

In order to understand the temporal process of resilience and its underlying complexity, a good strategy for researchers is to study a so-called “collective variable” in which the ongoing, dynamic interactions are manifested (Hill et al., 2018a). For example, the dynamic interactions between the psychological, physiological, and environmental components come together in athletes’ behavior demonstrated in a performance context. Time-series measurements (i.e., dense repeated measures) of such a collective variable provide insight into how athletes’ performance trajectory unfolds over time (Araújo et al., 2015; Den Hartigh et al., 2017). This approach allows researchers to study the shape of the resilience trajectory in response to a stressor (or perturbation in dynamical terms) as well as periods during which the system needs increasingly more time to demonstrate resilience (i.e., early warning signals). Such alterations of the performance trajectory may indicate that a system becomes unable to demonstrate resilience and that a critical transition may occur (i.e., critical slowing down; Dai et al., 2012; Scheffer et al., 2012; Van de Leemput et al., 2014).

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In sum, the basic assumption of the dynamical systems approach is that behavior emerges from ongoing, bidirectional interactions among a multitude of components over time, rather than being determined by specific components in a causal chain. This shifts the focus from untangling the underlying components to studying changes in the state of an entire system by looking at the temporal pattern of a collective variable.

9 | Integrating Themes into the Dynamical

Systems Approach

9.1 | Magnitude of the Adversity’s Impact

A critical point brought forward by Galli and Pagano (2018) as well as Bryan and colleagues (2018) is the magnitude of the impact an adverse event may have. The authors argued that the cognitive appraisal of an event is the main driving force behind the impact’s magnitude and thus a key factor mediating the process of resilience. Bryan et al. (2018) also added, in line with our target article, that the magnitude of the impact is further determined by how it is embedded in the temporal sequence of preceding events. For example, relative to athletes who won their previous matches, athletes who lost their previous matches may suffer more from losing a match. Indeed, the history-dependence of the subjective experience of a stressor has been demonstrated in research on psychological momentum in sports (Briki et al., 2013; Den Hartigh & Gernigon, 2018; Den Hartigh et al., 2014; Den Hartigh, Van Geert et al., 2016; Gernigon et al., 2010). However, instead of searching for what psychological components under what specific conditions determine the stressor’s magnitude, we would argue that the impact of a stressor can be derived from the behavioral response (i.e., the collective variable) following its occurrence (see also Kiefer et al., 2018). For example, if there is no negative change in the athletic performance, one may conclude that it had no deliberative impact2_{. In contrast,}

when the athletic performance suffers a decline, the impact of the stressor was negative. Either the magnitude of the decline or the time it takes to return to the previous level can signal the magnitude of the stressor’s impact (Dai, et al., 2012; Scheffer et al., 2012; Van de Leemput et al., 2014). The changing magnitude of a stressor in response to how it is embedded in the performance history of the athlete can be studied by exposing the athlete to the same (or similar) stressor(s) over time.

2_{Note that, in accordance with the dynamical systems perspective it is possible that a stressor causes}

quantitative changes in some of the system components, such as mental well-being or confidence, without causing qualitative changes in the collective variable (i.e., athletic performance, cf. Vallacher & Nowak, 1997).

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9.2 | Interconnected Timescales

Following the notion that the magnitude of stressors varies strongly across individuals and within individuals across time and contexts, Galli and Pagano (2018) raised the point that seemingly small stressors such as losing a single match, can have long-term consequences for athletes. Furthermore, the authors pointed out that events, which take place immediately before a competition, can have major influence on what happens during the competition. We fully agree that resilience is contingent on such phenomena and offer below an explanation as to how they can be integrated into a typical property of dynamical systems, namely interconnected timescales.

Broadly defined, a timescale reflects the period of time over which a process is analyzed. However, the timescale of adapting well to a stressor is not necessarily proportional to the objective magnitude of the event. The magnitude of the stressor is also a function of the system’s history or overarching trend, which is formed by a sequence of events. This overarching process (on a large timescale) may strengthen or weaken the effects of a subsequent event (on a short timescale). Reversibly, the single events on the short timescale shape the overarching process on the large timescale. This bidirectional influence of the different timescales constitutes the notion of interconnected timescales (for an empirical demonstration in sports, see Den Hartigh et al., 2016). Thus, as pointed out by Galli and Pagano (2018), a stressor which takes place just before a match can have a direct impact (both positive and negative) on the athlete’s subsequent performance. For instance, a stressor experienced before a competition could have a positive influence as it may signal that an increase in effort or concentration is required. However, the same stressor at the same time may cause a drastic, negative shift in performance if the athlete’s performance history features a recent series of losses (cf. Briki et al., 2012).

9.3 | Growing from Stressors

The final recurring theme in the commentaries is that we do not account for the possibility of growth beyond the baseline of the level of functioning in response to an adverse event (cf., Carver, 1998; Hardy et al., 2017). Although the commentaries use different terminologies (Kiefer et al., 2018, antifragility; Bryan et al., 2018, emergent resilience; Galli & Pagano, 2018, stress-related growth), they all refer to the possibility that performance can be strengthened as a result of dealing successfully with a stressor. Indeed, in our target article (Hill et al., 2018a), we mainly focused on the athlete’s ability to return to their previous level following adversity, which is what defines resilience (see also, Carver, 1998; Hosseini et al., 2016). Galli and Pagano (2018) challenged us to extend this model to detect patterns in the time-series data of athletic performance that could indicate when a system might actually grow, that is, demonstrate a positive transition.

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Using insights from complex biological systems, Kiefer and colleagues (2018) presented an ambitious research agenda that is specifically aimed at optimal growth in response to stressors (see also Kiefer, 2017; Silva, 2017). These authors explain growth through the notion of metastability. Simply put, a metastable state describes the ability of a complex biological system to enter multiple different pathways to complete a task at any given point in time, by making use of different functional interaction patterns between its components (Kiefer et al., 2018). Thus, metastable systems can form functional interactions between different components to produce a desired behavioral outcome (i.e., integration tendency), while simultaneously terminate dysfunctional interactions in order to avoid becoming trapped in an undesirable behavioral pattern (i.e., segregation

tendency). This means that the system is able to maintain positive states, resolve these

states once they are not functional anymore, and create new functional states in their place. Accordingly, from a dynamical systems perspective a system achieves growth following a stressor if it is able to form new, more adaptive interactions between its underlying components, from which more optimal behavioral solutions to a given problem emerge, which is referred to as antifragility.

Similar to our proposition of resilience, Kiefer et al. (2018) argued that system’s antifragility can be derived from the changes in behavioral patterns in response to a series of stressors. That is, signals in the temporal structure of a system’s behavior potentially indicate positive phase transitions in addition to the warning signal of negative transitions (Dai et al., 2012; Scheffer et al., 2012; Van de Leemput et al., 2014). These signals can be used to enhance athletes’ growth, or to prevent athletes’ breakdowns in resilience within a single performance context. We understand that this extension may be challenging to implement. However, we are intrigued to see how the two frameworks of antifragility and our dynamical systems approach to resilience could be combined in order to understand both growth over time and breakdowns of resilience.

10 | Moving Forward with Research on Resilience

In line with the causal chain approach on resilience, the extant literature has primarily focused on identifying psychosocial components that explain why some athletes are more resilient than others. However, as discussed, we propose that resilience is a complex process that is driven by the bidirectional interactions between psychological, physiological, and environmental components over time. Hence, we think that the next logical step is to develop a unified framework that accounts for this complexity of resilience processes. Embracing this versatility can spark various interdisciplinary research programs that may advance the field of resilience as a whole.

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Because the dynamical systems approach accounts for a comprehensive integration

of various underlying components (cf. Bryan et al., 2018, Galli & Pagano, 2018) and the changing impact of events on different timescales (Galli & Pagano, 2018), it represents a parsimonious account for studying the process of resilience over time. Moreover, it can be extended to studying how individuals grow from stressors (Kiefer et al., 2018). Based on the insights from the literature on (system) resilience and the typical properties of dynamical systems, and the commentaries to our target article, we would propose the following definition of resilience to guide future research: “The dynamic process by which a biopsychosocial system returns to the previous level of functioning, following a perturbation caused by a stressor”. This definition highlights that (1) the unit of analysis is the dynamic process over time, (2) the outcome is the return to the previous state thereby differentiating it from growth, and (3) stressors can be considered as perturbations to the system’s state.

10.1 | Practical and Data Analytical Implications

In their commentaries, Galli and Pagano (2018) as well as Kiefer and colleagues (2018) also focused on the practical applicability of the research on resilience. Although our primary aim was to propose a new theoretical perspective on resilience, one’s perspective guides the kind of practical intervention. For example, building upon the causal chain approach, an intervention aimed at enhancing athletes’ resilience may be to change a specific component that is considered a determinant of resilience. In contrast, from a dynamical systems perspective, an intervention should target the system as a whole as it determines the desired outcome (Kiefer & Myer, 2015). For example, an athlete may show an increase in time needed to recover from a recurring stressor (e.g., points made by the opponent). A simple intervention may be aimed at interrupting the sequence of stressors, for example, by taking a time-out. Such an interruption may give the system time to recover its previous state of functioning (Den Hartigh & Gernigon, 2018). Because the magnitude of a stressor is determined by how it is embedded in individuals’ history of performance, disrupting a negative sequence consequently reduces the magnitude of a potential subsequent stressor, preventing it from causing a critical transition.

In order to stimulate antifragility, Kiefer and colleagues (2018) proposed that an adaptive behavioral response reflects a system’s ability to form new functional interaction patterns as well as dissolving dysfunctional interactions between the underlying components. These newly formed patterns reflect the positive adaptation to the encountered stressor. Therefore, the proposed intervention involves training these adaptive responses by exposing an athlete to a controlled amount of stressors. After successful completion of the training, the athlete is able to explore new functional interactions and thus adaptive behavioral responses when encountering similar, and maybe even unfamiliar stressors.

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That said, concrete interventions to enhance resilience or the possibility for growth need to be further developed and tested.

From a data analytical point of view, a process emerging from a complex system is marked by variations over time. This means that fluctuations are inherent in a time-series from such a system. As transitions in a system’s behavior can be indicated by enhanced fluctuations (Kelso et al., 1986; for a sport-specific overview, see Hristovski et al., 2014) and a critical slowing down (Dai et al., 2012; Scheffer et al., 2012; Van de Leemput et al., 2014), a high degree of accuracy of the measurement systems used to establish the time-series is required. Thus, in order to study the process of resilience over time within a single performance context, an accurate, reliable, valid, and high-frequency measurement system of the collective variable (i.e., actual behavior) is necessary. In order to study the temporal process of resilience on a larger timescale, repeated (self-) reports of various performance indicators can be used to establish the time-series data (Hill et al., 2018a).

11 | Conclusion

We addressed some major themes provided by the commentary articles: The dynamical systems approach as the next logical step, changing magnitude of stressors’ impact, interconnected timescales, resilience versus growth, and practical as well as data analytical implications. We aimed to demonstrate how the comments and concerns could be integrated into the dynamical systems approach. To sum up, the dynamical systems approach focuses on unfolding the dynamical process over time and thereby embraces its underlying complexity. This complexity can be assessed by compiling time-series data of a collective variable that represents the ongoing interactions between the underlying components of the system (Araújo et al., 2015; Den Hartigh et al., 2017).

We would like to express our appreciations for the commentaries and thank Kiefer and colleagues (2018) for their suggestions to extent the dynamical systems framework; Bryan and colleagues (2018) for opening the discussion on causal processes and athletes’ growth experience in response to a stressor; and Galli and Pagano (2018) for their challenging comments on interconnected timescales and stress-related growth. We believe that the consensus to focus on the process of resilience will advance our understanding on how athletes deal with challenging situations and overcome adverse experiences and are excited to see the future results of this constructive exchange of ideas.

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