Assessing unpredictability in caregiver–child relationships: Insights from theoretical and empirical perspectives

There has been significant interest and progress in understanding the role of caregiver unpredictability on brain maturation, cognitive and socioemotional development, and psychopathology. Theoretical consensus has emerged about the unique influence of unpredictability in shaping children’s experience, distinct from other adverse exposures or features of stress exposure. Nonetheless, the field still lacks theoretical and empirical common ground due to difficulties in accurately conceptualizing and measuring unpredictability in the caregiver–child relationship. In this paper, we first provide an overview of the role of unpredictability in theories of caregiving and childhood adversity and present four issues that are currently under-discussed but are crucial to the field. Focusing on howmoment-to-moment and day-to-day dynamics are at the heart of caregiver unpredictability, we review three approaches aiming to address some of these nuances: Environmental statistics, entropy, and dynamic systems. Lastly, we conclude with a broad summary and suggest future research directions. Systematic progress in this field can inform interventions and policies aiming to increase stability in the lives of children.

Predictability is instrumental in shaping learning processes and stress-response systems (Doan & Evans, 2020;Smith & Pollak, 2021a), with important implications for psychosocial functioning across the lifespan (Baram et al., 2012;Kolak et al., 2018). Accordingly, the field of developmental psychopathology is increasingly recognizing the importance of unpredictability in children's lives as a source of environmental adversity (Ellis et al., 2022;McLaughlin et al., 2021;Young et al., 2020), fundamental to understanding the experience of stress throughout development (Smith & Pollak, 2021a). While existing theoretical and empirical orientations about distal unpredictability (e.g., parental transitions, income variability, residential transitions; Ellis et al., 2022) have grown substantially during the last decade , the majority of research on proximal experiences of unpredictability that occur within caregiver-child relationships have been derived from retrospective questionnaires measures completed in adolescence or adulthood about prior childhood experiences (Maranges et al., 2022;Mittal et at., 2015;Ross & McDuff, 2008). While useful, these have the well-known limitations of retrospective measures. Less research has centered on the processes by which concurrent experiences of proximal unpredictability shape children's socioemotional and cognitive development .
Positive and predictable care during early childhood promotes healthy long-term development Short et al., 2020). Contingent and consistent caregiving fosters attachment security by providing safety and external regulatory support of infants' and children's developing self-regulation (Feldman, 2021;. In animal models, predictability supports the development of hippocampal/limbic and rewardrelated brain circuitry (Bolton et al., 2018;Johnson et al., 2018;Molet et al., 2016), impacting prefrontal-subcortical development and maturation of the stress response system (Bolton et al., 2019;Tottenham, 2020). This does not pertain exclusively to positive features of caregiving, as predictability of aversive stimuli has been shown to reduce fear in infants (Gunnar et al., 1984) and increase perceived control (Maier & Seligman, 1976;Wang & Delgado, 2021). Conversely, unpredictability has been shown to have lasting adverse effects on neurodevelopment, disrupting the development of effortful control, memory, and stress responses (Davis et al., 2017;Granger et al., 2021;Noroña-Zhou et al., 2020). Such infant responses to caregiver unpredictability may be considered adaptive for the well-being of the child concurrently, conferring an immediate survival advantage to environmental demands Nketia et al., 2021). However, they also may convey maladaptive consequences for future health and well-being (Blair & Raver, 2012).
Despite the central roles of caregiver unpredictability in developmental theory, defining and assessing variation in caregiver unpredictability has proven elusive. This paper integrates different theoretical and empirical orientations to provide conceptual and methodological tools to assess caregiver-child unpredictability.
Our approach is informed by models of socialization theory that frame caregiver-child interactions as dynamic, bidirectional processes that may be expressed in situation-specific ways (Grusec et al., 2000;Kuczynski et al., 2015). That is, caregiver-child interactions are flexible in the face of changing features of both partners and situations, and the mechanisms that guide socialization and child outcomes across development may be different across varying domains of relationship context, as well as age or developmental stage of the child (Grusec, 2011). We focus on the immediate caregiving system across infancy and early childhood because it is the primary source of information about the type of environment young children can expect concurrently and probabilistically across their lifespan (Bateson et al., 2004;Tottenham, 2020). Hence, unpredictability in this foundational system may confer myriad and enduring consequences.
This article provides a brief overview of different theoretical perspectives of caregiving and childhood adversity and the role that unpredictability has been posited to play in each of these perspectives. Second, we highlight four under-discussed issues in the field. Third, we present three frameworks and corresponding methods that may improve how we assess variation in child-caregiver unpredictability: Life history theory and environmental statistics, information theory and entropy, and dynamic systems theory (DST). In a fourth and final section, we conclude with a broad summary and suggest potential future directions in the field.
The role of unpredictability in theoretical perspectives of caregiving and adversity Foundational developmental theories have emphasized the importance of predictability and stability in caregiver-child interactions and children's environments. Given the plethora of terms that have been used to consider unpredictability as an aspect of stressful early life experiences, Table 1 outlines our working definitions of key terms that repeatedly appear through the literature and within the current paper, recognizing that many of these definitions are subject to debate within and between disciplines.

Attachment theory
The importance of unpredictability in caregiver-child relationships gained prominence in developmental science with Bowlby's proposal of humans' biologically programmed need for attachment (Ainsworth et al., 1974;Bowlby, 1969). Caregiver responsiveness and interactions with their infants are critical for forming attachment relationships. Unpredictability in reciprocal interactions was understood in terms of inconsistent maternal availability, characterized by mothers' noncontingent responses to children's bids, relatively low availability and direct interference during infants' exploration (Ainsworth et al., 1978;Cassidy & Berlin, 1994). Attachment theory, as well as early empirical studies of inconsistent parenting in the 1970s and 1980s (Gardner, 1989;Stern, 1971), and Seligman's learned helplessness theory (Maier & Seligman, 1976), served as the underpinnings for Ross and Hill's conceptual introduction of family unpredictability (2000). In unpredictable families, caregivers did not provide consistent affective nurturance and exercised discipline inconsistently (Ross & Hill, 2004). Caregiver inconsistency predicted children's internalizing disorders (Mirabile, 2014) and unpredictable cognitive schema, or belief that people and the world are uncertain and chaotic, which led to greater risk-taking (Cabeza de Baca et al., 2016).
These convergent lines of research suggested that consistency was a solid indicator of effective parenting and, conversely, that inconsistency undermined child well-being. Yet, subsequent research has indicated that a linear translation of more consistency to more adaptive predictability was too simplistic (Bornstein, 2013). Excessive predictability in the context of caregiver-infant interactions (e.g., caregiver responding to cues that were not eliciting of a response) may indicate intrusion or vigilance (Beebe et al., 2020) or a coercive cycle between both partners (Lunkenheimer et al., 2016). Further, inconsistency has proven to be a challenging construct to measure; studies have often conflated inconsistency of maternal behaviors with overall lower levels of caregiver engagement (Cassidy & Berlin, 1994). Additionally, researchers have rarely considered that specific contextual demands (e.g., the need to elicit child compliance) that influence patterns of consistency of caregiver behaviors may allow children to form predictions about their proximal environment (Lunkenheimer et al., 2016). Despite these challenges, attachment theory has provided a framework to explore how variations in the moment-to-moment interactions within the dyad may be a significant source of unpredictability.

Bronfenbrenner's bioecological systems theory
Bronfenbrenner's emphasis on proximal processes and timescales of influence (Bronfenbrenner, 1999;Bronfenbrenner & Evans, 2000), when coupled with the emergence of the construct of household chaos (Wachs & Evans, 2010), led to proposals that environmental unpredictability was a significant determinant of child development. Environmental unpredictability was defined as temporal and spatial instability in children's lives, spanning from more proximal experiences of the child, such as a general lack of routines in day-to-day experiences, to more distal experiences like the accumulation of life events that challenged a family's continuity and cohesiveness through developmental time (Ackerman et al., 1999;Wachs, 1996). Scales such as the Chaos and Hubbub scale (Matheny et al., 1995) attempted to tap into day-to-day predictability, and the Family Instability Questionnaire (Ackerman et al., 1999) assessed the cumulative number of transitional experiences (e.g., family disruptions, residential instability; Forman & Davies, 2003). A crucial inference emerged from this work: The frequent and repeated experience of chaos and instability can reflect chronic states of unpredictability with adverse developmental consequences (Doom et al., 2018;Matheny et al., 1995). Repetition, including repeated experiences of unpredictability, informs children's predictions about their future environment, and these influences on children may differ depending on the timing of unpredictability (e.g., early childhood versus adolescence). Many studies focused on chaos and instability during childhood did not explore the specific role of unpredictability in the caregiver-child relationship, yet these studies shed light on how the influences of chaos and instability on child development are distinguishable from the influences of availability of familial social and economic resources (Wachs & Evans, 2010).

The integrated model of dimensions of environmental experience
Unpredictability from a life history perspective (the harshnessunpredictability model; Ellis et al., 2009;Ellis et al., 2022) and developmental cognitive neuroscience (the threat-deprivation model; McLaughlin & Sheridan, 2016) have focused on questions of why different dimensions of adversity drive different biobehavioral developmental trajectories and how children use information from their proximal environment to concurrently adapt, both neurally and behaviorally, to their immediate environment Table 1. Working definitions of constructs included in the manuscript

Introduction and theories
Unpredictability Stochastic variation (an absence of patterns in the variation) of environmental cues or experiences, including lack of temporal stability of aspects of the environment, and lack of organization, coherence, or consistency of caregiver behavior.
Adversity A wide range of experiences and contexts that are non-optimal for the developing child and can disrupt physical and psychological health.

Stress
The physiological or psychological response to external or internal stressors or stressful events.
Stressful events/experiences Acute or chronic induvial or community-based events or experiences that result in physical or emotional stress.
Distal cues Ecological factors linked to unpredictability.
Proximal cues Direct experiences of unpredictability.

Inconsistency
Behavioral variability in different aspects of caregiving such as affection or discipline.

Instability
Cumulative number of transitional experiences that challenge families' continuity and cohesiveness through developmental time.
Chaos General lack of structure or routines in day-to-day experiences and home organization.
Unpredictable schema A belief that people and the world are uncertain and chaotic.

Harshness
External causes of morbidity and mortality that are relatively insensitive to the decisions/actions of the organism.
Threat A feature of harshness involving harm or threat of harm imposed by other agents.

Deprivation
A feature of harshness involving lack of necessary resources for survival.

Perceived control
Perceived ability or awareness that the effects of one's actions influence the environment in accord with one's intentions.

Environmental statistics
Environmental statistics Ways to quantify the statistical structure of an environment, which is determined by how physical and social parameters vary over space and time, across and within generations, and the extent to which cues (experiences or events) provide reliable information about current and future conditions.

Adaptive plasticity
The degree to which organisms successfully adjust their phenotype to environmental conditions, which will depend on the statistical structure of the environment.
Ancestral cues Informative cues that signal potential unpredictability to which the human brain is able to detect quickly and adapt efficiently due to the processes of natural selection across evolutionary history favoring those biobehavioral capacities.

Statistical learning
The use of accumulated lived experiences as "raw data" to estimate and developmentally adjust to unpredictability across developmental time.
Level (mean) Average expression of the parameter across time

Variability
Deviations from a parameter's mean.

Autocorrelation
The degree to which past values correlate with current values of a given parameter.

Stationarity
If a parameter is stationary, the distributional characteristics of a parameter (e.g., mean, variability, and autocorrelation) do not change across time.

Trend
Stable directional changes in variability.
Informative or reliable cue Events or experiences that provide information about the current or future state of the environment.

Entropy
The degree of uncertainty or disorder of a random variable.
Entropy rate Average information required to predict a future observation given a previous observation in a sequence.
Sensory signals Auditory, tactile, and visual inputs from a caregiver Fragmentation Aberrant patterns of care, or the provision of care without a consistent or organized rhythm in rodent models.
First-order stationarity Markov chain A sequence of behaviors to calculate entropy rate. It is based on the following assumptions: (a) Proximal future states (e.g., at time t) depend exclusively on their most recent past state (e.g., t -1), such that each sequential transition is independent of preceding and following transitions and (b) the probability distribution is stationary or independent of time.
Visit entropy Transitional probabilities between all visited grids of a state-space grid.

Dynamic systems theory
Attractors Recurrent patterns of behaviors that become increasingly coherent and predictable through developmental time.
Phase transitions System-wide reorganizations in which relative stability and predictability periods are followed by disequilibrium and reorganization.

Perturbations
Exogenous influences on a system or attractor.
(Continued) (Ellis et al., 2022). Regarding the question of why, with its basis in evolutionary-developmental principles, life history theory suggests that distinct environmental conditions throughout the evolutionary history of our species posed specific selection pressures that required different solutions to increase the likelihood of successful reproduction (Ellis et al., 2022). Therefore, natural selection shaped developmental systems capable of detecting and flexibly adapting to specific dimensions of adversity. In both the harshness-unpredictability and threat-deprivation models, those adaptation processes reflect the question of how, and refer to variations in biological, psychological and behavioral mechanisms that reflect survival strategies, or life history traits (Belsky et al., 1991;Draper & Harpending, 1988;Figueredo et al., 2006). These life history traits reflect coordinated responses to contextual cues indicating either that a shorter lifespan is likely, leading to an adaptation of faster development, or a longer lifespan is likely, and hence a slower course of maturation. Faster to slower traits are evident in reproductive strategies such as the timing of puberty, earlier versus later engagement in reproduction, and degree of parental investment in offspring. Recent efforts to integrate these two-dimensional frameworks have converged on deprivation (e.g., lack of necessary resources for survival) and threat (e.g., harm imposed by other agents) as two features of environmental harshness (Ellis et al., 2022). Both features of harshness can be experienced as predictable or unpredictable depending on the stochastic variations of their cues, which can range from more distal to the child (ecological factors such as variation in household income) to proximal (immediate experiences such as caregiver behavior). Early experiences of these dimensions of adversity have the potential to regulate both immediate and future adaptive biobehavioral responses to the environment (Ellis et al., 2022). When it pertains to caregiving, dimensions of caregiver-related adversity may be better understood as continua (King et al., 2019), occurring to greater or lesser extents, rather than as binaries (absent versus present), and may be evidenced to varying degrees across different aspects of caregiving.

Topological approach for conceptualizing early adversity
Finally, Pollak (2021a, 2021b) proposed that specific biobehavioral responses to adversity are determined in part by features of the experience of adversity, rather than dimensions or subtypes of adverse events themselves. Grounded in theoretical perspectives of the broader stress literature (McEwen & Akil, 2020;Sapolsky, 2015), Smith and Pollak suggested that one of the critical features of adverse experiences is unpredictability, shaping young children's perceptions of uncertainty and volatility, altering stress response systems and ultimately disrupting biobehavioral development. Ultimately, Smith and Pollak (2021a) argued that both environmental and perceived unpredictability interact to shape experiences of stress and adversity. Therefore, children's perceptions of the unpredictability of stressful events in their caregiving experiences might drive individual differences in biological and psychosocial development, over and above the impact of exposure to those stressful events (Baldwin & Esposti, 2021;Smith & Pollak, 2021a, 2021b. Smith and Pollak's (2021a) focus on children's perception or subjective experience of caregiver unpredictability is an important additional consideration. Yet, it raises questions regarding the integration of developmental timing of unpredictability experiences with maturation of the capacities to form predictions. Within a few months after birth, infants start developing a basic understanding of cause and effect, or the predictability of expected outcomes in their immediate environments (Rochat, 1997;Sherman et al., 2015). Infants' abilities to perceive the predictability of their caregiver might be evident similarly early, although the extent to which this is true remains undetermined. Yet, perceiving the predictability of a caregiver's responses to hunger crying or of soothing contact when distressed might not occur along the same developmental course as perceptions of the predictability of maternal mood or emotional expression (Tottenham, 2020). It is plausible that capacities to evaluate those experiences that are more relevant to the basic elements of survival directly tied to infants' biological needs, such as the predictability of feeding patterns, may develop first. Additionally, both in infancy and across development, it is likely that both the actual experience and the perception of unpredictability guide processes of neural and behavioral adaptations (Gunnar, 2021). Nonetheless, Smith and Pollak's (2021a) introduction of the notion of perception re-centers the conversation on the ubiquitous nature of tendencies to make predictions and regulate development based on the violation of these predictions .

Integrative summary
All four of these theories propose that unpredictability is an understudied but core element of early adversity, manifesting across distal and proximal processes. Attachment theory emphasizes the role of caregiver responsiveness and interactions with their infants, identifying inconsistency in maternal availability as a source of unpredictability in these relationships. Bioecological Systems theory highlights that the influence of temporal and spatial instability is distinguishable from the overall availability of social and economic resources. Dimensional models propose that natural selection has shaped developmental systems that are capable of detecting and flexibly adapting to unpredictability, and that these adaptation processes reflect variations in biological, psychological, and behavioral mechanisms that reflect survival strategies or life history traits. These three models focus on whether events are in actuality unpredictable. The Topological approach, on the other hand, specifically focuses on the perception of unpredictability in human experience specifically, suggesting that whether an infant or child perceives their caregiver or their caregiving experiences as Dyadic contingency Pairing of caregiver and child states (affect and behavior codes) via temporally dependent sequences, estimated using the average transitional probability between them.

Dyadic variability
The number or rate of transitions between different cells in a state space grid.
unpredictable affects biobehavioral development, even if they are not unpredictable in actuality. Altogether, each of these theoretical and empirical perspectives has shed light on children's biological (Davis et al., 2017;Noroña-Zhou et al., 2020), cognitive (Ross & Hill, 2002;Young et al., 2018), and behavioral outcomes or adaptations (Barbaro & Shackelford, 2019;Fields et al., 2021) to unpredictable early-life experiences. However, based on the review of existing conceptual models, multiple theoretical and measurement issues continue to pose challenges to progress in this field, particularly in the realm of caregiver unpredictability.
Four emerging issues in the study of caregiver unpredictability As extensively discussed by Young and colleagues (2020), it is theoretically and methodologically challenging to conceptualize unpredictability and its consequences. This is equally true when considering unpredictability in the caregiver-child domain. Informed by socialization theory (Grusec et al., 2000;Kuczynski et al., 2015) as applied to the four theoretical foundations of current perspectives on unpredictability, we identify four issues to consider when thinking about proximal experiences or cues of caregiver unpredictability.

Issue #1. Statistical and perceived caregiver unpredictability
As highlighted by Smith and Pollak (2021a), events or experiences that are statistically predictable but occur through complex processes might not be experienced as predictable by individuals exposed to those stimuli. The regularity of the phenomena might not be apprehended by individuals experiencing it. Conversely, people may have a mistaken perception of predictability occurring for things that, in truth, are entirely unpredictable. At the heart of the concept of unpredictability are variability, organization, and other temporal and structural dynamics of human experience. Naturally, this challenges a static conceptual representation of unpredictability, introducing the need to consider its temporal complexity. As such, features harnessed under the umbrella term of unpredictability may occur in temporally predictable patterns that children may detect. Seemingly unpredictable experiences, either from the general environment or centered in caregiver-child relationships, might be characterized as more predictable depending on the extent to which (1) variation is patterned across time, for instance, because environmental conditions are autocorrelated  or (2) there are cues other than previous states of the environment that are informative of future experience (Frankenhuis, Panchanathan, & Barto, 2018;Frankenhuis, Nettle, & Dall, 2019). In other words, the extent to which there are trends and patterns within variability, or other informative cues, may affect the ability or likelihood of children to experience their caregiving relationship as more predictable or more unpredictable.
Humans detect and respond to distal or proximal cues of unpredictability either through ancestral cues or statistical learning (for an in-depth review, see Ellis et al., 2022;Young et al., 2020). Ancestral cues are reliable and informative contextual cues that signal potential unpredictability, to which the human brain can detect quickly and adapt efficiently by coordinating life history traits, due to the processes of natural selection across evolutionary history favoring those biobehavioral capacities (Ellis et al., 2022). For example, a single experience of a parental transition may be an ancestral cue that individuals use to draw inferences about the likelihood of environmental unpredictability (Ellis et al., 2022), regulating development without requiring repeated experiences.
Statistical learning refers to the use of accumulated lived experiences as "raw data" to estimate and developmentally adjust to unpredictability across developmental time . As noted above, the ability to detect patterns and regularities in the environment and form predictions or "if-then" expectations develops in infancy (Saffran, 2020;Sherman et al., 2015). Extracting contingencies and regularities promotes learning, reduces uncertainty, and gives children a sense of perceived control or influence over their environment (Saffran & Kirkham, 2018). Conversely, an absence of reliable "if-then" sequences threatens the development of these competencies. Thus, through informative cues (ancestral cues) or repeated exposures to transitions, changes, or inconsistency (statistical learning), it is possible that unpredictability may become predictable for some children. That is, children may learn to "expect the unexpected," or to understand their caregiver relationships, and by extension, their broader social worlds, as unpredictable (the unpredictability schema; Cabeza de Baca et al., 2016).
Yet, are ancestral cues of predictability, or evidence for statistical predictability of any environmental factor, necessarily predictable through a child's eyes? Specifically, ancestral cues or the statistical predictability of experiences may not be consciously detectable by the individual having those experiences. As mentioned, the topological approach to early adversity underscores the importance of perceptions of unpredictability as a driver of individual differences in biobehavioral development (Smith & Pollak, 2021a, 2021b. Individuals' capacity to perceive uncertainty depends on whether unpredictable events actually change the environment (e.g., by changing rewards) and internal stored information (e.g., lived experiences), leading to significant changes in behavior as a result of learning (Soltani & Izquerdo, 2019).
How, when, and to what extent young children can unconsciously or consciously track, perceive or interpret unpredictable events remains relatively unexplored. Munakata and colleagues (in press) suggest that the timescale of unpredictability might be fundamental to understanding whether, and how, children perceive and respond to unpredictability. Proximal unpredictability occurring in the scale of seconds (e.g., unpredictability of maternal sensory signals) might not involve traceable changes in the environment and therefore might be harder to perceive or recognize consciously. Conversely, unpredictability that is more easily traceable, occurring on a timescale of hours and days (e.g., unpredictability of daily routines), or distal unpredictability across months and years might be easier to perceive. Therefore, it is possible that perceptions of unpredictability (understood from a statistical learning perspective) might vary across timescales, in addition to differences stemming from experiences indicating unpredictability in our evolutionary past (ancestral cues; Ellis et al., 2022).

Issue #2. Domains and specificity of caregiver unpredictability
Is a caregiver being unpredictable all that "matters", or do the varying ways or domains in which the caregiver is unpredictable confer different cues for children's adaptation? It is possible that caregiver unpredictability and its impact on development might vary as a function of the particular caregiver behaviors being considered and the valence of such behaviors. Davis' pioneering observational work on caregiver unpredictability (Davis et al., 2017) has exclusively centered on sensory inputs to the infant (e.g., touch or vocalizations), which are not equivalent to or interchangeable with other inputs, such as caregivers' emotional expressions or responses to infants' bids or needs (Buhler-Wassmann & Hibel, 2021). Researchers have not yet considered whether caregiver unpredictability is domain-general, expressed similarly across different inputs or features of caregiving, or domain-specific, evident in specific inputs or valences. Regarding valence, unpredictability may not pertain exclusively to aversive experiences (e.g., maternal negative mood, rejection or punitive behavior; Cohodes et al., 2021;Glynn et al., 2018). Rewarding experiences (e.g., positive maternal affect, praise or face-to-face communication) might be unpredictable as well Lunkenheimer, Skoranski, et al., 2020), conveying distinct implications for children's adaptations.
Empirical work simultaneously examining different ecological levels (proximal to distal cues), behavioral inputs, or affective valences of unpredictability is scarce. Indications that the impact of unpredictability on neurodevelopmental adaptation may vary as a function of these differences primarily emerge from animal research. Rodent models of early life adversity have found that limiting dams of bedding and nesting resources induces unpredictable caregiving to pups (Baram et al., 2012;Molet et al., 2014;Rice et al., 2008). Most notably, dams spend the same time nursing or licking and grooming their pups as dams without limited resources, but they do so in more disorganized and shorter bouts than controls (Davis et al., 2017;Molet et al., 2016). Gallo and colleagues (2019) repeated the same paradigm while assessing dams' behaviors continuously across the circadian cycle, and half the dams subject to limited bedding and nesting also developed abusive-like behavior to their pups in the form of occasional maternal kicking, in addition to unpredictable care. Unpredictability without kicking predicted more anxiety-like behaviors during adulthood, whereas unpredictability accompanied by kicking predicted more risk-taking behaviors (e.g., further wandering in an open field). As rodent dam kicking can be interpreted as adding negative valence to unpredictability, the results underscore the importance of considering the complexity of the caregiver context, as the different ways unpredictability can be expressed might impact development differently (Luby et al., 2020).
Studies have yet to examine whether distal cues of unpredictability beyond the caregiver-child dyad correlate with or influence unpredictable patterns within the caregiver-child relationship. Exposure to social and nonsocial distal unpredictable events such as residential instability (McCoy & Raver, 2012) and marital partner transitions (Hartman et al., 2018) might increase the likelihood that a child will experience unpredictability in their most proximal environment, that is, within the dyad. However, this might not be the case (Li & Belsky, 2022), as caregivers facing external challenges that interfere with care might draw on different sources of resilience to provide consistent and contingent care to the child (e.g., social support, Masten et al., 2021). Further, caregiver unpredictability and distal experiences of unpredictability may lead to distinct behavioral outcomes based on adaptive learning (Munakata et al., in press). When availability of resources or opportunities in the environment is unpredictable (or volatile), it may be the case that the best way to maximize rewards is to take them the moment they are available; thus, these aspects of unpredictability could foster impulsivity and other present-oriented behaviors (Fenneman & Frankenhuis, 2020;Munakata et al., in press). On the other hand, when there is unpredictability in action-outcomes, such as a caregiver's responses to a child's behavior, it may be adaptive to seek more information before acting; thus, this feature of unpredictability could foster greater inhibitory control and more future-oriented behaviors (Munakata et al., in press).
Thus, the ways in which caregiver unpredictability across socialization contexts or domains, involving varying behaviors and affective valences, and expressed over different ecological levels (proximal and distal cues) are related to each other, and the extent to which they lead to convergent or distinct neurodevelopmental adaptations in children, remain as open questions pending further investigations.
Issue #3. Is caregiver unpredictability an individual or dyadic construct (or both)?
The degree to which a caregiver-child relationship is unpredictable may be attributable to either or both of the partners: The caregiver might be unpredictable, the child might be unpredictable, or both might be unpredictable. Alternatively to these individual and additive possibilities, unpredictability might be an emergent quality of the dyad, where the particular partners together form unpredictable patterns of interacting with each other in their day-to-day experiences (Beebe et al., 2016, Beebe & Lachmann, 2020. To date, caregiver unpredictability has often been studied as a univariate construct focused solely on the caregiver's behaviors or signals to the infant or child (Davis et al., 2017. However, starting in infancy, caregivers establish affective and behavioral patterns contingent on reciprocity between the caregiver and the child (Beebe et al., 2016;Feldman, 2021). Infants also display a range of emotions, with their emotional variability influencing caregivers' behaviors (Montirosso et al., 2010). Beyond infancy, children become increasingly agents in day-to-day co-regulation processes (Feldman, 2015), contributing to dyadic patterns of behavior and affect Lunkenheimer, Hamby, et al., 2020). Feldman (2021) posits that, from the neonatal period to adulthood, caregiver-offspring affective, and behavioral moment-to-moment coordination should be evaluated from the perspective of each individual and from the perspective of the dyad as a unit. More specifically, theories of socialization conceptualize children as taking an active role in shaping their caregivers' behavior (Kuczynski et al., 2015), and infants' and children's characteristics such as temperament and problem behaviors have been shown to decrease caregivers' sensitivity and consistency (Hastings et al., 2019;Zvara et al., 2018). This suggests that infants' or children's characteristics might also influence the likelihood that caregivers' behaviors might be unpredictable, or could set in motion a pattern of mutual unpredictability, where both partners contribute to a relationship context that is unpredictable (Kuczynski et al., 2015). However, both dyadic unpredictability and whether caregiver unpredictability can be influenced by children's characteristics remain relatively unexplored questions in empirical research.

Issue #4: developmental timing of caregiver unpredictability
The developmental effects of unpredictability might vary as a function of the relative sensitivity of the developing system and the time in which unpredictability is experienced Luby et al., 2020). For instance, the provision of an unpredictable caregiver's sensory signals during infancy promotes neurobiological vulnerability to memory impairments and is associated with problems in effortful control (Davis et al., 2017;Granger et al., 2021). Infancy is a sensitive period for sensory signals, as they shape specific visual, somatosensory, and stress-responsive hypothalamic brain synapses, circuits, and regions (McLaughlin & Gabard-Durnam, 2022). However, it is unknown whether early childhood continues to be a period sensitive to sensory unpredictability, specifically, or whether caregiver unpredictability in other domains of behavior might be pernicious at this age. During infancy and early childhood, caregivers play a fundamental role as coregulators of infants' physiological and affective needs, and consistent, predictable care fosters secure attachment and promotes infants' and children's expectation of control or influence over the environment (Cassidy et al., 2013;Gunnar et al., 1984). Thus, unpredictable or inconsistent maternal mood and affect might undermine the quality of dyadic interactions in ways that are particularly salient for the development of attachment security and self-regulation (Mohr et al., 2019).
It has been suggested that the first 5 years of life may be a sensitive period for unpredictability, with distal unpredictability having more profound effects on children's development of life history-related traits and behaviors (Simpson et al., 2012). Studies conducted in early childhood have shown that caregivers behaviors may mediate the impact of distal unpredictability on child characteristics (Belsky et al., 2012;Ellis et al., 2022; although see Li & Belsky, 2022). Conversely, studies conducted with older children and adolescents show that distal unpredictability might have more direct influences on older children, augmenting perceptions of volatility, uncertainty, and uncontrollability of the immediate or extended environment (Cabeza de Baca et al., 2016;Ellis et al., 2022;Hanson et al., 2017). During infancy and early childhood, caregivers might be more able to shield young children from recognizing distal unpredictability; older children and adolescents have more direct contact with the social realms outside the home, potentially making it more difficult for parents to maintain a sense of predictability within an unpredictable environment. Therefore, unpredictability in different spheres of life may have impacts on developmental processes at distinct periods of life, although this supposition requires further investigation.
Three theoretical and empirical approaches to characterize unpredictability Each of these issues presents important challenges for measurement models and analytic approaches that account for such complexity. How to develop standardized quantifications and measures of caregiver unpredictability is just as challenging as the conceptual question of defining it (Hodson, 2021). In the following sections, we present three major approaches that, collectively, provide some insight into each of these challenges.

Life history theory and environmental statistics
Evolutionary biology and life history theory suggest that species can support a range of phenotypes in response to environmental conditions, increasing the likelihood of survival and reproduction (Ellis et al., 2017;Nettle et al., 2013;Young et al., 2020). There is no "single best" strategy to adapt to the environment successfully. Strategies vary as a function of both social and physical parameters of the environment, such as food availability, neighborhood safety, and caregiver sensitivity (Ellis et al., 2017;Frankenhuis et al., 2013). Adaptation involves the coordination of life-history strategies (e.g., timing of puberty) and environmental conditions with specific statistical structures (Ellis et al., 2022). The statistical structure of an environment is determined by how physical and social parameters vary over space and time, across and within generations, and the extent to which cues (experiences or events) provide reliable information about current and future conditions (Frankenhuis, Nettle, et al., 2019;Young et al., 2020).
Several studies have used the life history model to compare the effects of environmental harshness versus unpredictability during development (Wu et al., 2020;Young et al., 2020). In Western societies, cues of harshness have included low socioeconomic status, direct and indirect experiences of violence (e.g., witness a shooting, gang activity), and parental maltreatment (Belsky et al., 2012;Ellis et al., 2022). Cues that signal unpredictability have been operationalized as frequent changes in physical or structural conditions of harshness, such as residential transitions (housing instability), inconsistent parental employment status (job instability), and caregiver's sequential partners in the home (family instability; Belsky et al., 2012;Simpson et al., 2012). Overall, these studies suggest that unpredictability favors fast-life history strategies, that is, evidence for heightened risk-taking and accelerated sexual development, relative to those seen in more predictable contexts (Usacheva et al., 2022). Research has shown that, beyond absolute levels of harshness experienced, familial, and ecological conditions reflecting such ancestral cues of unpredictability predict a variety of adverse child and caregiver outcomes in Western societies (Ellis et al., 2022). These include more externalizing behaviors (Doom et al., 2016;Hartman et al., 2018), lower emotional control (Szepsenwol et al., 2021), earlier and more frequent sexual risk-taking Usacheva et al., 2022), poorer quality of adult relationships (Barbaro & Shackelford, 2019), and diminished parental investment or quality of relationship with offspring (Belsky et al., 2012;Szepsenwol et al., 2015). The life history model has not been precise about how to operationalize unpredictability, Hence, Young and colleagues (2020) proposed to quantify environmental unpredictability using environmental statistics, which is particularly relevant to the challenge of statistical and perceived unpredictability (issue #1). Describing unpredictability in statistical terms could reduce ambiguity and encourage measurement precision and knowledge accumulation among different research groups interested in unpredictability (Frankenhuis & Walasek, 2020;Haslbeck et al., 2019;Young et al., 2020). Their focus has mainly been on quantifying unpredictability of physical features of the environment or distal cues. We posit that environmental statistics also can be used to quantify caregiver unpredictability, while acknowledging that it may be more challenging to apply this framework to aspects of the social environment.
Evolution and development are processes of adaptation operating on different timescales (Frankenhuis, Nettle, & Dall, 2019). We restrict our focus to individuals detecting and developmentally adjusting to environmental unpredictability across developmental time. Further, predictability is relative to a spatial and temporal scale (Fenneman & Frankenhuis, 2020). Here, we will focus exclusively on temporal unpredictability of caregiver behavior and affect within the lifetime of children. Our perspective is aligned with the statistical learning approach to encoding unpredictability, wherein learning and development are guided by an individual's ability to generate models of the statistical structure of the environment through an ongoing computational process using lived experiences as raw data.

Temporal features of predictable environments
Young and colleagues (2020) encouraged researchers to describe the definition of unpredictability (stochastic variations or changes in harshness; Ellis et al., 2009) in formal statistical terms. As alluded to in issue #1 (statistical and perceived unpredictability), seemingly unpredictable environments might be characterized as less versus more predictable depending on the extent to which variation is patterned across time, for instance, because present conditions are similar to the near future . Predictability will increase when it can be characterized by regular patterns allowing for predicting future behaviors (Ram & Gerstorf, 2009). In statistical terms, the degree of predictability of any parameter will depend on patterns with respect to time and the parameter's autocorrelation.
In the caregiving context, variability refers to deviations from a caregiver's mean (average expression of the parameter across time). This is often denoted as "within-person variance," and is indicated by indices of intraindividual variability of behaviors or affect across different timescales (e.g., from seconds to years; Ram & Gerstorf, 2009). For example, if variability in a caregiver's sensitivity is high, it means that it varies widely from very sensitive to insensitive across time. However, this will not necessarily reflect unpredictability, as caregiver's sensitivity might be contingent upon identifiable factors associated with the passage of time (Lazarus et al., 2021). Repeatedly measured variables often exhibit nonstationarity, such that distributional characteristics (e.g., mean, variability, and autocorrelation) might change across time (Molenaar & Campbell, 2009). This can produce consistent or predictable patterns of variability, which can be divided into two general groups: trends and cycles (Lazarus et al., 2021). Trends capture stable directional changes in variability. For instance, over the course of a day, variability of caregivers' positive or negative affect has been shown to increase or decrease depending on daily routines, stress, or time spent with their children (Erbas et al., 2018;Kerr et al., 2021;Musick et al., 2016). Variability can also be seasonal or cyclical, with patterns repeating over time. Therefore, rather than reflecting caregiver unpredictability, time-dependent variability may represent stable fluctuations with consistent temporal patterns.
Even if the variability of caregivers' behaviors or affect is high and does not change as a function of time, it can still be predictable if the degree of autocorrelation is high. This means that present conditions (exhibitions of behavior or affect) are similar to those in the near past and in the near future (Fawcett & Frankenhuis, 2015;Ram & Gerstorf, 2009). In the context of an individual, higher autocorrelation implies that if a person deviates from their mean at a particular occasion, this deviation is likely to persist for longer (Wang et al., 2012). If an autocorrelation is weaker, then deviations from the mean are independent of each other and may change abruptly, indicating higher unpredictability. For example, Ebner-Priemer and colleagues (2015) examined the variability and autocorrelation of hourly affect levels in individuals with borderline personality disorder (BPD). In comparison to healthy participants, those with BPD had greater variability and less autocorrelation of positive emotions, meaning they transitioned abruptly from positive to negative mood states. However, individuals with BPD also had higher autocorrelation of negative moods, such that negative mood states persisted for longer. Thus, autocorrelation differed within the same individual, depending on mood valence (Ebner-Priemer et al., 2015). Results also varied depending on the intervals between measures (Ebner-Priemer & Sawitzki, 2007).
Consequently, when using autocorrelation to evaluate the degree of unpredictability in caregivers' behaviors, researchers should consider three sets of questions. First, at what time scale is caregiver unpredictability operating, and what time intervals of observation are appropriate for capturing this process of interest (Lazarus et al., 2021)? Second, repeated observations of the same person are rarely ever truly independent; in other words, some degree of autocorrelation is typical or expected (Ram & Gerstorf, 2009). Therefore, what degree of autocorrelation in a caregiver's affect or behaviors would be considered normative, and conversely, how low would an autocorrelation need to be before the caregiver's actions would be considered unpredictable? Third, and as discussed in issue #2, whether we should expect an autocorrelation to be domain general, stable across different domains of behaviors or situations for a given caregiver, or to be more domain specific, as indicated in the work of Ebner-Priemer and colleagues (2015), remains an open question.
Altogether, variability can be decomposed into different parts that will determine its unpredictability: The absence of patterns with respect to time and low autocorrelation. Applying this framework to social aspects of the environment such as caregiver-child relationships is more complex, since caregiving both influences and arises from characteristics of the child. Thus, the statistical structure of the caregiving environmentits levels, variability, and autocorrelationmight vary depending on the time period chosen to measure, across different domains of behavior (issue #2), and the co-determination of unpredictability between both members of the dyad (issue #3, Frankenhuis, Nettle, & Dall, 2019).

Cue reliability in predictable environments
Individuals can encode unpredictability using both ancestral cues of environmental qualities and statistical learning, including caregiving (Burgess & Marshall, 2014;Young et al., 2020). Considering the former, reliable ancestral cues are events or experiences that provide information about the current or future state of the environment (Frankenhuis et al., 2018). Within life history theory, the human brain evolved to quickly detect and efficiently respond to reliable cues for setting up developmental trajectories. To have shaped our species' physiological and psychological mechanisms of development, caregiver-related experiences would have needed to occur with sufficient frequency across human evolution (Frankenhuis & Amir, 2022). Within current relationships, these caregiver-related experiences would convey information that could shape children's biobehavioral developmental trajectory accordingly. For example, across evolutionary time, the presence of a responsive caregiver might have been an ancestral cue of a safe environment for the child, which when experienced today, would confer a slower life history trajectory . However, it is difficult to know what constituted "responsive caregiving" in our evolutionary history, or what other aspects of caregiving were most meaningful for infants and children in eons past (Frankenhuis & Amir, 2022).
From a statistical learning perspective, the regularity of dyadic contingent exchanges may be an informative cue of environmental predictability to the child. Across the first year, infants' developmental changes across cognitive capacities support the formation of mental models about their caregiving system (Beebe et al., 2016;Sherman et al., 2015). Contingent exchanges between caregivers and children might be sources of information about the environment, as infants depend on their caregiver to regulate their primary needs (Beebe et al., 2010;. For instance, a responsive caregiving environment may produce an association between "needs þ needs-are-met," fostering infants' mental representation of security that contributes to a rule of regulation regarding the caregiver (Cassidy et al., 2013;Tottenham, 2020). Conversely, a non-contingent environment may create the association between "needs þ needs-are-not-met," and with repetition, these associations may contribute to an affective schema or mental model that contributes to children's ability to forecast caregivers' behavior (Tottenham, 2020).
Overall, children may use caregiver's quality of care as a cue to estimate environmental unpredictability (Belsky et al., 2012;Frankenhuis, Nettle, & Dall, 2019). However, how do infants and children encode these parental cues to generate expectations of their environment? From a statistical learning perspective, Frankenhuis, and colleagues (2013) proposed that infants may use social contingency analysis, that is, conditional probabilities of needs þ needs-are(-not)-met, as informative cues to estimate caregivers' profiles of quality of care (also Cassidy et al., 2013). The higher the cue reliability, the better children can adjust to the current state of their environment and leverage positive autocorrelation to adjust to future states of the environment (Walasek et al., in press;Young et al., 2020). However, stochastic variations in caregiver contingency profiles would likely decrease cue reliability, increasing unpredictability (Bjorklund & Ellis, 2014;Frankenhuis et al., 2013). Thus, fluctuations in caregivers' contingent responses to infants and children may be a cue to environmental unpredictability .
Still, there are some caveats to consider when applying such an approach. As highlighted in the previous section, caregivers' cues may not only influence but also be influenced by infants or children (Bell, 1968;Fawcett & Frankenhuis, 2015). Further, individual differences in infants' and children's proficiency for detecting contingencies may influence perceptions of unpredictability S. C. Johnson & Chen, 2011;Jozefowiez, 2021). Yet, experiences of early life stress such as variation in caregiver responsiveness may alter contingency detection and learning in infants and children (Harms et al., 2018).

Summary and implications
Environmental statistics can be used to quantify variation in caregiver unpredictability across different dimensions and timescales ranging from moment-to-moment to developmental time (Frankenhuis et al., 2018;Frankenhuis, Nettle, & Dall, 2019;Young et al., 2020). Particularly relevant to the theory and measurement of unpredictability, this approach may increase precision (Haslbeck et al., 2019) and knowledge accumulation (Smaldino, 2020) across research groups focusing on different dimensions or levels of unpredictability (issue #2), as statistical concepts can be applied to any source of intensive longitudinal data (see below). By using this approach, the field could reconcile different research findings and refine or update theory in light of new evidence (Borsboom et al., 2021;Frankenhuis & Walasek, 2020), strengthening the validity of the broad construct of unpredictability.
Nonetheless, a collection of challenges requires further attention as the field moves forward and attempts to apply environmental statistics to caregivers' behaviors. These include consideration of which time intervals are appropriate to capture caregiver unpredictability from a statistical learning perspective, what is typical and atypical of a caregiver's behavioral autocorrelation, what are the individual differences in children's ability to detect temporal patterns or cues, and how do these statistics unfold within a dyad where each partner influences and is influenced by the other. Regardless of these challenges (or "realistic noise"; Frankenhuis, Nettle, & Dall, 2019, p. 8), we believe environmental statistics are invaluable tools in dyadic research. For example, intensive and naturalistic measures of dyadic interactions that can produce time-series data are increasingly being used in tandem with larger longitudinal studies, including mobile eye tracking (Pérez-Edgar et al., 2020), wearable physical proximity monitors , and sound-activated audio recording devices (Gilkerson et al., 2017). As an example of research using the latter, Werchan and colleagues (2022) found that 3-month infants living in homes with noise exposure characterized by low autocorrelation (e.g., low predictability) had less sustained attention. Environmental statistics could be applied to such naturalistic time-series data to advance our understanding of dyadic rhythms and to formally quantify unpredictability. We highlight other directions for future research using environmental statistics to measure and understand caregiver unpredictability in Table 2. Pairing formally quantified unpredictability with procedures evaluating social information processing such as visual habituation paradigms that probe infants' or young children's expectations about their caregiver (S.C. Johnson et al., 2010) could be used to examine infants' and young children's perceptions of social contingencies. This would provide insightful information on the degree to which statistics of the environment correspond (or not) to perceptions of unpredictability (issue #1). The use of these procedures could help to shed light on how infants and young children process social information and make predictions about the behavior of their caregivers.

Shannon's information theory and entropy of maternal sensory and mood signals
One specific body of unpredictability research has focused on how patterns of care, or the provision of care without a consistent or organized rhythm, shape children's behaviors and neurobiology (Baram et al., 2012;Chen & Baram, 2016). A guiding premise of this work is that unpredictability of maternal sensory signals and mood influence the development of emotional and cognitive circuitry with important implications for children, adolescents, and even adult psychopathology (Davis et al., 2017;Howland et al., 2021). This has been termed unpredictability of sensory signals in humans, or fragmentation in rodent models (Davis et al., 2017). Entropy, an approach to characterize the randomness of stochastic processes, is used to quantify unpredictable maternal signals or fragmentation. Entropy quantifies the average information required to predict a future observation given a previous observation.
Although entropy is used here as a measure, it is not an atheoretical construct. In 1948, Claude Shannon at the Bell Telephone Laboratories proposed a mathematical theory of the engineering of communication, giving rise to information theory (Shannon, 1948). Shannon and Weaver (1949) suggested that the engineering (e.g., patterns of information) of communication is also relevant to the semantic aspects (e.g., meaning, content, valence) of communication. From this perspective, information is not equal only to its meaning, but also to the degree of randomness of an ensemble of messages that any given source will produce. The degree of randomness is quantified using entropy, with higher values indicating more unpredictability (Shannon & Weaver, 1949). Below, we present three different ways in which entropy has been used to characterize organization and predictability in caregiver and caregiver-child interactions.
Quantifying entropy rate of maternal sensory signals Caregiver unpredictability has been quantified using entropy rate of maternal sensory signals during infancy (Davis et al., 2017, using cross-species research to explore causal physiological mechanisms by which unpredictability influences infant and child Development and Psychopathology development. Using the limited bedding and nesting rodent model to induce unpredictability in dams, pups raised with unpredictable dams have enhanced anxiety-like behaviors and anhedonia, aberrant functional connectivity between reward and fear circuits, and memory-related disruptions through structural changes in the hippocampus related to elevated basal corticosterone levels (see Glynn & Baram, 2019 for a review).
These studies suggest that fragmented maternal care in rodents affects the development of biological systems that underlie internalizing-like behaviors (e.g., reward circuits) and memory-related disruptions through structural changes in the hippocampus. In humans, unpredictability of sensory signals, that is, the unpredictability of a caregiver's auditory, tactile, and visual inputs, has been calculated from a semi-structured 10-minute play episode. Infants experiencing higher unpredictability at 6 months had worse effortful control at 1 year of age, and this association persisted until 9.5 years of age (Davis et al., 2017, even after accounting for socioeconomic status and maternal sensitivity. Mirroring findings in rodent models, infants who experienced more unpredictability had poorer performance on a hippocampus-dependent memory task 4 years later and during late childhood and early adolescence (Davis et al., 2017;Granger et al., 2021). Unpredictability during infancy partially mediated the relation between maternal sensitivity and children's cognitive development (Davis et al., 2017).
In these studies of rodents and humans, caregiver unpredictability was quantified using entropy rate of maternal behavior. In rodents, entropy rate captured the degree of certainty in predicting dam's behaviors towards her pups (e.g., licking and grooming, nursing), and in humans, entropy rate reflected the certainty in predicting caregiver's next sensory behavior based on their current behavior (e.g., vocalization, touch). Greater certainty indicates a more organized process, whereas greater uncertainty indicates a more disorganized process. There is a subtle but important distinction between entropy rate and autocorrelation with regard to their dependency on time 1 . When applying autocorrelation to caregiver behavior, one measures the extent to which caregiver behavior at time t depends or is correlated to earlier behaviors (t-1, t-2, t-3 : : : t-n). Conversely, entropy divides caregivers' behaviors into discrete states that can be independent of time, such that current behavior t depends only on t-1 (Feutrill & Roughan, 2021).
Another convergent feature of these studies of rodents and humans is that maternal behavior was recorded continuously as time-series on a second-to-second basis. Entropy rate of rat dams' behaviors was measured by assessing seven behaviors continuously during 50-minute windows twice a day for 8 days, and entropy rate of human maternal sensory signals was measured during 10minute free play sequences, in which the caregiver's visual, auditory, and touch behaviors were coded continuously. In both rodents and humans, this sequence of behaviors was modeled as Table 2. Future directions on caregiver and caregiver-child unpredictability Method Environmental statistics 1. Identify specific neurodevelopmental and behavioral adaptations to "objective" caregiver unpredictability as indicated by environmental statistics versus adaptations to children's "subjective" perceptions of their caregiver's unpredictability, as evaluated using developmentally-appropriate measures (e.g., visual attention paradigms, questionnaires).
2. Using environmental statistics and naturalistic data, investigate whether proximal experiences of volatility (e.g., noise exposure) and unpredictability in action outcomes (e.g., responses to children utterances) differentially impact emotional and cognitive development.
Entropy 1. Expand animal models manipulating proximal (e.g., fragmentation) and distal (e.g., transient food insecurity, Lin et al., 2022) unpredictability to identify causal effects on behavioral, physiological, and brain development while controlling for genetic and other environmental factors.
2. Leverage existing longitudinal and panel studies with caregiver mood data and use causal inference methodologies (e.g., marginal structural models) to determine whether (1) distal unpredictable experiences (e.g., income volatility) are related to caregiver mood entropy and whether (2) proximal and distal cues of unpredictability lead to distinct neurodevelopmental changes from infancy to adolescence.
Dynamic Systems Theory 1. Examine the emergence and consolidation of individual and dyadic unpredictability employing an attractor framework (e.g., accounting for phase transitions) and state-space grid methodologies from infancy to early childhood.
2. Explore differences in children's biobehavioral regulation as a result of unpredictability in differently valenced aspects of caregiving, including rewarding (e.g., praise, encouragement, responsiveness) versus aversive experiences (punitive and harsh behaviors). Integrative directions for future research 1. Compare and contrast the nature of proximal caregiver unpredictability across the three different methods in the same samples to (1) identify shared and unique features and (2) evaluate whether the unique features captured by each method differentially influence cognitive, emotional, and neural development.
2. Identify sensitive periods for cognitive and emotional neurodevelopment to different "types" of caregiver unpredictability (e.g., sensory signals during infancy, affect and mood during early childhood) and evaluate the extent to which there is continuity or discontinuity in caregiver unpredictability across time, aspects, and situations.
3. Use acute societal stressors (e.g., natural disasters, massive layoffs) as natural experiments to determine whether the (1) distal unpredictability causally increases the likelihood of caregiver unpredictability (individual or dyadic) and (2) whether the timing of distal and caregiver unpredictability has distinct impacts in neurobehavioral adaptations across development.
4. Identify environmental and individual factors strongly linked to likelihood of caregiver and caregiver-child unpredictability to include in screening, intervention or policy relief efforts.
1 Autocorrelation examines temporal dependency of continuous processes with "long term memory" (e.g. current behavior t can depend from behavior that happened a long time ago, t-5). Conversely, entropy examines its organization by dividing the process into discrete states that can be independent of time, such that the dependence on past observations is low or non-existent, having "short term memory" (e.g., current behavior t depends only on t-1; Feutrill & Roughan, 2021). To quantify entropy, a probability distribution is needed. a first-order stationary Markov chain . The following assumptions are central to this Markov model: (a) Proximal future states (e.g., at time t) depend exclusively on their most recent past state (e.g., t -1), such that each sequential transition is independent of preceding and following transitions. Therefore, the best guess of the next caregiver behavior is based solely on her current behavior. (b) The probability distribution is stationary or independent of time (Lichtenberg & Heck, 1986;Vegetabile et al., 2019), such that the probabilities of occurrence of different outcomes are the same from the beginning to the end of the sequence. To our knowledge, entropy findings have been replicated across two independent cohorts of humans, linking unpredictable patterns of maternal sensory signals with worse effortful control years later (Davis et al., 2017. By very closely matching the task demands and coding processes for rodent studies that involved experimental manipulation to those of the human study that did not involve experimental manipulation, convergent findings across these two approaches indicates a greater likelihood of potential causal mechanisms at play in humans as seen in the experimental task with rodents. When attempting to translate this approach to observational data across a range of interaction tasks, researchers need to consider threats to internal and external validity imposed by the two assumptions detailed above. To date, sensory unpredictability has been measured using 10 minutes of free play with a standard set of toys in a carefully controlled laboratory setting. This method balances task duration, valence, and setting to comply with the assumption of stationarity . However, suppose that the interaction paradigm researchers are interested is a frustrating timed task for caregivers and children (e.g., a 5-minute impossible puzzle task). Behaviors will likely vary as a function of time, since caregivers and children might get frustrated and change the range of their behaviors as they rush to complete the activity. Thus, the probability distribution at the start of the activity is likely different than at the end, affecting the entropy rate and undermining internal validity. Further, the external validity of this approach, that is, the extent to which entropy findings can be generalized to "the real world" is yet to be explored. External or ecological validity is a well-known issue for carefully controlled laboratory tasks that are, by their nature, not reflective of naturalistic settings. Hence, more research is needed to establish the ecological validity of unpredictability as elicited or observed in laboratory tasks. Overall, predictability might be activity-and context-dependent, such that caregiver's entropy rate might vary depending on the nature of the activity they are performing and the environment they are in .
It is important to stress that this body of works examines sensory signals, as infants' brains are especially susceptible to this type of input (Luby et al., 2020). As such, entropy rate is estimated only in one member of the dyad (the caregiver) since it is calculated on a univariate sequence of sensory inputs to the child. Sensory signals are not necessarily comparable to other domains of caregiving, such as affect or regulatory behaviors. In fact, it is unclear whether the persistent impact of unpredictable patterns of caregiver sensory signals during infancy are a result of early disruptions exclusively and/or due to stability of caregiver unpredictability, either in sensory signals or in affective or regulatory behavioral interactions, as described in the issues of timing (#4) and domains and specificity (#2). Focusing on affect and regulatory behaviors naturally raises questions regarding their dyadic nature (#3). Caregivers develop affective and behavioral patterns as early as infancy, based on a back-and-forth with the child (Beebe et al., 2016;Feldman, 2021;Provenzi et al., 2018). Infants experience a wide spectrum of emotions, and their emotional variability influences caregivers' affect and behaviors (Montirosso et al., 2010). Beyond infancy, children increasingly become more active agents in daily coregulation processes (Feldman, 2015). Therefore, is sensory unpredictability stable throughout development and related to affective or behavioral interactions between caregivers and their children? In other words, is unpredictability domain-general, being continuous throughout development and expressing similarly across different features of caregiving?
Quantifying entropy of dyadic interactions using state-space grids Unpredictability of dyadic interactions has been measured by applying Shannon's entropy to state-space grids (SSGs) (Coburn et al., 2015;Dishion et al., 2004;Sravish et al., 2013). SSGs were introduced to analyze socioemotional behavior in a dynamic system framework and have primarily been used to analyze dyadic interactions in real-time (Hollenstein, 2007;Lewis et al., 1999). Using real-time observations, SSGs plot a dyad's trajectory across a grid of all possible behavioral combinations (Granic & Hollenstein, 2015). These grids are a graphical representation of a dyadic state-space, and each cell of a grid represents a specific combination or a joint state between caregiver and child (see Figure 1). Any time the dyad moves around each cell, a line is drawn from the previous point to the next, ultimately "drawing" a trajectory representing content or valence (occurrences and duration in joint states of behaviors or affect) and structure (patterns of change) of a particular interaction (Granic & Hollenstein, 2015).
Current SSG programs estimate visit entropy, calculated using transitional probabilities between dyadic states under the same assumptions as the entropy rate of sensory signals: stationarity and first-order sequences (Dishion et al., 2004;Granic & Hollenstein, 2015;Hollenstein, 2007). Entropy is often used as an index of dyadic flexibility/variability, which is supposed to capture how members in a dyad adapt to each other's behaviors (Hollenstein, 2007;Sravish et al., 2013;van Dijk & van Geert, 2015). Only two studies have examined caregiver-infant interactions using entropy, with inconsistent results. Entropy was positively related to mutual reciprocity and dyadic adaptive regulation during a 5-minute frustrating task (Coburn et al., 2015) and to infant negativity during a still-face paradigm (Sravish et al., 2013). Altogether, dyadic unpredictability can be measured using entropy of SSG, examining the role of both mother and child as equal contributors to shifts between states. However, researchers should refrain from making the a priori assumption that dyadic entropy is adaptive (or conversely, maladaptive), or apply it to tasks where the probability distribution is likely to change over time.
Quantifying entropy of maternal mood A distinct approach to studying the entropy rate of maternal mood is by applying Shannon's entropy to mood questionnaires Glynn et al., 2018). Each individual's responses to a specific questionnaire are transformed into a probability distribution based on the frequency of each response choice (see Glynn et al., 2018 for details). Maternal mood unpredictability, measured by applying Shannon's entropy formula to mothers' mood questionnaires, was hypothesized to indicate mood unpredictability (Glynn et al., 2018). Prenatal mood entropy was positively associated with intraindividual variability of maternal daily negative affect reported with EMA (convergent validity). It was unrelated to the entropy of a physical activity questionnaire (discriminant validity), discarding the alternative explanation of entropy being a tendency to answer all questionnaires in an unpredictable manner. Prenatal mood entropy predicted children's greater negative affectivity and poorer cognitive development at 12 months, 24 months, and 7 years of age (Glynn et al., 2018;Howland et al., 2021). Further, it was associated with child-reported anxiety and depressive symptoms at 12 years, even after accounting for possible confounds such as SES, cohabitation with the child's father, and prenatal and postnatal average mood levels (Glynn et al., 2018). Thus, maternal mood entropy appears to be a distinct risk factor possibly, affective unpredictabilitythat confers myriad risks to children's healthy development. To provide an empirical example of the validity of using this method of examining entropy of maternal mood as indicative of affective unpredictability, we used archival data assessing depressive symptoms in young mothers via questionnaires and examined the relation of mood entropy to emotion dysregulation and ecological momentary assessments of mothers' daily positive and negative emotions; please see supplemental material for results.
Exactly what mood entropy reflects and how it increases risk for psychopathology or disrupts cognitive development is unclear. It has been suggested that it might reflect trait-like mood instability and lack of emotional clarity (Glynn et al., 2018). Additionally, the fact that prenatal mood entropy is prospectively associated with developmental outcomes over and above postnatal experience suggests that the underlying biological substrates of this mood profile might influence the intrauterine environment (Demers et al., 2021) or that there might be genetic underlying characteristics that contribute to the variance both in caregiver mood entropy and children's development (Hannigan et al., 2018).

Summary and implications
Specific effects of entropy of maternal sensory signals in offspring's biobehavioral development are found in rodent models (Bolton et al., 2018;Gallo et al., 2019;Molet et al., 2016) and in human research (Davis et al., 2017Noroña-Zhou et al., 2020). Some of these findings also have been observed with entropy of maternal prenatal mood (Glynn et al., 2018;Howland et al., 2021). These associations remain even after adjusting for quality and quantity of care (e.g., maternal sensitivity) from infancy through early adolescence. Robust cross-species findings, replicability across cohorts, and initial replicability of mood entropy with our data (see supplements) are only some of the strengths of this line of work. Nonetheless, more research is needed to explore issues of domains and specificity (issue #2), timing (issue #4), and its dyadic nature (issue #3), extending caregivers' sensory unpredictability to behavioral and affective domains beyond and test whether the child's influence is relevant to caregiver entropy (Montirosso et al., 2010).
Future work should aim to establish ecological validity of entropy by testing short-term reliability and continuity across contexts of observation, including settings (e.g., lab and home) and situations (e.g., playing, daily routines). Maximizing ecological validity by measuring behaviors in ways similar to those in the "real world" will increase the match between measures and the broader construct of interest (unpredictability) as it occurs in day-to-day life (Gunther et al., 2022). To avoid statistical violations, researchers should make well-informed decisions about time constraints and task demands for each observation and by testing the stationarity of the behavior sequence (or states when using visit entropy) if treated as an ordinal times series (Keller et al., 2007). Table 2 includes more specific directions for future research in the realm of entropy, such as including cues of distal unpredictability in current animal models focusing on fragmentation. Altogether, this body of work has substantially increased our knowledge of the neurobiological and behavioral effects of early unpredictability, introducing new measures for characterizing caregiver unpredictability.
A dynamic systems approach to unpredictability in the caregiver-child relationship According to DST, variability and organization are intrinsic properties of development, providing theoretical and corresponding methodological instruments to describe the nature of dyadic interactions (Lunkenheimer et al., 2011). We propose that key DST concepts presented below can be applied to examine the degree of unpredictability of caregiver-child interactions, allowing us to distinguish valence and content of behaviors from their patterns and organization to evaluate domains and specificity (issue #2) in individuals or dyads (issue #3). It is important to note that, in contrast to prior work, DST has not been explicitly used to measure unpredictability. DST suggests that system variability (e.g., intraindividual variability, dyadic variability) is a driving force of change and a crucial source of information throughout development. Self-organizing systems become "patterned forms emerging from variability" over time (Lewis, 2011, p. 1). A self-organizing system will naturally generate internal order, developing recurrent patterns of behaviors that become increasingly coherent and predictable through developmental time (Granic & Patterson, 2006). These patterns are Figure 1. Example of state space grids of affect of two caregiver-child dyads. The left grid depicts a relatively flexible dyad (more variability) and the right grips portrays a relatively rigid dyad (less variability). Caregiver affect is plotted on the x-axis and child affect on the y-axis. Whenever there is a change in either person's affect, a new point is plotted on the grid, and a line is drawn to connect the new point to the previous point.
called attractors that a system will gravitate to, increasing its stability and predictability. Behaviors converge in attractors in realtime, at a scale of seconds to minutes, but the emergence and consolidation of an attractor occur over developmental time, across months and years (Lewis et al., 1999). A key signature of a dynamic system is its stabilitythe extent to which multiple patterns of behaviors range from unstable to stable. More stable patterns tend to be more predictable and resist change (Granic & Hollenstein, 2015). However, these stable, predictable patterns need to dissolve and reorganize to move development forward (Smith & Thelen, 2003). Phase transitions are system-wide reorganizations in which periods of stability and predictability are followed by disequilibrium and reorganization. During a phase transition, real-time behavior is highly variable and sensitive to perturbations from the external environment (Granic & Hollenstein, 2015).
Using attractors to characterize unpredictability in the caregiver-child relationship Dyads are inherently dynamic and flexible across situations and developmental stages, yet dyads also are self-organizing, ultimately stabilizing into a limited range of coherent interactions and behavioral patterns (Fogel, 2011). These emergent, predictable patterns of interactions or behaviors represent an attractor. Attractors can vary in domain and valence, leading to different outcomes in children and dyadic relationships. Examples include positive feedback loops between infants cooing and maternal mirroring that foster the emergence of conversational exchanges and creative play (Lavelli & Fogel, 2013), child-directed speech in lower income households decreasing from the beginning to the end of a month as financial pressures increase (Ellwood-Lowe et al., 2022), or coercive cycles of children's noncompliance and caregiver hostility (Granic & Patterson, 2006).
Attractors can also vary in depth (strength), and we posit that shallow (weak) attractors could indicate a higher degree of unpredictability in the caregiver-child relationship. If attractor strength is weak, patterns of behaviors should be unstable across contexts and exhibit high degrees of variability without discernible patterns of change (Hollenstein, 2007). Using sensitivity of real-time interactions as an example, the sensitive behaviors of more unpredictable caregivers might be intermittent, varying in their duration of expression, or across contexts that are potentially eliciting of sensitivity (Ainsworth et al., 1974;Lewis et al., 1999).
DST indicates that shallow attractors are more reactive to perturbations (Granic & Hollenstein, 2003). Therefore, more unpredictable caregivers would take longer to self-organize or return to a baseline state after a perturbation. Dyadic paradigms often introduce a stressor as a perturbation (e.g., "you have one minute to finish the activity"). For instance, Sravish and colleagues (2013) observed changes in dyadic affective variability in free play before and after the perturbation of maternal unresponsiveness, using a still-face paradigm. Variability increased significantly following the still-face for all dyads, but it did so more strongly for depressed caregivers. Thus, caregiver depression was related to a shallow attractor state for dyadic affect.
It is important to note that change is a necessary part of development and periods of heightened unpredictability might be normative. Dyadic patterns may destabilize during phase transitions (e.g., toddlerhood) and become more variable, eventually settling into a new predictable pattern (Granic & Hollenstein, 2015). Thus, repeated samples of behaviors may be needed to discern whether increased variability or shallow attractors are transitory products of the developmental stage or change, rather than an enduring characteristic of the dyad. Altogether, conceptualizing unpredictability in the caregiver-child relationship as a collection of shallow attractors is one way to operationalize the construct of unpredictability, providing a specific set of indices that may better characterize variation in unpredictability. This attractor framework can be applied to any data with intensive repeated measures, including video recorded observational data and ecologically momentary assessments.
Exploring dyadic unpredictability using state-space grids To increase our understanding of dyadic unpredictability specifically, we propose that variations in dyadic unpredictability could be captured by combining contingency and dyadic variability measures under a DST framework using SSGs Lunkenheimer, Skoranski, et al., 2020). Contingency is the consistent pairing of caregiver and child states (affect and behavior codes) via temporally dependent sequences (Cole et al., 2009;. Contingency is estimated using the average transitional probability between a specific pair of behaviors or expressed affect within a dyad (e.g., the probability that a child follows a command after a caregiver provides a command). Higher probabilities indicate more robust contingency or predictability of behavior between both partners (Lunkenheimer et al., 2017). In a dyad exhibiting a high degree of contingent affect-behaviors, current states are reliable cues to future states for both members. In a dyad exhibiting a low degree of contingent affect behaviors, current states are not reliable cues to future states for both members. Thus, contingency allows children and caregivers to develop expectancies of sequences of events and coherent day-to-day experiences (Beebe et al., 2016;Cassidy et al., 2013). Conversely, dyadic variability is operationalized as the number or rate of transitions between different cells in a SSG.
We propose that contingency and variability, if considered simultaneously, may be used to reveal dyadic unpredictability, with the degree of unpredictability evident from an interaction of low contingency and high variability. More unpredictable dyads would have higher behavioral variability coupled with lower probability of contingency of their behaviors. Although one could argue that variability and contingency on their own might constitute indices of unpredictability, the principles of environmental statistics and entropy suggest the contrary. Variability is not necessarily random, as trends and autocorrelation might increase predictability. Considering contingency on its own, if dyadic behavior is low in contingency, any given behavior from either partner is an unreliable cue of future behavior within the dyad. However, even with low contingency, making the best guess of the next dyadic behavior is easier for dyads with low behavioral variability, in comparison to dyads with high variability. Therefore, dyads exhibiting a greater number of behaviors (higher variability), none of which is a consistent or reliable indicator of the subsequent behavior (low contingency), could be prone to interactions that rarely settle into predictable patterns (Busuito & Moore, 2017). An empirical example illustrating this joint consideration of contingency and variability is provided in the supplemental materials.
Summary and implications DST concepts and methods, such as attractors and SSGs, may serve as lenses to examine caregiver unpredictability, or more precisely, unpredictability in the interactions and relationships between caregivers and children. The DST framework describes patterns and variation of behaviors and can be flexibly used to examine individuals or dyads (Hollenstein, 2007;van Dijk & van Geert, 2015).
Rather than focusing on the presence or absence of specific behaviors, DST centers on their organization: How, when, and where do they unfold. In addition, patterns are not bounded to the valence and overall quantity or intensity of these behaviors and can be examined independently. This method can tap both the content (e.g., sensitivity, positive versus negative affect) and the patterning of behavior, regardless of content (e.g., the latency of responses, temporal patterns; Granic & Hollenstein, 2015). As expressed in issue #2 (domains and specificity), it is not clear whether the impacts of unpredictability differ based on the valence of experience (e.g., aversive or rewarding), just as dyadic variability can impact preschool children differently depending on the valence of the content Lunkenheimer, Skoranski, et al., 2020). Focusing exclusively on interaction patterns, without regard to interaction contents, may obscure the meaningful contribution of precisely what is being communicated and experienced within these patterns . Examining the contribution of patterns, and the combination of both patterns and contents of caregiver or dyadic unpredictability, are future steps for the field that may be facilitated by using DST methodologies. Although these propositions are yet to be tested, we highlight how DST can be integrated to future research on caregiver unpredictability in Table 2.

Conclusion
There has been considerable progress in understanding the roles of unpredictability for brain maturation, cognitive and socioemotional development, and psychopathology. Theoretical consensus has emerged about its unique influence in shaping children's experience, distinct from other sources of adversity. Nonetheless, the field still lacks theoretical and empirical common ground given difficulties in conceptualizing and measuring environmental and caregiver unpredictability. Four key issues were presented. First, concepts that fall under the umbrella of unpredictability may occur in temporally predictable patterns . Yet, how children perceive these experiences and make meaning of unpredictability is unknown (Smith & Pollak, 2021a). Second, it is important to consider the specificity of unpredictability in the caregiver-child relationship, as it might vary within and between individuals depending on valence (i.e., positive or negative), input (i.e., sensory or affect), and levels (i.e., caregiver unpredictability or caregiving within an unpredictable environment). Third, unpredictability is likely a product of each individual's predictability as well as interactive patterns between caregiver and child (Beebe et al., 2016). Fourth, its characterization and effects will likely change in concert with the dyad's development . Each of the issues increase theoretical and measurement complexity, particularly when we aim to establish construct validity and reconcile different research findings and refine or update theory in light of new evidence (Borsboom et al., 2021;Frankenhuis & Walasek, 2020).
The three empirical approaches reviewed in this paper can inform each other to advance theory and research on caregiver unpredictability, particularly when considering the four issues identified in this paper. We highlight concrete, integrative directions across these three approaches for future research in Table 2. Considering issue #1 (statistical and perceived caregiver unpredictability), environmental statistics and entropy are ways to model the statistical properties of children's proximal environments. When paired with visual habituation paradigms that probe infants' or young children's expectations about their caregiver (S.C. Johnson et al., 2010) or with reliable retrospective measures of perceived unpredictability such as the Questionnaire of Unpredictability in Childhood , we can probe whether both aspects map onto each other within the same caregiver or dyad. Identifying whether, which and when children perceive (report, habituate) unpredictability in caregivers who display "truly" (observed and statistically demonstrated) unpredictable behaviors might enlighten several questions about the developmental biobehavioral implications of experiences and/or cognitions of unpredictability (Baldwin & Esposti, 2021;Danese & Widom, 2020;Rivenbark et al., 2020).
Regarding issue #2 (domains and specificity of unpredictability), using each of these approaches to model unpredictability at multiple levels and across different aspects of the caregiving environment might advance our knowledge of the why and how of unpredictability. Regarding the why, did developmental systems evolve to respond and adapt to different forms of unpredictability in similar or different ways? For example, using environmental statistics with naturalistic data of language and noise exposure, researchers could probe into the distinct behavioral outcomes of a volatile environment indicated by noise exposure (Werchan et al., 2022) from unpredictability in action-outcomes indicated by the inconsistency of child-initiated conversational turns . Whereas the former fosters present-oriented behaviors such as impulsivity, the latter fosters future-oriented behaviors such as information seeking (Fenneman & Frankenhuis, 2020;Munakata et al., in press). Therefore, both might be adaptive depending on the type of unpredictability that is experienced. Regarding the how, do the neurodevelopmental consequences of unpredictability vary as a function of the domain of unpredictability? We proposed to extend the concept of entropy to include different features of the caregiving context such as affect and behavior, and the integration of DST methods to disentangle both patterns and content of caregiver or dyadic unpredictability. Using these methods in tandem might unveil the extent to which caregiver unpredictability and its impact on neurodevelopment is domain-general, expressing similarly across different inputs or features of caregiving, or domain-specific, evident in specific inputs or valences. Altogether, using these approaches might help us understand why and how unpredictability and its impact on development varies between and within caregivers or dyads as a function of the particular inputs and the valence of such inputs (Lunkenheimer, Skoranski, et al., 2020).
In relation to issues #3 and #4, DST and state-space grids may be particularly useful for disentangling the extent to which unpredictability is an emergent dyadic quality across time. Implementing SSG-based quantitative approaches within longitudinal designs might inform how children calibrate development to both immediate environments concurrently and broader contexts in the future (Ellis et al., 2022). Such approaches could take into account the continuity or discontinuity between different aspects of proximal cues of unpredictability (e.g., entropy of caregiver mood) and their relation to distal cues of unpredictability (e.g., caregiver's job loss), and could identify whether there are sensitive periods for the adverse effects of unpredictability in distinct aspects of maternal or dyadic behavior (e.g., sensory signals versus emotional cues).
Overall, comparing and contrasting the quantification of unpredictability across these different methods using the same sources of information will clarify whether they provide distinct or complimentary perspectives to better understand variation in caregiver and caregiver-child unpredictability. As with other domains of the caregiving environment, unpredictability might be better understood as a continuum (King et al., 2019 where both very high and very low degrees of predictability may lead to maladaptive outcomes, as several studies converge on an optimum midrange model (Beebe et al., 2016;Granic & Lougheed, 2015;Lunkenheimer, Hamby, et al., 2020). Accurately measuring unpredictability will allow us to properly investigate which external and internal factors foster caregiver unpredictability, opening different avenues for intervention.
In the context of DST, we could also think about unpredictability from outside to within: Unpredictable events such as residential or intimate partner transitions are perturbations in a system a dyad or a caregiver. Families experiencing disadvantage are those most likely to lack stable, predictable, and well-structured environmental conditions (Pollak & Wolfe, 2020;Yoshikawa et al., 2012). Future work should integrate and attempt to bridge both macro and micro perspectives: caregiver unpredictability in the cultural and societal context in which this relationship is unfolding. The reason is two-fold. First, dyads do not exist in a vacuum, but in complex ecological niches with unique environmental demands that the dyad has to adapt to (Bronfenbrenner, 1999;Nketia et al., 2021). Focusing solely on the dyad may contribute to biased interpretations about the nature of caregiver unpredictability and how children develop in response to such environments, while ignoring structural determinants that may be driving caregiver unpredictability (Hastings et al., 2022). Greater attention to diversity and variation in caregiver unpredictability within and across cultures can provide insights into the ways in which aspects of "adverse" caregiving are socially constructed and processed, influencing well-being and psychopathology in the developing child (Frankenhuis & Amir, 2022).
Relatedly, studying dyads in a vacuum obscures the roles and responsibilities of society and public policy to support children and caregivers . Therefore, as the field moves forward, care must be taken to ensure measures of caregiver unpredictability are not only reliable but also ecologically valid and culturally sensitive (DeJoseph et al., 2021;Humphreys et al., 2021), considering the demands of the dyad environment, the cultural and societal structures in which the dyad is embedded, and structural determinants of development (Hastings et al., 2022). For instance, Liu and Fisher (2022) highlight the COVID-19 pandemic as an example of an unpredictable event that strongly impacted the caregiving environment, but to varying degrees across communities with different resources and histories of adversity. Similarly, massive forced migration and large-scale natural disasters expected from climate change might increase a sense of unpredictability and helplessness for caregivers and their children, particularly for already-vulnerable populations (Masten et al., 2021;Wuermli et al., 2021). Applying methodological and quantitative approaches to examining unpredictability within caregiver-offspring relationships in the context of the pandemic and the climate crisis could be informative for understanding the nature of the effects of distal and proximal unpredictability in caregivers and their children. Even after periods of crisis, elucidating protective policy pathways to ensure caregiver stability, such as universal child allowance (Shaefer et al., 2018), universal health coverage (Doan & Evans, 2020), and "grid" resilience to disasters (e.g., restoring power to maintain communications, household temperature, supply chains, and internet systems to support social and education continuity; Masten et al., 2021) may enhance prevention efforts that put systems in place to ensure continuity and stability in children's lives.
In this article, we identified three approaches to address the conceptualization and measurement of caregiver unpredictability. Each of these novel approaches has theoretical and statistical limitations to consider, challenging data collection procedures, and labor-intensive data processing, yet we have argued that their methods have strong potential for advancing the study of caregiver unpredictability in developmental science. Additionally, we advocate for greater consistency in the terms, metrics and statistical approaches used in these efforts. Doing so will make comparison and integration of findings across different working groups more manageable and likely to occur, reduce ambiguity and encourage knowledge accumulation, and ultimately advance our understanding of the implications of caregiver unpredictability for children's development.