The Complexity of Childhood Development: Variability in Perspective

The Good, the Bad, and the Neutral

Although variability can represent inconsistency and errors, not all variability in performance is necessarily detrimental to the outcome. Consider, for example, the tasks of picking up an object or having to navigate a sloping surface. In order to grasp a delicate object without dropping or crushing it, children need to accurately scale their load and grip forces to the characteristics of the object.¹⁴ Similarly, in order to navigate a sloping surface safely without picking up uncontrollable momentum, children need to adapt step frequency and step length to find the proper balance between their skill level and the steepness of the slope.¹⁵ These kinds of variations in performance reflect necessary adaptations to changes in the biomechanical properties of the growing musculoskeletal system or changes in the environmental conditions. The resulting variability in performance is essential to preserve the outcome and thus can be considered functional or “good” variability.

Another example of functional variability is having a variety of strategies available to accomplish the same task, thereby increasing the flexibility of performance. Examples of this can be found in locomotion, where children can choose to crawl, walk, or run across a room,^9,10,16 or in throwing a ball, which can be done bimanually, unimanually, underhand, or overhand,¹⁷ depending on, for example, skill level or motivation. Functional variability also is found when different components that contribute to performance counterbalance each other's variations so as to secure the outcome. An example of this type of variability is found in expert marksmen, where variable shoulder and wrist movements complement each other, thereby stabilizing the pistol and thus the aim on a target.¹⁸ Good variability in performance, therefore, is useful, and it is not necessary or even desirable to try to minimize it.

In contrast, variability in performance also can hurt the outcome and even cause insurmountable problems. This is the case in most precision tasks such as aiming and microsurgery, but it also can happen in everyday tasks such as locomotion. A newly walking child can easily become overwhelmed with the complexity of the new undertaking, and variability in postural control, muscular activity, and limb movements inevitably adds up to repeated falls.^19,20 Several months earlier, when this child was on the brink of reaching for an object, variability in movement control likewise presented severe problems. The child's flailing arm movements typically ended up colliding with the object or missing it all together.²¹ This kind of “bad” variability in movement control impairs performance and can result in falls, missed targets, or other failures to achieve the desired outcome. Minimizing bad variability is thus a must for reliable performance.

Finally, we can observe and measure a good deal of variability in performance that neither helps nor hurts the outcome. There may be small variations in effectors used, muscles activated, or forces generated, without any of these variations improving the performance or decreasing the consistency of the outcome. This kind of variability thus can be classified as being “neutral” to the performance and can be ignored without compromising the outcome. The big question is: When we come across variability in our observations and measurements, how do we know which kind of variability it is?

The Structure of Variability

There are several methods available for measuring the amount of variability, such as the standard deviation of a variable or coefficient of variation, but how can we judge the quality of variability? Preferably, we should have an analysis method that can allocate instances of variability to the appropriate good, bad, and neutral bins. Ideally, we should be able to do this without additional concern or knowledge about the person, the context, and the task. Unfortunately, no such method exists, not in the least because most variability we come across is person-specific, task-specific, and context-specific. Unless we know who was trying to do what and under which circumstances, how could we judge either the performance or its variability? When looking at a trail of footprints, for example, lack of step-to-step variability might be indicative of the exquisite skill of a tight-rope artist, or the rigid stereotypy of a clinical patient. Likewise, the presence of step-to-step variability may reflect the flexible adaptation of a hiker using stepping stones to cross a river, or the clumsy first steps of a wobbling, newly walking infant. What methods do we have available to help us judge the quality of variability?

An obvious place to start when trying to understand the quality, or structure, of variability is by separating variability in execution variables from variability in outcome variables. As long as the outcome is preserved and the task is accomplished, variability in execution is either functional or harmless—in other words, good or neutral. Furthermore, when execution variables co-vary so as to stabilize the outcome, they share a functional relationship called a “synergy.”²² This is the starting point for the so-called uncontrolled manifold concept, a computational method for distinguishing good variability from bad variability in a given task by identifying controlled and uncontrolled variables.²³ Consider, for example, the simple task of exerting a specific amount of force using 2 fingers. As long as force changes in one finger are complemented by equal but opposite force changes in the other finger, the 2 fingers together will produce a stable force output. Similarly, pointing at a target can be achieved by many different configurations of the shoulder, elbow, and wrist joints. The combination of all configurations that lead to accurate pointing form the task solution or manifold. Variability that occurs along the manifold provides flexibility without increasing outcome variability or decreasing accuracy of pointing.^22,23 In contrast, variability away from the manifold leads to increased outcome variability and errors in pointing. The uncontrolled manifold concept is an elegant and promising tool that enables quantification of synergies and has led to important insights regarding the structure of variability and strategies of motor control. However, its application requires that the functional relationship between execution and outcome variables be known, implying major simplifications and the use of rather artificial tasks.²²

Clinical applications so far have been limited as well but produced some promising results. For example, the higher variability in motor patterns displayed by people with Down syndrome generally is interpreted as a bad thing. However, using the uncontrolled manifold concept, Black and colleagues²⁴ were able to show that part of this increased variability was surprisingly functional and contributed to the body's stability during treadmill walking. Similarly, underneath the difficulty people with poststroke hemiparesis have in reaching with their affected arm, strong multijoint synergies are nevertheless present to stabilize the path of the hand across reaches.²⁵ In contrast, the higher variability seen in elderly people in a 4-finger force production task turned out to reflect an impaired ability to coordinate individual digits, which may be a factor contributing to generally degraded performance of everyday manual tasks.²⁶

As the previous examples illustrate, increased variability can reflect an underlying problem but also the solution to a problem, stressing again the need to consider the structure of variability and not just the amount. A second approach highlighted here focuses on the structure of variability in terms of its complexity. Two such complexity measures in particular have provided valuable results with respect to clinical assessment and differentiation of healthy from pathological conditions: the Lyapunov exponent and approximate entropy.^27,28 The Lyapunov exponent measures stability by quantifying the rate of separation or divergence of initially close movement trajectories. Rigid, repetitive movements are characterized by overlapping trajectories that do not diverge, indicated by a maximal Lyapunov exponent close to zero. This finding points to minimal change in the structure of variability and a highly regular, predictable system with little or no flexibility. Lyapunov exponents for random white noise, on the other hand, are considerably larger, whereas those for complex, flexible systems are in between these 2 extremes.

The second measure, approximate entropy, quantifies the degree of regularity or predictability in a time series. Values close to 2 represent maximum irregularity and independence between data points, such as in white noise, whereas values close to zero reflect maximum regularity and dependence between data points, such as in a periodic signal. Again, values in between these 2 extremes reflect complex systems with some, but not complete, dependence between data points, thereby allowing the system to balance between flexibility and stability.

Both measures have provided important new insights about movement function and dysfunction. For example, the typical initial instability of infants learning to sit was shown to be not just noise and random wobbling, but to contain elements of orderly patterns and early strategies for postural control.²⁹ In a similar study of infants with typical versus delayed development, the only measure of several that could differentiate between the 2 groups was the Lyapunov exponent. The exponent was smaller for infants with delayed development, indicating that their swaying patterns while sitting were more repetitive and thus less adaptive.³⁰ Studies such as these illustrate that complexity measures can quantify patterns in the variability of performance that range from rigid to chaotic and that a certain amount of variability can be crucial and necessary for the development of new skills.³¹

The third and final approach highlighted here is the fractal analysis approach. Like approximate entropy, it is used to investigate the structure of variability by focusing on complex, interdependent fluctuations in time series. However, unlike approximate entropy, which can be calculated from relatively short time series, fractal analyses require extended time series in order to reveal the hidden structure of variability. Several examples of fractal analysis can be found in the extensive literature on stride-to-stride variability in gait.³² Analyzing the fluctuations of successive stride intervals indicated that these intervals contained long-range, power-law correlations.³³ This finding points to a fascinating characteristic of normal gait: variations in the current step are influenced not only by the immediately preceding step or 2, but by steps at remote previous times as well.³³ In other words, instabilities and perturbations in the current step still reverberate in our gait pattern hundreds of steps later.³² The power-law signature indicates that this influence decays across steps, with nearby steps having stronger influence than faraway steps.

Fractal analyses of stride interval fluctuations have been applied successfully in studies of aging and neurological diseases, leading to important new insights about changes in underlying control processes. For example, gait patterns of elderly people who were healthy were shown to be less fractal and less long-range correlated than gait in younger adults who were healthy. This finding suggests that even healthy aging is associated with gait fluctuations becoming more random and less structured.³⁴ In people with Huntington disease, a similar change toward less correlated and more random gait fluctuations was observed that was directly related to the degree of functional impairment.³⁴ These findings indicate that the functional integrity of the entire system should be an important part of clinical assessment and intervention.

Examples of long-range, power-law correlations also are found in the literature on variability in repeated responses in simple response tasks such as reaction time, interval estimation, mental rotation, and serial and parallel searches.^35,36 Just as stride intervals in gait are correlated over hundreds of steps, so are response times over a thousand key strokes. Recent extensions of this work used wavelet-based multifractal analyses to show that in addition to the long-range correlations, most response series contained a combination of periods with small, regular fluctuations and periods with large, irregular fluctuations that aligned across timescales. This nonhomogeneous structure indicates that variability is multifractal, which is caused by underlying interactions between timescales.³⁷ These interactions and alignment of variability become especially strong when performance is about to deteriorate beyond a critical level, thereby enabling functional adaptations of the system in order to rectify performance.³⁷ In a subsequent study on prolonged, relaxed standing in young adults who were healthy, similar alignment of postural sway variability and interactions between timescales were shown to coincide with shifts in posture that restored balance (Ihlen EAF, Lund S, Vereijken B; unpublished research). These findings suggest that in a healthy system, posture is controlled in an intermittent, ballistic-like fashion rather than continuously.

Current work applies these analyses of (multi)fractal structure and temporal alignment of fluctuations across timescales to different clinical populations. Questions addressed include whether we observe a change from intermittent postural control to more continuous postural control with age and disease, which would inform about underlying changes in motor control. Similarly, the buildup of variability alignment across timescales and the subsequent reaction of the system to rectify performance, or its breakdown, might be changed with age and disease, again pointing to underlying changes in motor function and control.

Increased Consistency in Performance

The best-known change in variability with increased experience and skill is an increase in consistency of performance. With practice, we learn which solutions fit a given challenge, and we learn to further improve upon these solutions. Our movements typically become smoother, more economical, and more proficient, and these improvements, in turn, lead to more consistent outcomes. Newborn infants face a profusion of challenges ahead that need to be tackled with an initially very limited repertoire of skills. Not in the least, they have to figure out that they have a body, what its characteristics are, and how to control its movements.³⁹ The first attempts at any movement are notoriously awkward and often unsuccessful, but infants are nothing if not very persistent. Repeated attempts that literally amount to thousands of trials eventually lead to proficient skills, just as repeated practice improves skills in adult athletes, musicians, and chess players. When 3-month-old infants are supported on a treadmill, their initial stepping movements are irregular and infrequent, and exhibit inconsistent timing between the 2 legs.^40,41 However, even a month of repeated practice induces regular, frequent stepping movements, with consistent alternative phasing between the legs.⁴¹

Around the end of the first year, children taking their first independent steps present an imposing picture of thrashing legs, waving arms, and wobbling upper bodies that repeatedly move outside their limits of stability, resulting in endless crashes to the floor or into loving arms of parents. With increased experience, the upper body is gradually stabilized, the arms increasingly contribute to the task rather than creating disruptive forces, and subsequent steps become more regular and unswerving in a progressively straighter line to the target.^10,42 Looking at the level of the outcome, developmental progression thus is clearly characterized by a decrease in variability. However, underneath the steady decrease in outcome variability and increase in outcome consistency, variability across infants persists. This variability is partly caused by infants having different body anthropometrics and, therefore, different constraints that influence their set of possible solutions.⁴³ In addition, infants have different prior experiences, temperaments, levels of motivation, and so on, each contributing to a range of idiosyncratic solutions across infants and situations. Getting rid of this kind of variability is not a feature of developmental progress, as will be illustrated next.

Increased Flexibility of Performance

As skill level increases as a result of practice and experience, so does the ability to withstand internal or external perturbations. For example, newly walking infants typically do not cope well with sloping surfaces, but repeated practice gradually equips them with the skills and wherewithal to prospectively adapt their posture and gait to these changes in the environment.¹⁵ Similarly, obstacles in the environment are not reliably avoided at first, but children learn to adjust their trunk orientation and footsteps while approaching the obstacle, and later to clear around it in one fluent chain of adjustments.⁴⁴ In adult studies as well, repeated practice leads to increased flexibility of performance. If a top table tennis player initiates an attacking forehand drive slightly later, he slightly accelerates the drive so as to stabilize temporal accuracy of ball/bat contact.⁴⁵ If the shoulder moves too far to the left in expert marksmen, the wrist compensates to the right to secure a steady aim on the target.¹⁸ As was outlined above, in order for this kind of flexibility to emerge, subcomponents contributing to task performance need to be coordinated so that variation in one subcomponent is counteracted by variation in other subcomponents.

The above examples reflect how variability can be functional and increase flexibility at the execution level. In addition, there is functional variability that increases flexibility at the outcome level by having multiple solutions available to achieve the same goal. My colleagues and I came across a striking example of this in an earlier study on crawling, in which we observed no fewer than 25 different patterns of belly crawling.⁹ Across multiple weeks of belly crawling, infants kept coming up with new combinations of body parts to be used for propulsion and support. Even after 10 weeks of crawling on their belly, infants still discovered new patterns they had not displayed before. In sharp contrast to this wealth of available patterns of belly crawling, all infants converged almost instantly to the standard pattern of diagonal hands-and-knees crawling once they lifted their bellies off the ground. This consistency of hands-and-knees crawling may have been induced by the biomechanical constraints of keeping balance in mid-air while moving forward, with a diagonal crawling pattern representing the least destabilizing movement pattern.⁹ By the time we reach adulthood, we have fully developed bodies, a plethora of available skills, and plenty of experience that we can draw upon. Although adults are perfectly capable of displaying variability in outcome, performance often reflects the influence of similar constraints, leading to similar solutions and thus low inter-individual variability.

Variability and Timescales of Analyses

There is an important relationship between issues of variability and timescales of analysis. As was described above, averaging across multiple repetitions of a task deletes variability and all information that is contained in that variability, including its structure. A similar loss of information happens when we study processes of change resulting from development or disease by sampling at coarse intervals. The coarsest interval is the before-and-after snapshot, indicating at best that a change has happened, but stripped bare of all information concerning the trajectory of that change. U-shaped development would be blatantly missed by the before-and-after sampling interval, as would any other information about the shape of developmental change.⁴⁶ The same word of caution applies to studies about variability. Obviously, sampling over increasingly coarser intervals reduces precision and sensitivity to fluctuations in the data. More importantly though, sensitivity is affected in power-like fashion and drops off surprisingly rapidly,⁴⁶ indicating that sampling frequency may need to be as high as costs for the researcher and taxation for the subjects permit. Furthermore, the relationship among variability at different timescales can be highly informative. When measures of variability (such as standard deviation or variance) across increasingly frequent sampling intervals reach an asymptote, the sampling frequency is sufficient to capture the phenomenon of interest, and further increases in sampling frequency will not reveal further detail. When measures of variability increase linearly with increasing sampling frequency, the underlying structure is characterized by a 1/f power relationship.⁴⁷

Finally, when measures of variability do not converge to a limit with increasing sampling frequency, the underlying structure is fractal.³⁷ Looking at the rate at which variability changes across different sampling frequencies thus provides valuable information about the complexity of the underlying control system and how densely spaced data collections should be in order to capture it.

Variability and Selection

The first theoretical perspective draws upon Darwin's insight that variation is necessary for selection to take place and for species to evolve. Edelman based his theory of brain development and function, or neuronal group selection, on the same idea of variation and selection.^48,49 The cornerstone of Edelman's theory is that organisms start with enormous neural diversity in terms of cell type, number, and connectivity. This neural diversity forms the raw material for subsequent experience-based selection. Neurons that fire together wire together,⁵⁰ and dense, reciprocal connections between neurons gradually lead to the formation of neuronal groups.⁴⁸ The temporal and spatial coherence of sensory input signals leads to sensations that are correlated across perceptual domains. Continued perceptual and motor experience molds the brain by selecting and strengthening certain neuronal groups while deselecting and weakening other groups of neurons that are less adaptive for the task at hand.⁴⁸ Sporns and Edelman⁵¹ applied this framework to early motor development, postulating that the brain's initial structural variability allows for the dynamic variability that is seen in the many different possible outputs of the system. The infant's initial spontaneous movements form a basic repertoire from which movements can be selected as a solution to a given task. With continued selection and subsequent feedback, movements become more and more adaptive to ongoing changes in biomechanical characteristics or environmental demands.⁵¹

The application of Edelman's theory of neuronal group selection, particularly the ideas about variation and selection, has led to interesting hypotheses and new insights in clinical research. For example, the reduced variation typically seen in children with cerebral palsy or developmental coordination disorder might be caused by a limited repertoire of neuronal networks or impaired selection.⁵² Furthermore, recent developments in studies of preterm infants suggest that diffuse damage of the cerebral white matter might be associated with an overall reduction in movement variability and an increase in stereotyped behavior.⁵³ On the account of variation and selection, variability is thus necessary and a hallmark of normal development, whereas the lack of variability can be indicative of neurological and developmental disorders. Clinical interventions in these cases should be geared toward helping children to increase the variability of their repertoire and stimulating them to create and explore a variety of possible solutions.

Variability and Transitions

Few theoretical approaches are as well equipped to handle processes of change in complex systems as dynamic systems theory. Originally developed in physics and mathematics to study the emergence of organized patterns in complex systems, it has found broad application in fields as diverse as biology, weather systems, and the stock market. The basic tenet of dynamic systems theory is that interactions among the elements of a system give rise to patterns that are organized in space and time without the need for instructions or prescriptions, so-called self-organization. The formed patterns can be envisioned as attractors in a landscape of possible organizations.⁵⁴ Changes from one attractor to another are made possible by destabilization of the current attractor and a subsequent transition to a new attractor. Most importantly in the current context, decreasing stability of an attractor is accompanied by an increase in the variability of that pattern, which subsequently facilitates change to a different pattern. An upcoming transition thus is signaled by increased variability. In contrast, lack of variability traps the system in a specific attractor, leading to rigid stability.

One of the first proponents of a dynamic systems approach to child development was Thelen.^40,55 She used the ideas and principles of dynamic systems theory as an inspiration for unusual study designs and alternative interpretations of well-known phenomena. For example, by adding little weights to the legs of newborn infants or submerging their legs in water, she was able to reinterpret the U-shaped development of infant stepping as a reflection of asynchronous growth of leg mass and muscle strength rather than cortical inhibition of infantile reflexes.⁵⁶ Similarly, a series of reaching experiments led to a reinterpretation of the classic “A-not-B error”⁵⁷ in terms of reaching dynamics, particularly perseveration, rather than invoking the concept of object permanence.⁵⁸ Dynamic systems approaches to development acknowledge the complexity of childhood by placing environmental, physical, and biomechanical factors, as well as the child's prior history and experiences, on a par with neural and genetic factors as potential explanatory factors. This feature in particular has led many empirical and applied developmental researchers to embrace dynamic systems approaches, and their work shows that reduced variability and increased rigidity can indeed be indicative of disease and disorders.^59,60 Again, clinical practice in this spirit would welcome variability, and seek to increase it, as a necessary condition for flexibility and developmental progress.

Controlling and Exploiting Variability

As indicated above, Bernstein¹³ noted that variability was part and parcel of human movement, irrespective of amount of experience or level of skill. He realized that all movements take place in an environment, and as the details of the environment change from one repetition to the next, so must the details of the repeated performance. He labeled these performance changes “context-conditioned variability” and made it one of the central issues in his work on motor control.

Another central issue that Bernstein¹³ highlighted was the abundance of degrees of freedom or movement possibilities of the musculoskeletal system. Many different configurations can be used to accomplish a task, but is this a curse or rather a blessing? Bernstein¹³ formulated explicit hypotheses about how the nervous system can handle the abundant degrees of freedom so that they do not pose a problem at the beginning of a learning process and can be utilized later when expertise has increased. He postulated 3 learning stages that were later corroborated by empirical evidence. In the first stage of learning, the control problem is simplified by reducing the number of degrees of freedom by freezing them or coupling them rigidly together.⁶¹ This reduction in degrees of freedom often is visible as stiffening of posture and excessive levels of coactivation during movement, as in a child trying to use new skates for the first time.

As learning progresses, the learner can explore additional degrees of freedom and increasingly incorporate them in the task solution, thereby adding flexibility to the performance.⁶² Stiffening and coactivation decrease, and movements become more fluent and integrated. When multiple degrees of freedom become functionally linked together so that they behave as a single unit in order to stabilize task performance, they are referred to as a “coordinative structure.”¹³

In the final stage of learning, expertise has progressed to a level where reactive forces are no longer fought or resisted but actively exploited within the coordinative structures.⁶³ Although most empirical research on learning observes evidence for one or more of these stages, the stages are not obligatory. Whether or not a learner freezes degrees of freedom is influenced by the need or desire to stay in control over reactive forces,⁶ and we do not necessarily reach the expert stage of exploitation in every single task we set out to learn. Depending on where one is in the learning process, the abundance of degrees of freedom thus can be either a curse that needs to be minimized or a blessing that can be exploited.

The decreases and increases in degrees of freedom closely parallel the observed decreases and increases in variability across development and learning. The child's initial lack of control over an abundance of degrees of freedom leads to high variability in performance and little consistency.⁶⁴ When degrees of freedom are eliminated in order to minimize disruptive reactive forces, the variability of performance likewise is reduced.⁶⁵ Exploration of degrees of freedom leads to an increase in performance variability,⁹ whereas successful exploitation of degrees of freedom leads to increased flexibility and reduced outcome variability. Variability thus can be both a curse and a blessing, depending on one's ability to control it. On this account, developmental progress is not aimed toward reducing variability, but toward learning to control and exploit variability.

Although this framework has not been applied extensively in clinical settings, findings on 2-handed ball catching in children with developmental coordination disorder confirm that they demonstrate tighter intralimb and interlimb couplings and reduced flexibility in motor behavior compared with age-matched controls.⁶⁶ There also is some evidence of changing levels of stiffness and exploration across the development of walking in toddlers with Down syndrome.⁶⁷ When encountering increased variability in clinical populations, the practitioner thus should carefully evaluate whether it is part of the solution, indicated by underlying structure in the variability as in infants learning to sit,²⁹ or part of the problem, indicated by a lack of underlying structure and poor consistency of performance, such as in individuals with an ataxic movement disorder.³¹ Further investigations of controlling and exploiting variability in clinical settings would be useful and might help pinpoint underlying problems of and possible solutions to coordination and motor control.