Advances in Mathematical Modeling for Reliability

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Natural selection favors systems that tend to construct adaptive phenotypes, which increase fitness. The term fitness is often used to denote individual survival and reproduction. However, fitness should actually be assigned to developmental systems or strategies, genotypes , not to individuals, and the appropriate measure of fitness depends on the environmental context and species. Individuals change over time, depending on influences internal e. Models describe such changes using state variables , which quantify the current state of the individual and predict its future state, if only probabilistically.

State variables can represent any factor of interest. For example, a model of growth might describe the composition of the body using variables representing skeletal size, bone density, muscle mass, fat levels, the types of tissues present and their degree of differentiation, patterns of gene methylation, brain wiring, hormone levels, receptor densities, and so on. Each variable takes on a specific value, which might change over time. Age is typically not a state but rather a crude aggregate measure, because individuals of the same age might be in different developmental and physiological states.

Developmental models require an initial state , which depends on the research question. For models of epigenetics, the initial state could specify which genes are methylated or hormone levels inherited from parents; for models of social learning, an individual's knowledge before any social interactions have occurred. State changes occur throughout the lifetime, but early changes are often the most important. These may have lifelong effects.

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To understand the fitness consequences of early developmental responses, it is necessary to take later effects into account. Models describe developmental processes by changes in the values of state variables. Because development in real organisms is multifactorial i. Even if we know an organism's current state, we cannot predict its next state with certainty. Some sources of stochasticity are internal. If an animal ingests food, it burns some fraction, stores another, and excretes the remainder. We can predict patterns e. Other sources are external. If an animal forages, it might find food, encounter a mate, contract disease, be predated on, or be killed by a rival.

The probabilities of these different outcomes depend on the animal's foraging behavior e. Despite stochastic influences, state changes are not completely at random. The probability that a given change in state will occur e. In particular, an animal might use cues, that is, observations that provide information i. An animal might also estimate future conditions, forecasting the future over the timescale of hours e.

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Cues are often imperfect: They reduce uncertainty but do not eliminate it. Animals also use social cues Taborsky, A potential mate might show courtship cues, which probabilistically predict its willingness to have sex. A rival might show threat signals, which predict its ability to fight. So, what might a model look like? The answer will depend on the environment. We can, for instance, imagine an environment that fluctuates between different states e. These states are autocorrelated over time; that is, this year's level of mortality predicts next year's level but not perfectly.

We may then use an optimization technique to compute optimal developmental strategies, which specify the best decision for every possible state of the developmental system.

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We agree that developmental mismatch can result from changing conditions over ontogeny. However, even evolutionary developmental psychologists often overlook that inferring the present state of the world poses challenges for organisms, just as predicting future conditions does. Such mismatch even occurs when: a individuals have the opportunity to repeatedly sample cues, b individuals obtain cues at no cost throughout their entire lifetimes, and c there is a cost to being mismatched.

These mismatches do not result from malfunction; rather, they are produced by a developmental system responding optimally to noisy inputs in a context it is evolutionarily adapted to. Consider agents that have opportunities that are either profitable or dangerous.

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Before pursuing or declining an opportunity, an agent samples a cue informative about the level of environmental danger. Next, an agent chooses to pursue or decline, following the optimal decision rule which maximizes its expected fitness. If an agent pursues, there is a good or bad outcome, and an agent gains additional information about the level of danger. If an agent declines, however, it does not gain further information e.

Because cues are stochastic, some individuals sample more danger cues than others before making decisions. These individuals may set their sensitivity to threat higher than necessary, becoming overly anxious. Their anxiety, in turn, leads them to decline opportunities, preventing them from learning the environment is actually safe.

A system that has evolved in a variable environment is uncertain about the conditions early in ontogeny.

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Models represent the distribution of environmental states experienced by a species as a prior probability distribution a prior. If a species experienced a narrow range of environmental states, the prior is centered on those states, and the system starts out with a good estimate, if the current environment is still within the range in which the system has evolved. By contrast, if a species experienced a wider range, the prior is more dispersed, and so it will be more challenging for the developmental system to match phenotypes to current conditions.

Note, however, that if an environmental state is truly novel, meaning it has never occurred before in a species' evolutionary history, developing individuals should assign zero probability to it, irrespective of the shape of their priors. Such bet hedging illustrates a point we made earlier: Fitness should be assigned to strategies not to individuals.

Natural selection might result in strategies that produce detrimental outcomes for some individuals. Such mismatch is likely to occur when it is adaptive to commit to a developmental trajectory early in life, even if doing so implies having had few opportunities to learn about the environmental state, thus increasing the risk of mismatch. Committing early might be favored, for example, when it takes time to build conditional adaptations e. A general lesson is that natural selection maximizes the fitness of developmental systems not of individuals , and these systems are likely to produce some mismatched individuals, even when these systems function optimally in a context they are evolutionarily adapted to.

Why do some adopted children adapt swiftly to their new environment, but others remain burdened by their difficult past? Biologists have wondered why all organisms are not Darwinian demons, that is, why they are unable to always perfectly match their brains, bodies, and behavior to the current conditions. Of course, organisms do retain some degree of plasticity in many traits and behaviors throughout their lifetimes.

This degree of plasticity, however, tends to change increase or decrease over the life course, and individuals differ in their trajectories of change. There are several reasons for this variation. Individuals might start out with different priors because they have inherited different information from their distant ancestors e. Priors can differ in their means and variances. Individuals whose ancestors have been exposed to higher levels of harshness e.

Individuals whose ancestors have been exposed to greater environmental variability might adjust more flexibly when their experience is discrepant with inherited information, because their priors are more dispersed. The extent to which experience e. Individuals might sample cues of different reliabilities.

The reliability of a cue depends on its likelihood of occurring in different states of the environment. For example, a child who observes that her entire community suffers from death and disability can draw a stronger inference about environmental conditions i.

The reason is that widespread and severe suffering is unlikely to happen except when conditions are harsh, whereas some occasional suffering could happen even in beneficial conditions, if there is a streak of bad luck due to chance e. Moreover, the extent to which organisms can discriminate between different environmental states depends both on the cue reliability and on the ability of sensory systems to accurately perceive cues. Discrimination is a product of cue reliability discounted by perceptual inaccuracy. Even when classes of cues are reliable and well perceived, individuals might receive misleading instances of those cues by chance variation akin to sampling variation in classical statistics.

As cues are noisy, some individuals will have more consistent experiences than others e.

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For example, when two people live in an affluent neighborhood in which robberies rarely occur, one might be victimized twice, the other never. As both have beneficial experiences as well, the victim overall has more heterogeneous experiences some good and some bad ones.

Hence, this individual might retain more plasticity for longer, adjusting more easily to harsher conditions if their environment changes. In addition to the variation in priors, cue reliabilities, and stochasticity in cues, mathematical models also suggest other factors that should affect the retention and decline of plasticity over the life course.

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This inference, however, is not necessarily warranted. On this view: the organism presets its physiology in expectation of that physiology matching its future environment.


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PARs, therefore, are a form of phenotypic plasticity in which the resulting phenotype is not necessarily advantageous in the environment concurrent with or immediately following the inducing cue, but is likely to be advantageous in an anticipated future environment. The cue thus acts as a predictor of the nature of this environment.

Crucially, the internal—external PAR distinction exists at an ultimate level of explanation evolutionary history and adaptive value and not at a proximate level developmental and physiological processes. Natural selection favors external PARs only when environmental conditions are stable over individuals' lifetimes e. Internal PARs do not require such stability; rather, these require that individuals' somatic conditions are stable over their lifetimes e. If an environment is completely unpredictable, natural selection does not favor external PARs, but it is likely to favor internal PARs, if earlier somatic states are correlated with later ones.

Such somatic autocorrelation exists in many species. Studies in humans, however, suggest that having a good start in life a silver spoon improves fitness more than matching environmental conditions early and later in life e. Perhaps this is because humans are long lived, like the macaques and reindeer, to which we turn next. The females of lower somatic quality engaged in reproductive events at a lower body mass than females of higher somatic quality.

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