Opinion
Bayesian Models of Development

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Bayesian models of development offer a simple and tractable way to model how information from ancestors (e.g., via genes or parental effects) combines with information from a series of personal experiences over the lifetime to affect the development of phenotypic traits.

Bayesian models show how individuals’ naive prior distributions and subsequent cue exposures limit developmental plasticity and generate individual differences in plasticity.

Current Bayesian models make novel predictions about developmental plasticity and developmental trajectories, some of which are already supported by empiricists.

Even in the absence of any costs of plasticity, Bayesian models predict that limited developmental plasticity and individual differences in plasticity will be widespread if individuals make optimal developmental decisions based on the information that is available to them.

Until recently, biology lacked a framework for studying how information from genes, parental effects, and different personal experiences is combined across the lifetime to affect phenotypic development. Over the past few years, researchers have begun to build such a framework, using models that incorporate Bayesian updating to study the evolution of developmental plasticity and developmental trajectories. Here, we describe the merits of a Bayesian approach to development, review the main findings and implications of the current set of models, and describe predictions that can be tested using protocols already used by empiricists. We suggest that a Bayesian perspective affords a simple and tractable way to conceptualize, explain, and predict how information combines across the lifetime to affect development.

Section snippets

Why A Bayesian Framework for Development?

A basic premise in biology is that the phenotype of an organism is, at least to some extent, based on its estimates of variables in the external environment 1, 2. Theory suggests that information about the external environment can come from the genes of an organism 3, 4, parental effects 5, 6, and the many types of personal experience that can occur over the course of a lifetime. The question, then, is how information from all of these sources combines across ontogeny to affect the development

Variation among Bayesian Models of Development

Although Bayesian models of development are based on shared assumptions (Box 1), they also differ in important ways. Two-state models assume that all possible states of the world fall into two discrete categories (e.g., high food versus low food) 7, 8, 11, 12, whereas continuous models assume that many possible states vary continuously between minimum and maximum possible values (e.g., the level of danger) 9, 10. Two-state models are analytically simpler and more tractable, and provide a useful

Factors Affecting Bayesian Updating

Here, we use ‘E’ to refer to an individual's current point estimate of the state of the world, and ‘ΔE’ to indicate the difference between the prior and the posterior as a result of exposure to a given cue, stimulus, or experience (Box 1). ΔE provides the foundation for any Bayesian model of development 2, 15, which share the assumption that changes in E encourage changes in phenotype. Of course, many factors besides ΔE can also affect trait development, including the benefits and costs of

Specific Predictions of Bayesian Models of Development

Current Bayesian models make several interesting predictions about patterns of potential and realized developmental plasticity and developmental trajectories (Box 2).

Limited Plasticity and Individual Differences in Plasticity

Bayesian models help shed light on one of the most contentious questions in modern biology: why organisms do not exhibit ‘perfect’ plasticity 31, 53. Most theoreticians have explained limited plasticity and individual differences in developmental plasticity by invoking costs of plasticity 31, 54, but, despite considerable effort, empiricists have had difficulty documenting such costs 53, 54, 55. Less attention has been paid to the ways that information might limit the evolution and expression

Future Directions: Somatic State in Bayesian Models

Most current Bayesian models of development focus exclusively on the effects of information on development. However, experiences early in life can affect development not only because they provide information about the external world, but also because they have direct effects on an individual's somatic state (i.e., its body size, strength, motor skills, or other enduring aspects of the phenotype with broad implications for fitness) [57]. Thus far, only one Bayesian model [12] has predicted the

Concluding Remarks

An emerging trend in ecology and evolution is to model developmental plasticity and developmental trajectories using Bayesian updating. Here, we have reviewed the current set of Bayesian models and shown that these make several predictions, some of which are already supported by empirical data. As more Bayesian models of development are generated and tested, the value of the approach will become increasingly clear. Our prior estimate is that Bayesian approaches might become as central to the

Acknowledgments

The authors would like to thank Sinead English, Marc Mangel, Karthik Panchanathan, Barbara Taborsky, and Fritz Trillmich for their comments and suggestions on previous drafts. This research was supported by a Veni grant from the Netherlands Organization for Scientific Research (NWO) (016.155.195) awarded to W.F.

Glossary

ΔE
the difference between E for the prior and E for the posterior as a result of exposure to a given cue.
Confidence
an individual's level of confidence (degree of belief) in its current estimate of the state, E. In two-state models, confidence is determined by the value of p: lowest for p = 0.5, and highest for p = 0 or p = 1. In continuous models, confidence can be represented by the variance of the prior or the posterior.
Cue
a stimulus, experience, or event that can provide information about the

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