Balancing sampling and specialization: an adaptationist model of incremental development

Abstract

Development is typically a constructive process, in which phenotypes incrementally adapt to local ecologies. Here, we present a novel model in which natural selection shapes developmental systems based on the evolutionary ecology, and these systems adaptively guide phenotypic development. We assume that phenotypic construction is incremental and trades off with sampling cues to the environmental state. We computed the optimal developmental programmes across a range of evolutionary ecological conditions. Using these programmes, we simulated distributions of mature phenotypes. Our results show that organisms sample the environment most extensively when cues are moderately, not highly, informative. When the developmental programme relies heavily on sampling, individuals transition from sampling to specialization at different times in ontogeny, depending on the consistency of their sampled cue set; this finding suggests that stochastic sampling may result in individual differences in plasticity itself. In addition, we find that different selection pressures may favour similar developmental mechanisms, and that organisms may incorrectly calibrate development despite stable ontogenetic environments. We hope our model will stimulate adaptationist research on the constructive processes guiding development.

Figure 1.

Reliance on sampling. The horizontal axis depicts the prior probability distribution, reflecting the likelihood of being born in one state of the world or the other. The vertical axis depicts the cue validity, the probability of sampling a particular cue, given a particular state of the world. Fitness correlates with the degree of specialization in a (a) diminishing, (b) linear or (c) increasing fashion. The contour lines show the expected fraction of ontogeny spent sampling cues (as opposed to specializing), following the optimal developmental programme. These expectations are taken across the two environmental states, and across individuals.

Figure 2.

Optimal developmental programmes. The horizontal axis depicts ontogeny. The left, vertical axis depicts the degree of belief of being in World 1. The right, vertical axis depicts the difference in the numbers of cues sampled to each state of the world. Fitness correlates with the degree of specialization in a (a–c) diminishing, (d–f) linear or (g–i) increasing fashion. Sampled cues (a,d,g) weakly, (b,e,h) intermediately, or (c,f,i) strongly indicate the environmental state. Organisms begin ontogeny with a prior probability distribution, reflecting the evolutionary distribution of environments (here, the prior is 0.5; see the electronic supplementary material, appendix S2 for other priors). In each time period, the organism makes one decision: black represents sampling, blue specializing towards phenotype 1 and red specializing towards phenotype 0. The area of a circle is proportional to the probability of reaching a particular state. Within a time period, these areas sum to one. The beige lines represent developmental pathways. The thickness of a line is proportional to the probability of having reached the source state from which the line emanates multiplied by the probability of reaching the destination state.

Figure 3.

Distributions of mature phenotypes. The triangular plots show phenotypic distributions at the end of development, obtained by simulating 10 000 individuals who follow the optimal developmental programme. To see what a field researcher might observe in a particular ecological setting, we fixed the environment to state 1. Each column of plots depicts a specific cue validity, (a,d,g) 0.55, (b,e,h) 0.75 and (c,f,i) 0.95. Fitness correlates with the degree of specialization in a (a–c) diminishing, (d–f) linear or (g–i) increasing fashion. The evolutionary prior is 0.5, meaning that organisms are equally likely to develop in either environmental state (see electronic supplementary material, appendix S3 for other priors). Phenotypes are characterized by three numbers: the number of sampling bouts (top corner), the degrees of specialization for environment 1 (lower left corner) and environment 0 (lower right corner). The shading of a circle is proportional to the posterior belief: dark represents certainty of being in World 1, white of being in World 0 and grey uncertainty. The areas of circles are proportional to fractions of individuals. Individuals on the right side of the triangle are miscalibrated (i.e. specialized for environment 0 despite developing in environment 1). The number inside the triangle represents the fraction of correctly calibrated specialists: the number of correctly calibrated individuals (left side of the triangle) divided by all the specialists (left and right sides). Generalists, organisms partially specializing for both environments (bottom side), are left out of this fraction.

Figure 4.

Fitness of the optimal policy. We compare the optimal developmental programme against a ‘specialist’, which adapts from birth towards the more likely prior environmental state, and a ‘generalist’, which specializes halfway towards each phenotypic target. For each subplot, the lower right axis depicts a range of priors the lower left axis depicts a range of cue validities, and the vertical axis fitness. The (a,d,g) left column of plots shows the expected fitnesses of the optimal developmental programmes. The (b,e,h) centre and (c,f,i) right columns show the fitnesses of the (non-sampling) specialist and generalist strategies as fractions of the optimal policies' fitnesses. When this fraction equals one, the optimal policy is equivalent to the non-sampling strategy. The top row of plots depicts (a–c) diminishing fitness returns, the middle row (d–f) linear returns, and the bottom row (g–i) increasing returns.