Abstract
Recently, there has been much interest in characterizing statistical properties of natural stimuli in order to better understand the design of perceptual systems. A fruitful approach has been to compare the processing of natural stimuli in real perceptual systems with that of ideal observers derived within the framework of Bayesian statistical decision theory. While this approach has provided a deeper understanding of the information contained in natural stimuli as well as of the computational principles employed in perceptual systems, it does not directly consider the process of natural selection, which is ultimately responsible for design. We propose a formal framework for analyzing how the statistics of natural stimuli and the process of natural selection interact to determine the design of perceptual systems. The framework consists of two components. One is a standard Bayesian ideal observer with a utility function appropriate for natural selection. The other is a Bayesian formulation of natural selection. In the Bayesian formulation of natural selection, each allele vector in each species under consideration is represented by a fundamental equation, which describes how the number of organisms carrying that allele vector at time t+1 is related to (1) the number of organisms carrying that allele vector at time t, (2) the prior probability of a state of the environment at time t, (3) the likelihood of a stimulus given the state of the environment, (4) the likelihood of a response given the stimulus, and (5) the birth and death rates given the response and the state of the environment. The process of natural selection is represented by iterating these fundamental equations in parallel over time, while updating the allele vectors using appropriate probability distributions for mutation and sexual recombination. We show that simulations of Bayesian natural selection can yield new insights, for example, into the co-evolution of camouflage and color vision. Supported by NIH grants EY11747 and EY02688 to WSG and DC00427 to RLD.