Bayesian natural selection and the evolution of perceptual systems

Abstract

In recent years, 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 form of optimization theory 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. Here we propose a formal framework for analysing 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 complementary components. The rst is a maximum tness ideal observer, a standard Bayesian ideal observer with a utility function appropriate for natural selection. The second component is a formal version of natural selection based upon Bayesian statistical decision theory. Maximum tness ideal observers and Bayesian natural selection are demonstrated in several examples. We suggest that the Bayesian approach is appropriate not only for the study of perceptual systems but also for the study of many other systems in biology. BACKGROUNDThe evolution of a species occurs as the result of interactions between its environment and its genome. Thus, achieving a rigorous account of evolution depends as much on understanding the properties of environments as it does on understanding the properties of nucleic acid and protein chemistry. Although many laws of nature are usefully described in deterministic terms, the complexity of evolution often requires a description of both environments and genetics in statistical/probabilistic terms. Research in the areas of population genetics and theoretical ecology has emphasized genetics and its relationship to natural selection. However, recent advances in measuring the statistical regularities of natural environments, especially in the area of perceptual systems, raise the possibility of developing more complete theories of evolution by combining precise statistical descriptions of the environment with precise statistical descriptions of genetics.Here we show that a constrained form of Bayesian statistical decision theory provides an appropriate framework for exploring the formal link between the statistics of the environment and the evolving genome. The framework consists of two components. One is a Bayesian ideal observer with a utility function appropriate for natural selection. The other is a Bayesian formulation of natural selection that neatly divides natural selection into several factors that are measured individually and then combined to characterize the process as a whole. In the Bayesian * Author for correspondence (geisler@psy.utexas.edu). formulation, each allele vector (i.e. each instance of a polymor...

A Bayesian approach to the evolution of perceptual and cognitive systems

“…In population genetics the focus is on the statistics of genetic variation within and across species and how those statistics change over time. Bayesian natural selection also focuses on the statistics of genes, and it is consistent with basic formulas in population genetics (Geisler & Diehl, 2002); however, its unique contribution is to place a corresponding emphasis on the statistics of natural environments and to provide a formal representation of the interactions between the environment and genome.…”

“…Here, we mention only one of these factors: Evolution through natural selection is an incremental process where each change must produce an increase in fitness; thus the real observer may correspond to a local maximum in the space of possible solutions, whereas the ideal observer corresponds to the global maximum in the space of possible solutions. Geisler and Diehl (2002) proposed an extended Bayesian framework to represent these additional factors that may limit performance. The framework consists of two complementary components: a maximum-fitness ideal observer theory that allows inclusion of specific anatomical and physiological constraints, and a Bayesian formulation of the theory of natural selection referred to as "Bayesian natural selection."…”

“…In addition to co-evolution, we also simulated situations where the predator evolved stable polymorphisms of allele vectors (Geisler & Diehl, 2002). In both cases, we found that the predator's visual system converged to the optimum defined by a maximum-fitness ideal (A) This plot shows the effect on the prior probability (at equilibrium) of a prey (a target) being within detection range of an individual predator, as a function of the nominal birth-rate of the predator.…”

“…This would be a correct inference under "normal ordinary conditions" because self-motion, unlike object motion, is usually accompanied by bodily cues and by retinal motion over a large fraction of the visual field. Such stimulus factors, which were treated informally by Helmholtz, are rigorously specified in the Bayesian framework by prior probability and likelihood distributions (Freeman, 1994;Knill, Kersten, & Yuille, 1996;Yuille & Bülthoff, 1996;Brainard & Freeman, 1997;Geisler & Diehl, 2002; also see Fig. 2).…”

“…(1)), this is a very abstract description, and thus most of the scientific effort will come in applying the framework to specific cases. To begin exploring how the framework might be applied, we (Geisler & Diehl, 2002) conducted several simulations of co-evolution for the hypothetical species and environment shown in Fig. 1.…”