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. The 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 correspondenc e (geisler@psy.utexas.edu). formulation, each allele vector (i.e. each instance of a polymorphism) 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: (i) the number of organisms carrying that allele vector at time t; (ii) the prior probability of a state of the environment at time t; (iii) the likelihood of a stimulus given the state of the environment; (iv) the likelihood of a response given the stimulus; and (v) 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. Our proposal draws upon two important research traditions in sensation and perception: ideal observer theory (De Vries 1943; Rose 1948; Peterson et al. 1954; Barlow 1957; Green & Swets 1966) and probabilistic functionalism (Brunswik & Kamiya 1953; Brunswik 1956 ). After reviewing these two research traditions, we motivate and derive the basic formulae for maximum tness ideal observers and Bayesian natural selection. We then demonstrate the Bayesian approach by simulating the evolution of camou age in passive organisms and the evolution of two-receptor sensory systems in active organisms that search for prey. Although we describe Bayesian natural selection in the context of perceptual systems, the approach is quite general and should be appropriate for systems ranging from molecular mechanisms within cells to the behaviour of organisms.
The difference is that REF provide a formal framework based on Bayesian statistical decision theory, whereas the current work explores empirically a set of specific constraints or shortcuts that seem to dominate visual feature development and thus should be incorporated in the formal framework.
Bayesian natural selection and the evolution of perceptual systems
Philosophical transactions of the Royal Society of London. Series B, Biological sciences
Philosophical transactions of the Royal Society of London. Series B, Biological sciences
Medicine Biology