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 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.Enjoy.

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 fitness ideal observers and Bayesian natural selection. We then demonstrate the Bayesian approach by simulating the evolutionof camouflage 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.

## Tuesday, November 23, 2004

### My Best Pharyngula Impression

OK, so I'm no PZ Myers. Hell, I'm not even a biologist. That doesn't mean I can't post about evolution, does it? Well, I guess it does, so I'm not even going to try to write something about evolution research. Instead, I'm just going to refer you to a paper that I found very interesting when I read it a couple years ago. I'm not really qualified to evaluate the paper's claims, so I won't even do that. You'll have to check out "Bayesian natural selection and the evolution of perceptual systems" for yourself. Here's a passage from the introduction, just to give you an idea of what the paper is all about:

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