Bayes and Darwin: How replicator populations implement Bayesian computations

Bayesian learning theory and evolutionary theory both formalize adaptive competition dynamics in possibly high-dimensional, varying, and noisy environments. What do they have in common and how do they differ? In this paper, we discuss structural and dynamical analogies and their limits, both at a computational and an algorithmic-mechanical level. We point out mathematical equivalences between their basic dynamical equations, generalizing the isomorphism between Bayesian update and replicator dynamics. We discuss how these mechanisms provide analogous answers to the challenge of adapting to stochastically changing environments at multiple timescales. We elucidate an algorithmic equivalence between a sampling approximation, particle filters, and the Wright-Fisher model of population genetics. These equivalences suggest that the frequency distribution of types in replicator populations optimally encodes regularities of a stochastic environment to predict future environments, without invoking the known mechanisms of multilevel selection and evolvability. A unified view of the theories of learning and evolution comes in sight.

Automated summary

This paper discusses the similarities and differences between Bayesian learning theory and evolutionary theory at the computational and algorithmic-mechanical levels. It highlights the mathematical equivalences between their dynamic equations and explores the algorithmic equivalence between sampling approximation, particle filters, and the Wright-Fisher model of population genetics. The paper emphasizes the importance of the frequency distribution of types in replicator populations for predicting future environments.