Bayes and Darwin: How replicator populations perform Bayesian calculations

Statistical inference is an essential component of both animal behavior and artificial intelligence algorithms. It focuses on two main tasks: combining information learned from the past and perceiving the present to try to predict the future (our teammate passes the ball to us, how to move to catch it, knowing our teammate and seeing the arc of the ball) while trying to make use of various past experiences for this prediction.

A new study by IE researchers shows that the population of the basic units of evolution, the self-reproducing replicators, are capable of performing exactly these calculations. The basis of this analogy is to view the competition of replicators as a competition for hypotheses about the future.

Bayesian learning theory and evolutionary theory both formalize adaptive competitive dynamics in a multidimensional, changing, and noisy environment. In this study, we discuss structural and dynamic analogies and their limitations, both at the computational and algorithmic-mechanical levels. We point out the mathematical equivalences between their basic dynamic equations, generalizing the isomorphism between Bayesian inference and replicator dynamics. We discuss how these mechanisms provide analogous responses to the challenge of adapting to a stochastically changing environment across multiple time scales. We shed light on the algorithmic equivalence between 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 the regularities of the stochastic environment to predict future environments, without reference to known mechanisms of multilevel selection and evolution. A unified approach to the theories of learning and evolution comes to the fore.

This theoretical link may lead to a better understanding of the diverse adaptations of biological evolution by showing a new adaptation goal emerging at the level of the population and not the individual. On the other hand, using this exact mathematical analogy, artificial evolutionary systems can become a more fundamental building block of intelligence.

Dániel Czégel, Giaffar Hamza, Josh Tenenbaum and Eörs Szathmáry
Bioessays. 2022 Feb 25: e2100255