Fitness and Overfitness: Implicit Regularization in Evolutionary Dynamics

TL;DR

This paper introduces a mathematical framework linking evolutionary dynamics and learning theory, showing how organism complexity adapts to environmental complexity through implicit regularization, with implications for understanding biological complexity.

Contribution

It establishes a novel isomorphism between evolutionary processes and Bayesian learning, revealing how complexity evolves to match environmental demands and explaining phenomena like overfitness and underfitness.

Findings

Frequent environmental changes reduce organism complexity.

Optimal complexity balances environmental structure and adaptability.

Evolutionary and learning dynamics share implicit regularization mechanisms.

Abstract

A common assumption in evolutionary thought is that adaptation drives an increase in biological complexity. However, the rules governing evolution of complexity appear more nuanced. Evolution is deeply connected to learning, where complexity is much better understood, with established results on optimal complexity appropriate for a given learning task. In this work, we suggest a mathematical framework for studying the relationship between evolved organismal complexity and enviroenmntal complexity by leveraging a mathematical isomorphism between evolutionary dynamics and learning theory. Namely, between the replicator equation and sequential Bayesian learning, with evolving types corresponding to competing hypotheses and fitness in a given environment to likelihood of observed evidence. In Bayesian learning, implicit regularization prevents overfitting and drives the inference of hypotheses whose complexity matches the learning challenge. We show how these results naturally carry over to the evolutionary setting, where they are interpreted as organism complexity evolving to match the complexity of the environment, with too complex or too simple organisms suffering from \textit{overfitness} and \textit{underfitness}, respectively. Other aspects, peculiar to evolution and not to learning, reveal additional trends. One such trend is that frequently changing environments decrease selected complexity, a result with potential implications to both evolution and learning. Together, our results suggest that the balance between over-adaptation to transient environmental features, and insufficient flexiblity in responding to environmental challenges, drives the emergence of optimal complexity, reflecting environmental structure. This framework offers new ways of thinking about biological complexity, suggesting new potential causes for it to increase or decrease in different environments.