Introduction to the statistical theory of Darwinian evolution

TL;DR

This paper introduces statistical models of Darwinian evolution, covering deterministic and stochastic dynamics, finite population effects, coevolution, and large-scale models inspired by statistical mechanics.

Contribution

It provides a comprehensive overview of evolutionary models using statistical mechanics, including new insights into finite populations and coevolutionary dynamics.

Findings

Deterministic quasispecies equations describe evolution under simple fitness landscapes.

Finite populations lead to stochastic escape and adaptive walks.

Large-scale coevolution models like Bak-Sneppen offer new perspectives.

Abstract

These lectures contain a brief description of evolutionary models inspired by the statistical mechanics of disordered systems. After an introduction describing the Darwinian paradigm of evolving populations, the deterministic quasispecies equation is described, and the simplest fitness landscapes are discussed. The effect of finite population size is then considered, from the opposing points of view leading to stochastic escape and to adaptive walks. A synthesis is attempted. Finally the effects of coevolution are considered, and the promising models of large-scale inspired by the Bak-Sneppen models are described.