Nihal Koduri and Andrew W. Lo

PNAS June 29, 2021 118 (26) e2015572118

Significance

We develop a mathematical theory of how natural selection operates in the presence of interaction between replicating units. Our results show that with interaction, natural selection does more than seek to selfishly maximize fecundity. It also seeks to minimize correlation of fecundity between replicating units. We argue that correlation is a mechanism by which evolution can select for cooperation. This mechanism is distinct from standard biological explanations like kin selection, group selection, and reciprocity, and relies only on natural selection, and without recourse to notions of evolutionary stability.

Abstract

We construct an evolutionary model of a population consisting of two types of interacting individuals that reproduce under random environmental conditions. We show that not only does the evolutionarily dominant behavior maximize the number of offspring of each type, it also minimizes the correlation between the number of offspring of each type, driving it toward −1. We provide several examples that illustrate how correlation can be used to explain the evolution of cooperation.

See: https://www.pnas.org/content/118/26/e2015572118

Figure 1: Total population growth vs. time. Values of ρ range from −0.9−0.9 (lightest) to 0.9 (darkest). The number of offspring for both types follows a lognormal distribution with μ=0.1μ=0.1 and σ=1.0σ=1.0.