The arrow of evolution when the offspring variance is large

TL;DR

This paper models how large offspring variance, influenced by environmental and demographic stochasticity, can reverse traditional evolutionary outcomes, favoring cooperation over defection in population dynamics.

Contribution

It introduces a new model incorporating offspring variance dependent on mean, revealing how high variance can reverse classical selection trends.

Findings

Large offspring variance can favor cooperation over defection.

Reproductive over-dispersion leads to new social interaction dynamics.

Classical models with fixed or Poisson variance do not predict these effects.

Abstract

The concept of fitness is central to evolution, but it quantifies only the expected number of offspring an individual will produce. The actual number of offspring is also subject to noise, arising from environmental or demographic stochasticity. In nature, individuals who are more fecund tend to have greater variance in their offspring number -- sometimes far greater than the Poisson variance assumed in classical models of population genetics. Here, we develop a model for the evolution of two types reproducing in a population of non-constant size. The frequency-dependent fitness of each type is determined by pairwise interactions in a prisoner's dilemma game, but the offspring number is subject to an exogenously controlled variance that may depend upon the mean. Whereas defectors are preferred by natural selection in classical well-mixed populations, since they always have greater fitness than cooperators, we show that large offspring variance can reverse the direction of evolution and favor cooperation. Reproductive over-dispersion produces qualitatively new dynamics for other types of social interactions, as well, which cannot arise in populations with a fixed size or Poisson offspring variance.