Replicators in Fine-grained Environment: Adaptation and Polymorphism

TL;DR

This paper models how populations adapt and maintain diversity in fluctuating environments using multi-player replicator dynamics, revealing that environmental changes can lead to stable polymorphisms despite decreasing mean fitness.

Contribution

It introduces a novel multi-player replicator model capturing adaptation and polymorphism in time-periodic environments, extending traditional two-player models.

Findings

Multi-player terms emerge from environmental adaptation.

Stable polymorphisms can arise in fluctuating environments.

Mean fitness decreases as polymorphisms establish.

Abstract

Selection in a time-periodic environment is modeled via the two-player replicator dynamics. For sufficiently fast environmental changes, this is reduced to a multi-player replicator dynamics in a constant environment. The two-player terms correspond to the time-averaged payoffs, while the three and four-player terms arise from the adaptation of the morphs to their varying environment. Such multi-player (adaptive) terms can induce a stable polymorphism. The establishment of the polymorphism in partnership games [genetic selection] is accompanied by decreasing mean fitness of the population.