Seasonal Floquet states in a game-driven evolutionary dynamics

TL;DR

This paper introduces the concept of Floquet states in evolutionary game dynamics, showing how season-dependent mating preferences lead to metastable, time-periodic states in finite populations that become stable as population size grows.

Contribution

It combines Floquet theory with evolutionary game theory to reveal metastable periodic states in finite populations with seasonal mating preferences.

Findings

Metastable Floquet states exist in finite populations.

Lifetime of these states increases with population size.

States become attractors as population size approaches infinity.

Abstract

Mating preferences of many biological species are not constant but season-dependent. Within the framework of evolutionary game theory this can be modeled with two finite opposite-sex populations playing against each other following the rules that are periodically changing. By combining Floquet theory and the concept of quasi-stationary distributions, we reveal existence of metastable time-periodic states in the evolution of finite game-driven populations. The evolutionary Floquet states correspond to time-periodic probability flows in the strategy space which cannot be resolved within the mean-field framework. The lifetime of metastable Floquet states increases with the size $N$ of populations so that they become attractors in the limit $N \rightarrow \infty$.