Persistence and neutrality in interacting replicator dynamics
Abstract
We study the large-time behavior of an ensemble of entities obeying replicator-like stochastic dynamics with mean-field interactions as a model for a primordial ecology. We prove the propagation-of-chaos property and establish conditions for the strong persistence of the -replicator system and the existence of invariant distributions for a class of associated McKean-Vlasov dynamics. In particular, our results show that, unlike typical models of neutral ecology, fitness equivalence does not need to be assumed but emerges as a condition for the persistence of the system. Further, neutrality is associated with a unique Dirichlet invariant probability measure. We illustrate our findings with some simple case studies, provide numerical results, and discuss our conclusions in the light of Neutral Theory in ecology.
Cite
@article{arxiv.2310.02809,
title = {Persistence and neutrality in interacting replicator dynamics},
author = {Leonardo Videla and Mauricio Tejo and Cristóbal Quiñinao and Pablo A. Marquet and Rolando Rebolledo},
journal= {arXiv preprint arXiv:2310.02809},
year = {2024}
}