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. 2025 Jan 3;90(2):15.
doi: 10.1007/s00285-024-02174-w.

Persistence and neutrality in interacting replicator dynamics

Leonardo Videla  1 , Mauricio Tejo  2 , Cristóbal Quiñinao  3 , Pablo A Marquet  4   5   6   7 , Rolando Rebolledo  8
Affiliations

Persistence and neutrality in interacting replicator dynamics

Leonardo Videla et al. J Math Biol. .

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 N-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.

Keywords: Emergence of ecologies; Invariant distributions; McKean–Vlasov equation; Propagation of Chaos; Stochastic persistence; Stochastic replicator dynamics.

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Conflict of interest statement

Declarations. Conflict of interest: The authors declare that have no financial or personal relationship with other people or organizations that could inappropriately influence or bias the content of this paper. Also, the authorsdeclare that they have no Conflict of interest.

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