A probabilistic interpretation of replicator-mutator dynamics

2017/12/21 by Ömer Deniz Akyıldız, Akyıldız, Ömer Deniz · 2 citations
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · Social Sciences · #Applications (stat.AP) #Evolution and Genetic Dynamics #Evolutionary Game Theory and Cooperation #FOS: Biological sciences #FOS: Computer and information sciences #Opinion Dynamics and Social Influence #Populations and Evolution (q-bio.PE)

paper · pdf · doi:10.48550/arxiv.1712.07879

openalex publication_date 2017/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note, we investigate the relationship between probabilistic updating mechanisms and discrete-time replicator-mutator dynamics. We consider the recently shown connection between Bayesian updating and replicator dynamics and extend it to the replicator-mutator dynamics by considering prediction and filtering recursions in hidden Markov models (HMM). We show that it is possible to understand the evolution of the frequency vector of a population under the replicator-mutator equation as a posterior predictive inference procedure in an HMM. This view enables us to derive a natural dual version of the replicator-mutator equation, which corresponds to updating the filtering distribution. Finally, we conclude with the implications of the interpretation and with some comments related to the recent discussions about evolution and learning.

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