Mean-field interacting multi-type birth–death processes with a view to applications in phylodynamics

William S. DeWitt, Steven N. Evans, Ella Hiesmayr and Sebastian Hummel

Theoretical Population Biology, 2024, vol. 159, issue C, 1-12

Abstract: Multi-type birth–death processes underlie approaches for inferring evolutionary dynamics from phylogenetic trees across biological scales, ranging from deep-time species macroevolution to rapid viral evolution and somatic cellular proliferation. A limitation of current phylogenetic birth–death models is that they require restrictive linearity assumptions that yield tractable message-passing likelihoods, but that also preclude interactions between individuals. Many fundamental evolutionary processes – such as environmental carrying capacity or frequency-dependent selection – entail interactions, and may strongly influence the dynamics in some systems. Here, we introduce a multi-type birth–death process in mean-field interaction with an ensemble of replicas of the focal process. We prove that, under quite general conditions, the ensemble’s stochastically evolving interaction field converges to a deterministic trajectory in the limit of an infinite ensemble. In this limit, the replicas effectively decouple, and self-consistent interactions appear as nonlinearities in the infinitesimal generator of the focal process. We investigate a special case that is rich enough to model both carrying capacity and frequency-dependent selection while yielding tractable message-passing likelihoods in the context of a phylogenetic birth–death model.

Keywords: Mean-field interaction; Propagation of chaos; Self-consistent; Carrying capacity; Frequency-dependent selection; Phylogenetic birth–death model (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:thpobi:v:159:y:2024:i:c:p:1-12

DOI: 10.1016/j.tpb.2024.07.002

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