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Mean-field interacting multi-type birth–death processes with a view to applications in phylodynamics.
- Source :
-
Theoretical Population Biology . Oct2024, Vol. 159, p1-12. 12p. - Publication Year :
- 2024
-
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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00405809
- Volume :
- 159
- Database :
- Academic Search Index
- Journal :
- Theoretical Population Biology
- Publication Type :
- Academic Journal
- Accession number :
- 179629011
- Full Text :
- https://doi.org/10.1016/j.tpb.2024.07.002