Mean-field interacting multi-type birth-death processes with a view to applications in phylodynamics
arxiv(2023)
摘要
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.
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