Evolving phylogenies of trait-dependent branching with mutation and competition, Part I: Existence

[摘要] We propose a type-dependent branching model with mutation and competition for modelling phylogenies of a virus population. The competition kernel depends on the total mass, the types of the virus particles, and the genetic information available through the number of nucleotide substitutions separating the virus particles. We consider evolving phylogenies in the huge population, short reproduction time and frequent mutation regime, show tightness in the space of marked metric measure spaces and characterize the limit through a martingale problem. Due to heterogeneity in the branching rates, the phylogenies are not ultra-metric. We therefore develop new techniques for verifying compact containment. (C) 2018 Elsevier B.V. All rights reserved.

[发布日期] 2019-12-01

[关键词] Tree-valued Markov process;Marked Gromov-weak topology;Branching;Selection;Competition;Non-ultrametric