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

Sandra Kliem and Anita Winter

Stochastic Processes and their Applications, 2019, vol. 129, issue 12, 4837-4877

Abstract: 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.

Keywords: Tree-valued Markov process; Marked Gromov-weak topology; Branching; Selection; Competition; Non-ultrametric (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1016/j.spa.2018.07.011

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