2017/05/09 by Sandra Kliem, Kliem, Sandra, Anita Winter +1
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · #60J25 (Primary) 60J80 #60K35 #92D25 (Secondary) #Evolution and Genetic Dynamics #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Probability (math.PR) #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.1705.03277
openalex publication_date 2017/05/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose a type-dependent branching model with mutation and competition for\nmodeling phylogenies of a virus population. The competition kernel depends for\nany two virus particles on the particles' types, the total mass of the\npopulation as well as genetic information available through the number of\nnucleotide substitutions separating the virus particles. We consider the\nevolving phylogenies of this individual based model in the huge population,\nshort reproduction time and frequent mutation regime, and show tightness in the\nstate space of marked metric measure spaces. Due to heterogeneity in the\nnatural branching rates, the phylogenies are in general not ultra-metric. We\ntherefore develop new techniques for verifying a compact containment condition.\nFinally, we characterize the limit as a solution of a martingale problem.\n