2025/04/28 by Airam Blancas, Blancas, Airam, María Clara Fittipaldi +3
Biochemistry, Genetics and Molecular Biology · #60J80 #92D25 #Cancer Genomics and Diagnostics #Evolution and Genetic Dynamics #FOS: Mathematics #Genetic Associations and Epidemiology #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.2504.20030
openalex publication_date 2025/04/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The mother-dependent neutral mutations model describes the evolution of a population across discrete generations, where neutral mutations occur among a finite set of possible alleles. In this model, each mutant child acquires a type different from that of its mother, chosen uniformly at random. In this work, we define a multitype allele tree associated with this model and analyze its scaling limit through a Markov chain that tracks the sizes of allelic subfamilies and their mutant descendants. We show that this Markov chain converges to a continuous-state Markov process, whose transition probabilities depend on the sizes of the initial allelic populations and those of their mutant offspring in the first allelic generation. As a result, the allele tree converges to a multidimensional limiting object, which can be described in terms of the universal allele tree introduced by Bertoin (2010).