2018/10/16 by Ian Letter, Letter, Ian, Servet Martı́nez +2
Biochemistry, Genetics and Molecular Biology · Mathematics · #05C05 #60J27 #92D25 #Evolution and Genetic Dynamics #FOS: Mathematics #Gene Regulatory Network Analysis #Microbial Metabolic Engineering and Bioproduction #Probability (math.PR) #math.PR #msc:05C05 #msc:60J27 #msc:92D25
paper · pdf · doi:10.48550/arxiv.1810.07238
28 pages, 2 figures, submitted
openalex publication_date 2018/10/16 · arxiv created 2020/04/16 · arxiv updated 2020/04/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the continuous-time evolution of the recombination equation of population genetics. This evolution is given by a differential equation that acts on a product probability space, and its solution can be described by a Markov chain on a set of partitions that converges to the finest partition. We study an explicit form of the law of this process by using a family of trees. We also describe the geometric decay rate to the finest partition and the quasi-stationary behavior of the Markov chain when conditioned on the event that the chain does not hit the limit.