A diploid population model for copy number variation of genetic elements

2022/04/23 by Peter Pfaffelhuber, Pfaffelhuber, Peter, Anton Wakolbinger +1
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · #60F17 #60G57 #60J80 #92D15 #Evolution and Genetic Dynamics #FOS: Biological sciences #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Populations and Evolution (q-bio.PE) #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2204.11140

openalex publication_date 2022/04/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the following model for a diploid population of constant size N: Every individual carries a random number of (genetic) elements. Upon a reproduction event each of the two parents passes each element independently with probability \tfrac 12 on to the offspring. We study the process X^N = (X^N(1), X^N(2),...), where X_t^N(k) is the frequency of individuals at time t that carry k elements, and prove convergence (in some weak sense) of X^N jointly with its empirical first moment Z^N to the ``slow-fast'' system (Z,X), where X_t = Poi(Z_t) and Z evolves according to a critical Feller branching process. We discuss heuristics explaining this finding and some extensions and limitations.

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