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arXiv · 2204.11140

A diploid population model for copy number variation of genetic elements

Peter Pfaffelhuber·Anton Wakolbinger
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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 $X_t = \text{Poi}(Z_t)$ 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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Peter Pfaffelhuber, Anton Wakolbinger. 2022-04-23. A diploid population model for copy number variation of genetic elements. https://arxiv.org/abs/2204.11140

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