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 on to the offspring. We study the process , where is the frequency of individuals at time t that carry k elements, and prove convergence (in some weak sense) of jointly with its empirical first moment to the “slow-fast” system , where and Z evolves according to a critical Feller branching process. We discuss heuristics explaining this finding and some extensions and limitations.
PP is partly supported by the Freiburg Center for data analysis and modeling (FDM). AW is partly supported by DFG SPP 1590.
We thank Peter Czuppon, Jonathan Henshaw and Judith Korb for discussions concerning the dynamics of transposable elements.
"A diploid population model for copy number variation of genetic elements." Electron. J. Probab. 28 1 - 15, 2023. https://doi.org/10.1214/23-EJP934