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2023 A diploid population model for copy number variation of genetic elements
Peter Pfaffelhuber, Anton Wakolbinger
Author Affiliations +
Electron. J. Probab. 28: 1-15 (2023). DOI: 10.1214/23-EJP934


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 12 on to the offspring. We study the process XN=(XN(1),XN(2),...), where XtN(k) is the frequency of individuals at time t that carry k elements, and prove convergence (in some weak sense) of XN jointly with its empirical first moment ZN to the “slow-fast” system (Z,X), where Xt=Poi(Zt) and Z evolves according to a critical Feller branching process. We discuss heuristics explaining this finding and some extensions and limitations.

Funding Statement

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.


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Peter Pfaffelhuber. Anton Wakolbinger. "A diploid population model for copy number variation of genetic elements." Electron. J. Probab. 28 1 - 15, 2023.


Received: 13 May 2022; Accepted: 14 March 2023; Published: 2023
First available in Project Euclid: 21 March 2023

MathSciNet: MR4563525
zbMATH: 1519.92148
MathSciNet: MR4529085
Digital Object Identifier: 10.1214/23-EJP934

Primary: 92D15
Secondary: 60F17 , 60G57 , 60J80

Keywords: Feller branching diffusion , Poisson approximation , slow-fast system , transposable elements

Vol.28 • 2023
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