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We study the following model for a diploid population of constant size $N$:Every individual carries a random number of (genetic) elements. Upon areproduction event each of the two parents passes each element independentlywith 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 criticalFeller branching process. We discuss heuristics explaining this finding andsome extensions and limitations.

A diploid population model for copy number variation of genetic elements