Population genetics of active transposable elements: overdispersion arises naturally from transposition-deletion-selection balance

Abstract

Active transposable element (TE) families often show overdispersion (variance greater than the mean), which is in contrast to the predictions of classical Poisson-based models and related theories built on the same approximation. To address this gap, we develop a diploid stochastic model of TE dynamics under free recombination, based on a biparental Moran model with transposition, excision, purifying selection, and derive mean and variance dynamics of TE copy numbers at two stages of the life cycle: before and after transposition and excision. We show that overdispersion arises naturally through transposition generating positive linkage disequilibrium between TE insertion sites with the disequilibrium persisting even under free recombination. The higher the transposition rate, the stronger the resulting overdispersion. Underdispersion and Poisson-like variation are instead stage-dependent: neither is expected after transposition and excision, while both remain possible beforehand, governed by the curvature of the fitness function. We further show that maintaining positive equilibrium copy numbers, and thus sustaining overdispersion, requires the net transposition rate to remain below roughly 0.5 insertions per copy per generation, a constraint satisfied by observed natural populations to maintain genome stability. A qualitative comparison with the DPGP3 Zambian Drosophila melanogaster dataset, focusing on TE insertions in high-recombination euchromatic regions shows that most TE families are overdispersed and that many also exhibit the predicted right-skewness and excess-kurtosis patterns, which are predicted by our model. These results identify overdispersion as a natural outcome of active TE dynamics and provide a mechanistic framework for understanding the full distribution of TE copy numbers in highly recombining regions.