Transposable elements (TEs) are self-reproducing selfish DNA sequences that can invade the genome of virtually all living species. Population genetics models have shown that TE copy numbers generally reach a limit, either because the transposition rate decreases with the number of copies (transposition regulation) or because TE copies are deleterious, and thus purged by natural selection. Yet, recent empirical discoveries suggest that TE regulation may mostly rely on piRNAs, which require a specific mutational event (the insertion of a TE copy in a piRNA cluster) to be activated — the so-called TE regulation “trap model”. We derived new population genetics models accounting for this trap mechanism, and showed that the resulting equilibria differ substantially from previous expectations based on a transposition–selection equilibrium. We proposed three sub-models, depending on whether or not genomic TE copies and piRNA cluster TE copies are selectively neutral or deleterious, and we provide analytical expressions for maximum and equilibrium copy numbers, as well as cluster frequencies for all of them. In the full neutral model, the equilibrium is achieved when transposition is completely silenced, and this equilibrium does not depend on the transposition rate. When genomic TE copies are deleterious but not cluster TE copies, no long-term equilibrium is possible, and active TEs are eventually eliminated after an active incomplete invasion stage. When all TE copies are deleterious, a transposition–selection equilibrium exists, but the invasion dynamics is not monotonic, and the copy number peaks before decreasing. Mathematical predictions were in good agreement with numerical simulations, except when genetic drift and/or linkage disequilibrium dominates. Overall, the trap-model dynamics appeared to be substantially more stochastic and less repeatable than traditional regulation models.

转座因子 (TE) 是自我复制的自私 DNA 序列，可以侵入几乎所有生物的基因组。群体遗传学模型表明，TE 拷贝数通常会达到一个极限，这要么是因为转座率随着拷贝数的增加而降低（转座调节），要么是因为 TE 拷贝是有害的，因此会被自然选择清除。然而，最近的经验发现表明，TE 调控可能主要依赖于 piRNA，这需要特定的突变事件（在 piRNA 簇中插入 TE 拷贝）才能被激活——即所谓的 TE 调控“陷阱模型”。我们推导出了新的群体遗传学模型来解释这种陷阱机制，并表明由此产生的平衡与之前基于换位-选择平衡的预期有很大不同。我们提出了三个子模型，这取决于基因组 TE 拷贝和 piRNA 簇 TE 拷贝是选择性中性还是有害的，我们提供了最大和平衡拷贝数的分析表达式，以及所有它们的簇频率。在完全中性模型中，当转置完全沉默时达到平衡，并且这种平衡不依赖于转置率。当基因组 TE 拷贝是有害的而不是成簇 TE 拷贝时，长期平衡是不可能的，并且活跃的 TE 在活跃的不完全入侵阶段后最终被消除。当所有 TE 拷贝都是有害的时，存在转座-选择平衡，但入侵动力学不是单调的，拷贝数在下降前达到峰值。数学预测与数值模拟非常吻合，除非遗传漂移和/或连锁不平衡占主导地位。总体而言，陷阱模型动力学似乎比传统监管模型更具随机性和可重复性。