piRNA Clusters Need a Minimum Size to Control Transposable Element Invasions

piRNA clusters are thought to repress transposable element (TE) activity in mammals and invertebrates. Here, we show that a simple population genetics model reveals a constraint on the size of piRNA clusters: The total size of the piRNA clusters of an organism must exceed 0.2% of a genome to repress TE invasions. Moreover, larger piRNA clusters accounting for up to 3% of the genome may be necessary when populations are small, transposition rates are high, and TE insertions are recessive. If piRNA clusters are too small, the load of deleterious TE insertions that accumulate during a TE invasion may drive populations extinct before an effective piRNA-based defense against the TE can be established. Our findings are solely based on three well-supported assumptions: 1) TEs multiply within genomes, 2) TEs are mostly deleterious, and 3) piRNA clusters act as transposon traps, where a single insertion in a cluster silences all TE copies in trans. Interestingly, the piRNA clusters of some species meet our observed minimum size requirements, whereas the clusters of other species do not. Species with small piRNA clusters, such as humans and mice, may experience severe fitness reductions during invasions of novel TEs, which is possibly even threatening the persistence of some populations. This work also raises the important question of how piRNA clusters evolve. We propose that the size of piRNA clusters may be at an equilibrium between evolutionary forces that act to expand and contract piRNA clusters.