Some prokaryotes possess CRISPR-Cas systems that provide adaptive immunity to viruses guided by DNA segments called spacers acquired from invading phage. However, the patchy incidence and limited memory breadth of CRISPR-Cas systems suggest that their fitness benefits are offset by costs. Here, we propose that cross-reactive CRISPR targeting can lead to heterologous autoimmunity, whereby foreign spacers guide self-targeting in a spacer-length dependent fashion. Balancing antiviral defense against autoimmunity predicts a scaling relation between spacer length and CRISPR repertoire size. We find evidence for this scaling through comparative analysis of sequenced prokaryotic genomes, and show that this association also holds at the level of CRISPR types. In contrast, the scaling is absent in strains with nonfunctional CRISPR loci. Finally, we demonstrate that stochastic spacer loss can explain variations around the scaling relation, even between strains of the same species. Our results suggest that heterologous autoimmunity is a selective factor shaping the evolution of CRISPR-Cas systems.

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