Abstract
Prokaryotes are ubiquitous across environments able to support life, and so are the viruses that infect them. Bacteria and archaea possess a variety of immune systems in order to defend themselves against these viral pathogens. One example is the CRISPR adaptive immune system, which is found across diverse prokaryotic lineages. Many prokaryotes have a CRISPR locus, and, surprisingly, many have more than one CRISPR locus. Here we examine how the multiplicity of CRISPR immune systems in a genome is related to the pathogenic environment. We use a comparative genomics approach to demonstrate that having more than one CRISPR array is adaptive on average across prokaryotes. This adaptive signature appears to be a function of the diversity of CRISPR arrays rather than their multiplicity alone. We then develop a simple deterministic model of CRISPR immune memory turnover. We show how a tradeoff between memory span and learning speed can lead to an optimal two-array solution in certain pathogenic environments.