eLife assessment
In this important work, the authors develop a theory for the co-evolutionary dynamics of bacteria and phages, where the major evolutionary pressure comes from CRISPR-Cas adaptive immunity in bacteria. Through extensive stochastic numerical simulations and analytical calculations, the paper presents a compelling analysis of the emergent properties of immune interactions, in the regime of a single proto-spacer and a single spacer. Some of the trends highlighted by the model are recovered from experimental data. The main results concern how diversity in both phage and bacteria population are linked and are shaped by immunity, and should be of broad interest in immunology.