Features of the CRISPR-Cas system, in which bacteria integrate small segments of phage genome (spacers) into their DNA to neutralize future attacks, suggest that its effect is not limited to individual bacteria but may control the fate and structure of whole populations [1]. In our model, we find that early dynamics of large phage clones is largely independent of bacterial dynamics but crucially depends on the burst-size of phage infections. In contrast, the fates of early phage mutants are strongly influenced by the feedback from bacterial population that creates a time-dependent fitness landscape for that phage type. Taken together, we quantify the role of population parameters in maintaining phage and bacterial diversity where CRISPR-cas is in the play. 
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