RESUMO
Bacteria are infected by mobile genetic elements like plasmids and virulent phages, and those infections significantly impact bacterial ecology and evolution. Recent discoveries reveal that some plasmids carry anti-phage immune systems like CRISPR-Cas, suggesting that plasmids may participate in the coevolutionary arms race between virulent phages and bacteria. Intuitively, this seems reasonable as virulent phages kill the plasmid's obligate host. However, the efficiency of CRISPR-Cas systems carried by plasmids can be expected to be lower than those carried by the chromosome due to continuous segregation loss, creating susceptible cells for phage amplification. To evaluate the anti-phage protection efficiency of CRISPR-Cas on plasmids, we develop a stochastic model describing the dynamics of a virulent phage infection against which a conjugative plasmid defends using CRISPR-Cas. We show that CRISPR-Cas on plasmids provides robust protection, except in limited parameter sets. In these cases, high segregation loss favours phage outbreaks by generating a population of defenceless cells on which the phage can evolve and escape CRISPR-Cas immunity. We show that the phage's ability to exploit segregation loss depends strongly on the evolvability of both CRISPR-Cas and the phage itself.