Epidemiological and evolutionary consequences of different types of CRISPR-Cas systems

Bacteria have adaptive immunity against viruses (phages) in the form of CRISPR-Cas immune systems. Currently, 6 types of CRISPR-Cas systems are known and the molecular study of three of these has revealed important molecular differences. It is unknown if and how these molecular differences change the outcome of phage infection and the evolutionary pressure the CRISPR-Cas systems faces. To determine the importance of these molecular differences, we model a phage outbreak entering a population defending exclusively with a type I/II or a type III CRISPR-Cas system. We show that for type III CRISPR-Cas systems, rapid phage extinction is driven by the probability to acquire at least one resistance spacer. However, for type I/II CRISPR-Cas systems, rapid phage extinction is characterized by an a threshold-like behaviour: any acquisition probability below this threshold leads to phage survival whereas any acquisition probability above it, results in phage extinction. We also show that in the absence of autoimmunity, high acquisition rates evolve. However, when CRISPR-Cas systems are prone to autoimmunity, intermediate levels of acquisition are optimal during a phage outbreak. As we predict an optimal probability of spacer acquisition 2 factors of magnitude above the one that has been measured, we discuss the origin of such a discrepancy. Finally, we show that in a biologically relevant parameter range, a type III CRISPR-Cas system can outcompete a type I/II CRISPR-Cas system with a slightly higher probability of acquisition.