Fig. 2.

(A) Bacteria, phage, and nutrients at steady state as a function of the probability of phage success $p_V$ for a model without CRISPR (spacer effectiveness $e=0$, solid lines) and for a model where bacteria have CRISPR systems and are able to acquire spacers ($e=0.5$, dashed lines). Population sizes are normalized by the inflow nutrient concentration $C_0$, and phages are additionally scaled by the burst size $B$. As the probability of phage success $p_V$ increases, bacteria decrease in number. Below $p_V=p_V^0$, phages cannot persist and the fraction of bacteria with spacers is 0. Phages increase with increasing $p_V$ and then decrease at high $p_V$ because the bacterial population is too small to support more phages. (B) Normalized total bacteria as a function of spacer acquisition probability $\eta$ and spacer effectiveness (equal for all spacers). (C) Fraction of bacteria with spacers ($\nu$) as a function of $\eta$ and $e$.