The Value of a Prophage-Borne Defense System: A Theoretical Analysis of Phage–Phage Competition

Temperate phages that incorporate into their bacterial hosts’ genomes often encode defense systems that protect their hosts from superinfection by unrelated phages. Yet the evolutionary value of such defenses to the phage remains unclear. We present a minimal theoretical framework to quantify the selective advantage of a prophage-borne defense system in competition between temperate phages infecting the same bacterium. The model reveals regimes in which a defensive phage can invade and persist despite growth costs, and others in which all phage types coexist due to a rock–paper–scissors dynamic between defensive, non-defensive, and defense-loss variants. Because defense systems can be non-transitive, true rock-paper-scissors relations can lead to persistent oscillations. These results identify simple conditions under which phage-encoded defense systems are evolutionarily stable, providing testable predictions for the prevalence and maintenance of these systems in natural microbial communities.