Alternating lysis and lysogeny is a winning strategy in bacteriophages due to Parrondo's Paradox

Temperate bacteriophages lyse or lysogenize the host cells depending on various parameters of infection, a key one being the host population density. However, the effect of different propensities of phages for lysis and lysogeny on phage fitness is an open problem. We explore a nonlinear dynamic evolution model of competition between two phages, one of which is disadvantaged in both the lytic and lysogenic phases. We show that the disadvantaged phage can win the competition by alternating between the lytic and lysogenic phases, each of which individually is a "loser". This counter-intuitive result recapitulates Parrondos paradox in game theory, whereby individually losing strategies can combine to produce a winning outcome. The results suggest that evolution of phages optimizes the ratio between the lysis and lysogeny propensities rather than the phage reproduction rate in any individual phase. These findings are expected to broadly apply to the evolution of host-parasite interactions.