Optimization of lysogeny frequency for temperate phages

Upon infection temperate phages chose between lysogenic and lytic developmental strategies. We suggest to apply the game-theoretic bet-hedging strategy introduced by Kelly to derive the optimal lysogenic fraction of the total population of phages. Our proposed "Well-temperate" phage is realized when the lysogenization frequency is approximately equal to the probability of lytic population collapse.. We further predict the existence of sharp boundaries in system's environmental parameters separating the regions where this temperate strategy is optimal from those dominated by purely virulent or dormant strategies. Our formalism predict that progressively more temperate or even dormant strategies are favored in highly fluctuating environments.