Well-temperate phage: optimal bet-hedging against local environmental collapses

TL;DR

This paper uses game theory to determine the optimal balance between lysogenic and lytic strategies in temperate phages, predicting conditions favoring each strategy based on environmental stability and diversity.

Contribution

It introduces a bet-hedging model for phage developmental strategies, identifying optimal lysogenization fractions and environmental boundaries for strategy shifts.

Findings

Optimal lysogenic fraction equals the probability of lytic collapse.

Sharp boundaries separate strategy regimes based on environmental parameters.

Virulent strategies favor diverse, accessible environments; temperate strategies dominate in unstable conditions.

Abstract

Upon infection of their bacterial hosts temperate phages must chose between lysogenic and lytic developmental strategies. Here we apply the game-theoretic bet-hedging strategy introduced by Kelly to derive the optimal lysogenic fraction of the total population of phages as a function of frequency and intensity of environmental downturns affecting the lytic subpopulation. "Well-temperate" phage from our title is characterized by the best long-term population growth rate. We show that it 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, ecological, and biophysical parameters separating the regions where this temperate strategy is optimal from those dominated by purely virulent or} dormant (purely lysogenic) strategies. We show that the virulent strategy works best for phages with large diversity of hosts, and access to multiple independent environments reachable by diffusion. Conversely, progressively more temperate or even dormant strategies are favored in the environments, that are subject to frequent and severe temporal downturns.