Optimal foraging models reveal barriers and stepping stones to the evolution of host-range generalism in bacteriophage

6 The nature and stability of coexistence of specialist species with more generalized 7 competitors present theoretical questions that have been difficult to resolve. Recent 8 surveys of bacteriophage host-ranges suggest that generalist phage often coexistent 9 with specialists. However, previous theoretical work has explained this coexistence only 1 0 in terms of strict genetic trade-offs, which are not consistently observed when phage are 1 1 challenged to evolve to multiple hosts in laboratory environments. Here we use the 1 2 framework of optimal foraging to identify conditions that might prevent generalists from 1 3 outcompeting specialist relatives. Our analysis shows that heterogeneities in phage life-1 4 history properties make host-range specialist more viable, and that endogenous 1 5 fluctuations in host density permit a narrow window of stable coexistence between 1 6 specialists and generalists without the need for genetic trade-offs. These results are 1 7 especially relevant for understanding the barriers to the evolution of broader host-1 8 ranges in bacteriophage and other pathogens with similar life-cycles.