Adaptation rates of lytic viruses depend critically on whether host cells survive the bottleneck.

We use a branching process approach to estimate the substitution rate, the rate at which beneficial mutations occur and fix, in populations of lytic viruses whose growth is controlled by periodic population bottlenecks. Our model predicts that substitution rates, and by extension adaptation rates, are profoundly affected by the survival of infected host cells at the bottleneck. In particular, we find that direct transfer (or environmental) bottlenecks, in which some fraction of both free virus and host cells are preserved, are associated with relatively slow adaptation rates for the virus. In contrast, viruses can adapt much more quickly when only free virus is transferred to a new host population, as is typical in an epidemiological setting. Finally, when premature lysis of the host-cell population is induced at the bottleneck, we predict that adaptation rates for the virus will, in general, be faster still. These results hold irrespective of the life-history trait affected by the beneficial mutation. The substitution rates in the presence of environmental bottlenecks are predicted to be as much as an order of magnitude lower than in the other two cases.