Lytic viruses are obligate parasites whose adaptation rates have attracted considerable scientific interest, as they are a key model organism in experimental evolution. Adaptation experiments using these viruses are characterized by growth, mutation, and periodic sampling (population bottlenecks) that ultimately influence the fate of a rare beneficial mutation.;We first assume that the host-cell density is constant, and compute the fixation probability for mutations that increase the attachment rate, decrease the lysis time, increase the burst size, or reduce the probability of clearance. The fixation probability of these four types of beneficial mutations can be vastly different. We also explored mutations that affect lysis time, assuming that the burst size is constrained by the lysis time. For all mechanisms of mutational action explored, we predict that the fixation probability of beneficial alleles is remarkably sensitive to the time between population bottlenecks.;We then incorporate two important features of host-cell dynamics - the possibility of clearance or death of an infected cell before lysis, and the possibility of changing host-cell density. We compute the fixation probabilities of rare alleles that confer reproductive benefit through either an increase in attachment rate or burst size, or a reduction in lysis time. We find that host-cell clearance significantly reduces the fixation probabilities of all types of beneficial mutations, having the largest impact on mutations that reduce the lysis time, but has only modest effects on the pattern of fixation probabilities previously observed. We further predict that exponential growth of the host-cell population preferentially selects for mutations that affect burst size or lysis time, and exacerbates the sensitive dependence of fixation probabilities on the time between population bottlenecks. Even when burst size and lysis time are constrained to vary together, our results suggest that lytic viruses should readily adapt to optimize these traits to the timing between population bottlenecks.;We also 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 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 transfered 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.;The goal of this research has been to study the adaptation rates and fixation probabilities of beneficial mutations of lytic viruses, and the impact of the environment on these probabilities. To achieve this goal, we first develop a life-history model for lytic viruses. The model first assumes that attachment times are exponentially distributed, but that the lysis time, the time between attachment and host-cell lysis, is constant. We include the possibility that clearance may occur at a constant rate, for example through washout in a chemostat. Our model predictions are extremely sensitive to the assumptions regarding the organism's life history.;Keywords: Life-history; lytic virus; population bottlenecks; experimental evolution; host dynamics; lysis time; branching process.
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