Originally published as Genetics Published Articles Ahead of Print on August 30, 2008.

Genetics, Vol. 180, 459-470, September 2008, Copyright © 2008
doi:10.1534/genetics.108.090555

Fixation Probability for Lytic Viruses: The Attachment-Lysis Model

Z. Patwa and L. M. Wahl1

Department of Applied Mathematics, University of Western Ontario, London, Ontario N6A 5B7, Canada

1 Corresponding author: Department of Applied Mathematics, Middlesex College, Room 255, University of Western Ontario, London, ON N6A 5B7, Canada.
E-mail: lwahl{at}uwo.ca

The fixation probability of a beneficial mutation is extremely sensitive to assumptions regarding the organism's life history. In this article we compute the fixation probability using a life-history model for lytic viruses, a key model organism in experimental studies of adaptation. The model assumes that attachment times are exponentially distributed, but that the lysis time, the time between attachment and host cell lysis, is constant. We assume that the growth of the wild-type viral population is controlled by periodic sampling (population bottlenecks) and also include the possibility that clearance may occur at a constant rate, for example, through washout in a chemostat. We then 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 and depends critically on the time between population bottlenecks. We also explore mutations that affect lysis time, assuming that the burst size is constrained by the lysis time, for experimental protocols that sample either free phage or free phage and artificially lysed infected cells. In all cases we predict that the fixation probability of beneficial alleles is remarkably sensitive to the time between population bottlenecks.