Date of Award


Degree Type


Degree Name

Master of Science


Applied Mathematics


Dr. Lindi Wahl


Estimating the fixation probability of a beneficial mutation has a rich history in theoretical population genetics. However, fixation probabilities are extremely sensitive to assumptions regarding life history. We develop a “burst-death” life history model which assumes that generation times are exponentially distributed, but the number of offspring per individual is fixed. Using this model, we estimate the fixation probability for populations of constant size, and for populations which grow exponentially between periodic population bottlenecks. We then predict the optimal time at which to impose bottlenecks, maximizing the probability that beneficial mutations occur and are not ultimately lost. We find that the optimal bottleneck time only weakly depends on the selective advantage but depends strongly on the death rate and burst size. Most importantly, the optimal sampling fraction is a constant with respect to these parameters; sampling about 20% of the population will maximize the rate of adaptation.



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