The Probability of Fixation in Populations of Changing Size

The Probability of Fixation in Populations of Changing Size S. P. Otto and M. C. Whitlock Department of Zoology, University of British Columbia, Vancouver, BC, Canada V6T 1Z4 The rate of adaptive evolution of a population ultimately depends on the rate of incorporation of beneficial mutations. Even beneficial mutations may, however, be lost from a population since mutant individuals may, by chance, fail to reproduce. In this paper, we calculate the probability of fixation of beneficial mutations that occur in populations of changing size. We examine a number of demographic models, including a population whose size changes once, a population experiencing exponential growth or decline, one that is experiencing logistic growth or decline, and a population that fluctuates in size. The results are based on a branching process model but are shown to be approximate solutions to the diffusion equation describing changes in the probability of fixation over time. Using the diffusion equation, the probability of fixation of deleterious alleles can also be determined for populations that are changing in size. The results developed in this paper can be used to estimate the fixation flux, defined as the rate at which beneficial alleles fix within a population. The fixation flux measures the rate of adaptive evolution of a population and, as we shall see, depends strongly on changes that occur in population size. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Genetics Genetics Society of America

The Probability of Fixation in Populations of Changing Size

Genetics, Volume 146 (2): 723 – Jun 1, 1997

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Publisher
Genetics Society of America
Copyright
Copyright © 1997 by the Genetics Society of America
ISSN
0016-6731
eISSN
1943-2631
Publisher site
See Article on Publisher Site

Abstract

S. P. Otto and M. C. Whitlock Department of Zoology, University of British Columbia, Vancouver, BC, Canada V6T 1Z4 The rate of adaptive evolution of a population ultimately depends on the rate of incorporation of beneficial mutations. Even beneficial mutations may, however, be lost from a population since mutant individuals may, by chance, fail to reproduce. In this paper, we calculate the probability of fixation of beneficial mutations that occur in populations of changing size. We examine a number of demographic models, including a population whose size changes once, a population experiencing exponential growth or decline, one that is experiencing logistic growth or decline, and a population that fluctuates in size. The results are based on a branching process model but are shown to be approximate solutions to the diffusion equation describing changes in the probability of fixation over time. Using the diffusion equation, the probability of fixation of deleterious alleles can also be determined for populations that are changing in size. The results developed in this paper can be used to estimate the fixation flux, defined as the rate at which beneficial alleles fix within a population. The fixation flux measures the rate of adaptive evolution of a population and, as we shall see, depends strongly on changes that occur in population size.

Journal

GeneticsGenetics Society of America

Published: Jun 1, 1997

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