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Originally published as Genetics Published Articles Ahead of Print on June 11, 2007.
Genetics, Vol. 176, 2441-2449, August 2007, Copyright © 2007
doi:10.1534/genetics.106.068585
Testing the Extreme Value Domain of Attraction for Distributions of Beneficial Fitness Effects
Craig J. Beisel*,
,
Darin R. Rokyta*,
,
Holly A. Wichman*, and
Paul Joyce*,,1
Department of Mathematics, Department of Biological Sciences and * Initiative for Bioinformatics and Evolutionary Studies (IBEST), University of Idaho, Moscow, Idaho 83844
1 Corresponding author: Department of Mathematics, University of Idaho, 413 Brink Hall, Moscow, ID 83844-1103.
E-mail: joyce{at}uidaho.edu
In modeling evolutionary genetics, it is often assumed that mutational effects are assigned according to a continuous probability distribution, and multiple distributions have been used with varying degrees of justification. For mutations with beneficial effects, the distribution currently favored is the exponential distribution, in part because it can be justified in terms of extreme value theory, since beneficial mutations should have fitnesses in the extreme right tail of the fitness distribution. While the appeal to extreme value theory seems justified, the exponential distribution is but one of three possible limiting forms for tail distributions, with the other two loosely corresponding to distributions with right-truncated tails and those with heavy tails. We describe a likelihood-ratio framework for analyzing the fitness effects of beneficial mutations, focusing on testing the null hypothesis that the distribution is exponential. We also describe how to account for missing the smallest-effect mutations, which are often difficult to identify experimentally. This technique makes it possible to apply the test to gain-of-function mutations, where the ancestral genotype is unable to grow under the selective conditions. We also describe how to pool data across experiments, since we expect few possible beneficial mutations in any particular experiment.
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