scholarly journals THE POPULATION GENETICS OF ADAPTATION: THE ADAPTATION OF DNA SEQUENCES

Evolution ◽  
2002 ◽  
Vol 56 (7) ◽  
pp. 1317-1330 ◽  
Author(s):  
H. Allen Orr
Keyword(s):  
Population Genetics ◽  
Dna Sequences ◽  
Genetics Of Adaptation

scholarly journals The Population Genetics of Adaptation: Multiple Substitutions on a Smooth Fitness Landscape

Genetics ◽  
2009 ◽  
Vol 183 (3) ◽  
pp. 1079-1086 ◽  
Author(s):  
Robert L. Unckless ◽  
H. Allen Orr
Keyword(s):  
Population Genetics ◽  
Recent Work ◽  
Adaptive Evolution ◽  
Theoretical Study ◽  
Fitness Landscape ◽  
Selective Advantage ◽  
Analytic Solutions ◽  
Strong Selection ◽  
Genetics Of Adaptation ◽  
New Mutations

Much recent work in the theoretical study of adaptation has focused on the so-called strong selection–weak mutation (SSWM) limit, wherein adaptation is due to new mutations of definite selective advantage. This work, in turn, has focused on the first step (substitution) during adaptive evolution. Here we extend this theory to allow multiple steps during adaptation. We find analytic solutions to the probability that adaptation follows a certain path during evolution as well as the probability that adaptation arrives at a given genotype regardless of the path taken. We also consider the probability of parallel adaptation and the proportion of the total increase in fitness caused by the first substitution. Our key assumption is that there is no epistasis among beneficial mutations.

scholarly journals A faster and more accurate algorithm for calculating population genetics statistics requiring sums of Stirling numbers of the first kind

2020 ◽  
Author(s):  
Swaine L. Chen ◽  
Nico M. Temme
Keyword(s):  
Population Genetics ◽  
Dna Sequences ◽  
Cumulative Distribution Function ◽  
Beta Function ◽  
Stirling Numbers ◽  
Cumulative Distribution ◽  
Incomplete Beta Function ◽  
Improved Method ◽  
Direct Estimate ◽  
Improve Accuracy

AbstractStirling numbers of the first kind are used in the derivation of several population genetics statistics, which in turn are useful for testing evolutionary hypotheses directly from DNA sequences. Here, we explore the cumulative distribution function of these Stirling numbers, which enables a single direct estimate of the sum, using representations in terms of the incomplete beta function. This estimator enables an improved method for calculating an asymptotic estimate for one useful statistic, Fu’s Fs. By reducing the calculation from a sum of terms involving Stirling numbers to a single estimate, we simultaneously improve accuracy and dramatically increase speed.

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