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After testing for the mutation rate, the comparison of topologies assuming a particular mutation rate distribution allows us to check for which topology presents a higher posterior probability.
Recently, genome-wide analyses suggested that the gammar-distribution fits the population mutation rate distribution for the microsatellite loci in human [ 24].
From this distribution of counts, we can directly calculate the coefficient of variation and skewness of the mutation rate distribution because these statistics are scale invariant.
We estimate analogously to R2: Now we develop theory to connect R2 with the variance of the mutation rate distribution, f.
Combining this R 2 ^ value with our R 3 ^ value, we estimate the skewness of the mutation rate distribution to be γ ^ = 0.81 (bootstrap 95% confidence interval of 0.11 1.61).
Using the theory developed in Methods and the R 2 ^ value from cSNPs, we estimate the coefficient of variation for the mutation rate distribution to be c v ^ = 1.22 (bootstrap 95% confidence interval of 1.18 1.27).
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If the true mutation rate distributions were to follow the gamma distribution, then the probability of having a mutation rate greater than 0.05/(4 Ne) is vanishingly low and the infinite sites assumption works well.
For the mutation rate prior distribution, we used a lognormal distribution with a mean rate of 1.4% sequence divergence per million years as estimated for Richardsonius, and specified a range of 1.0%to2.4%4% sequence divergence per million years to cover the range of mutation rates for cyt b for closely related genera [ 55] as well as reported mutation rates for CR in other cyprinids [ 77, 78].
Repetition of these calculations at each mismatch load for many generations allows simulating the evolution of a given initial distribution of sequence frequencies in a population under a given mutation rate and distribution of uptake bias values towards sequences at different mismatch loads.
Because the number of PCR doublings is large compared the average mutation rate, the distribution of mutations among sequences should be well described by the Poisson distribution [ 40, 41].
For example, the mutation rate, the distribution of allelic effects, the carrying capacity, and the birth rate can affect times to extinction in this model.
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