Reconstructing the Prior Probabilities of Allelic Phylogenies

In general when a phylogeny is reconstructed from DNA or protein sequence data, it makes use only of the probabilities of obtaining some phylogeny given a collection of data. It is also possible to determine the prior probabilities of different phylogenies. This information can be of use in analyzing the biological causes for the observed divergence of sampled taxa. Unusually “rare” topologies for a given data set may be indicative of different biological forces acting. A recursive algorithm is presented that calculates the prior probabilities of a phylogeny for different allelic samples and for different phylogenies. This method is a straightforward extension of Ewens' sample distribution. The probability of obtaining each possible sample according to Ewens' distribution is further subdivided into each of the possible phylogenetic topologies. These probabilities depend not only on the identity of the alleles and on 4Nμ (four times the effective population size times the neutral mutation rate) but also on the phylogenetic relationships among the alleles. Illustrations of the algorithm are given to demonstrate how different phylogenies are favored under different conditions.

Maximum Likelihood Estimation of Recombination Rates From Population Data

We describe a method for co-estimating r = C/μ (where C is the per-site recombination rate and μ is the per-site neutral mutation rate) and Θ = 4Neμ (where Ne is the effective population size) from a population sample of molecular data. The technique is Metropolis-Hastings sampling: we explore a large number of possible reconstructions of the recombinant genealogy, weighting according to their posterior probability with regard to the data and working values of the parameters. Different relative rates of recombination at different locations can be accommodated if they are known from external evidence, but the algorithm cannot itself estimate rate differences. The estimates of Θ are accurate and apparently unbiased for a wide range of parameter values. However, when both Θ and r are relatively low, very long sequences are needed to estimate r accurately, and the estimates tend to be biased upward. We apply this method to data from the human lipoprotein lipase locus.

Maximum Likelihood Estimation of Population Growth Rates Based on the Coalescent

We describe a method for co-estimating 4Neμ (four times the product of effective population size and neutral mutation rate) and population growth rate from sequence samples using Metropolis-Hastings sampling. Population growth (or decline) is assumed to be exponential. The estimates of growth rate are biased upwards, especially when 4Neμ is low; there is also a slight upwards bias in the estimate of 4Neμ itself due to correlation between the parameters. This bias cannot be attributed solely to Metropolis-Hastings sampling but appears to be an inherent property of the estimator and is expected to appear in any approach which estimates growth rate from genealogy structure. Sampling additional unlinked loci is much more effective in reducing the bias than increasing the number or length of sequences from the same locus.

Estimation of the Amount of DNA Polymorphism When the Neutral Mutation Rate Varies Among Sites

Knowing the amount of DNA polymorphism is essential to understand the mechanism of maintaining DNA polymorphism in a natural population. The amount of DNA polymorphism can be measured by the average number of nucleotide differences per site (π), the proportion of segregating (polymorphic) site (s) and the minimum number of mutations per site (s*). Since the latter two quantities depend on the sample size, θ is often used as a measure of the amount of DNA polymorphism, where θ = 4Nμ, N is the effective population size and μ is the neutral mutation rate per site per generation. It is known that θ estimated from π, s and s* under the infinite site model can be biased when the mutation rate varies among sites. We have therefore developed new methods for estimating θ under the finite site model. Using computer simulations, it has been shown that the new methods give almost unbiased estimates even when the mutation rate varies among sites substantially. Furthermore, we have also developed new statistics for testing neutrality by modifying Tajima's D statistic. Computer simulations suggest that the new test statistics can be used even when the mutation rate varies among sites.

The Amount of DNA Polymorphism Maintained in a Finite Population When the Neutral Mutation Rate Varies Among Sites

The expectations of the average number of nucleotide differences per site (π), the proportion of segregating site (s), the minimum number of mutations per site (s*) and some other quantities were derived under the finite site models with and without rate variation among sites, where the finite site models include Jukes and Cantor's model, the equal-input model and Kimura's model. As a model of rate variation, the gamma distribution was used. The results indicate that if distribution parameter α is small, the effect of rate variation on these quantities are substantial, so that the estimates of θ based on the infinite site model are substantially underestimated, where θ = 4Nv, N is the effective population size and vis the mutation rate per site per generation. New methods for estimating θ are also presented, which are based on the finite site models with and without rate variation. Using these methods, underestimation can be corrected.

A quantitative test of the neutral theory using pooled allozyme data.

Neutral theory predicts a positive correlation between the amount of polymorphism within species and evolutionary rate. Previous tests of this prediction using both allozyme and DNA data have led to conflicting conclusions about the influence of selection and mutation drift. It is argued here that quantitative conclusions about the adequacy of neutral theory can be obtained by analyzing genetic data pooled from many sources. Using this approach, a large database containing information on allozyme variation in over 1500 species is used to examine the relationship between heterozygosity and genetic distance. The results provide support for the hypothesis that a major percentage of protein variation can be explained by variation in neutral mutation rate, and a minor percentage by strong selection.

Molecular population genetics of an electrophoretically monomorphic protein in the alcohol dehydrogenase region of Drosophila pseudoobscura.

Nucleotide sequence data from the alcohol dehydrogenase (Adh) region of 18 isochromosomal strains of Drosophila pseudoobscura were used to determine whether the lack of amino acid polymorphism in ADH results from a low neutral mutation rate or a recent directional selection event. We estimated the neutral mutation parameter, 4Nmu, in synonymous sites for 17 subregions of Adh. The nucleotide diversity data were tested for departures from an equilibrium neutral model with two statistical tests. The Tajima test and the Hudson, Kreitman and Aguade test each failed to reject a neutral model. These results suggest that the ADH enzyme of D. pseudoobscura lacks amino acid polymorphisms because the neutral mutation rate of nonsynonymous sites is low. The neutral mutation parameter for synonymous sites is heterogeneous between domains of the Adh region. These data indicate that selective constrains on synonymous sites can vary between functional domains.

Branching diffusion processes in population genetics

A branching random field is considered as a model of either of two situations in genetics in which migration or dispersion plays a role. Specifically we consider the expected number of individualsNAin a (geographical) setAat timet, the covariance ofNAandNBfor two setsA, B, and the probabilityI(x, y, u) that two individuals found at locationsx, yat timetare of the same genetic type if the population is subject to a selectively neutral mutation rateu.The last also leads to limit laws for the average degree of relationship of individuals in various types of branching random fields. We also find the equations that the mean and bivariate densities satisfy, and explicit formulas when the underlying migration process is Brownian motion.