The population genealogy of the infinitely-many neutral alleles model

A process analogous to Kingman's coalescent is introduced to describe the genealogy of populations evolving according to the infinitelymany neutral alleles model. The process records population frequencies in old and new classes, and labels the new classes in order of decreasing age. Its marginal distribution is characterized in a form which is amenable to explicit calculations and the transition densities of the associated K-allele models follow readily from this representation.     

Integrating genealogy and epidemiology: the ancestral infection and selection graph as a model for reconstructing host virus histories

We model the genealogies of coupled haploid host-virus populations. Hosts reproduce and replace other hosts as in the Moran model. The virus can be transmitted between individuals of the same and succeeding generations. The epidemic model allows a selective advantage for susceptible over infected hosts. The coupled host-virus ancestry of a sample of hosts is embedded in a branching and coalescing structure that we call the Ancestral Infection and Selection Graph, a direct analogue to the Ancestral Selection Graph of Krone and Neuhauser [1997. Theoret. Population Biol. 51, 210-237]. We prove this and discuss various special cases. We show that the inter-host viral genealogy is a scaled coalescent. Using simulations, we compare the viral genealogy under this model to earlier published models and investigate the estimatability of the selection and infectious contact rates. We use simulations to compare the persistence of the disease with the time to the ultimate ancestor.     

The distribution of the coalescence time and the number of pairwise nucleotide differences in a model of population divergence or speciation with an initial period of gene flow

This paper is concerned with a model of “isolation with an initial period of migration”, where a panmictic ancestral population split into n descendant populations which exchanged migrants symmetrically at a constant rate for a period of time and subsequently became completely isolated. In the limit as the population split occurred an infinitely long time ago, the model becomes an “isolation after migration” model, describing completely isolated descendant populations which arose from a subdivided ancestral population. The probability density function of the coalescence time of a pair of genes and the probability distribution of the number of pairwise nucleotide differences are derived for both models. Whilst these are theoretical results of interest in their own right, they also give an exact analytical expression for the likelihood, for data consisting of the numbers of nucleotide differences between pairs of DNA sequences where each pair is at a different, independent locus. The behaviour of the distribution of the number of pairwise nucleotide differences under these models is illustrated and compared to the corresponding distributions under the “isolation with migration” and “complete isolation” models. It is shown that the distribution of the number of nucleotide differences between a pair of DNA sequences from different descendant populations in the model of “isolation with an initial period of migration” can be quite different from that under the “isolation with migration model”, even if the average migration rate over time (and hence the total number of migrants) is the same in both scenarios. It is also illustrated how the results can be extended to other demographic scenarios that can be described by a combination of isolated panmictic populations and “symmetric island” models.     

Genetic and morphological studies of Nothobranchius (Cyprinodontiformes) from Malawi with description of Nothobranchius wattersi sp. nov.

Molecular and morphological data were used to explore evolutionary differentiation among populations of Nothobranchius in the Lake Malawi–upper Shire River and the Lakes Chilwa–Chiuta drainage systems in Malawi. The aim of the study was to test the hypothesis that Nothobranchius of the Malawi–Shire system constitute a separate evolutionary group from Nothobranchius kirki. Mitochondrial and nuclear sequence data show a strongly supported phylogenetic split into two monophyletic groups separating the Lake Malawi basin fish from N. kirki. Unlike N. kirki, Lake Malawi–Shire fish do not deviate from neutrality and express an excess of rare haplotypes and mutations in terminal branches, characteristic of recently expanded populations. Further, the two groups significantly differ in morphology. Two body characters (dorsal‐fin base length and pre‐pelvic–pre‐anal distance) are significantly different between the two species in both sexes. Several other characters are significantly different in either male or female comparisons with respect to both standard and head lengths, and robust morphological differentiation is detected by multivariate analysis. The two groups are readily distinguished on the basis of male colouration, especially in scale centres and the caudal fin. On the basis of this differentiation at the molecular and morphological levels, in addition to colouration, the Lake Malawi–Shire fish are hereby formally recognized as constituting a new species, Nothobranchius wattersi. This distinction is in agreement with the geomorphologic and recent climatic history in the region.     

The distribution of the coalescence time and the number of pairwise nucleotide differences in the "isolation with migration" model

This paper is concerned with the “isolation with migration” model, where a panmictic ancestral population gave rise to a symmetric n-island model, time τ ago. Explicit analytical expressions are derived for the probability density function of the coalescence time of a pair of genes sampled at random from the same subpopulation or from different subpopulations, and for the probability distribution of the number of pairwise nucleotide differences.     

Genetic identification of a small and highly isolated population of fin whales (Balaenoptera physalus) in the Sea of Cortez, México

For many years, researchers have speculatedthat fin whales are year-round residents in theSea of Cortez (= Gulf of California). Previouswork by Bérubé and co-workers has shownthat the degree of genetic diversity among finwhales in the Sea of Cortez at nuclear andmitochondrial loci is highly reduced. However,the relatively unobstructed connection with theNorth Pacific Ocean argues that Sea of Cortezfin whales are part of a much larger easternNorth Pacific population given the extensivemigratory ranges observed in fin whales andbaleen whales in general. The low degree ofgenetic variation might thus simply be due tohistoric fluctuations in the effectivepopulation size of an eastern North Pacificpopulation. In order to test if the reducedgenetic variation detected among fin whales inthe Sea of Cortez is due to small populationsize or a past bottleneck in an otherwise largeeastern North Pacific population, we analyzedthe geographic distribution of geneticvariation at a single mitochondrial (controlregion) and 16 nuclear loci in samplescollected from fin whales in the eastern NorthPacific (n = 12) as well as the Sea of Cortez(n = 77). Our results showed that fin whalesobserved in the Sea of Cortez constitute ahighly isolated and thus evolutionary uniquepopulation, which warrants special conservationmeasures given the current low estimate ofabundance of approximately 400 individuals.     

On the size distribution of private microsatellite alleles

Private microsatellite alleles tend to be found in the tails rather than in the interior of the allele size distribution. To explain this phenomenon, we have investigated the size distribution of private alleles in a coalescent model of two populations, assuming the symmetric stepwise mutation model as the mode of microsatellite mutation. For the case in which four alleles are sampled, two from each population, we condition on the configuration in which three distinct allele sizes are present, one of which is common to both populations, one of which is private to one population, and the third of which is private to the other population. Conditional on this configuration, we calculate the probability that the two private alleles occupy the two tails of the size distribution. This probability, which increases as a function of mutation rate and divergence time between the two populations, is seen to be greater than the value that would be predicted if there was no relationship between privacy and location in the allele size distribution. In accordance with the prediction of the model, we find that in pairs of human populations, the frequency with which private microsatellite alleles occur in the tails of the allele size distribution increases as a function of genetic differentiation between populations.