Inference of gene flow in the process of speciation: Efficient maximum-likelihood implementation of a generalised isolation-with-migration model.

The 'isolation with migration' (IM) model has been extensively used in the literature to detect gene flow during the process of speciation. In this model, an ancestral population split into two or more descendant populations which subsequently exchanged migrants at a constant rate until the present. Of course, the assumption of constant gene flow until the present is often over-simplistic in the context of speciation. In this paper, we consider a 'generalised IM' (GIM) model: a two-population IM model in which migration rates and population sizes are allowed to change at some point in the past. By developing a maximum-likelihood implementation of this model, we enable inference on both historical and contemporary rates of gene flow between two closely related populations or species. The GIM model encompasses both the standard two-population IM model and the 'isolation with initial migration' (IIM) model as special cases, as well as a model of secondary contact. We examine for simulated data how our method can be used, by means of likelihood ratio tests or AIC scores, to distinguish between the following scenarios of population divergence: (a) divergence in complete isolation; (b) divergence with a period of gene flow followed by isolation; (c) divergence with a period of isolation followed by secondary contact; (d) divergence with ongoing gene flow. Our method is based on the coalescent and is suitable for data sets consisting of the number of nucleotide differences between one pair of DNA sequences at each of a large number of independent loci. As our method relies on an explicit expression for the likelihood, it is computationally very fast.

Hybrid asexuality as a primary postzygotic barrier between nascent species: On the interconnection between asexuality, hybridization and speciation.

Although sexual reproduction is ubiquitous throughout nature, the molecular machinery behind it has been repeatedly disrupted during evolution, leading to the emergence of asexual lineages in all eukaryotic phyla. Despite intensive research, little is known about what causes the switch from sexual reproduction to asexuality. Interspecific hybridization is one of the candidate explanations, but the reasons for the apparent association between hybridization and asexuality remain unclear. In this study, we combined cross-breeding experiments with population genetic and phylogenomic approaches to reveal the history of speciation and asexuality evolution in European spined loaches (Cobitis). Contemporary species readily hybridize in hybrid zones, but produce infertile males and fertile but clonally reproducing females that cannot mediate introgressions. However, our analysis of exome data indicates that intensive gene flow between species has occurred in the past. Crossings among species with various genetic distances showed that, while distantly related species produced asexual females and sterile males, closely related species produce sexually reproducing hybrids of both sexes. Our results suggest that hybridization leads to sexual hybrids at the initial stages of speciation, but as the species diverge further, the gradual accumulation of reproductive incompatibilities between species could distort their gametogenesis towards asexuality. Interestingly, comparative analysis of published data revealed that hybrid asexuality generally evolves at lower genetic divergences than hybrid sterility or inviability. Given that hybrid asexuality effectively restricts gene flow, it may establish a primary reproductive barrier earlier during diversification than other "classical" forms of postzygotic incompatibilities. Hybrid asexuality may thus indirectly contribute to the speciation process.

Inference of Gene Flow in the Process of Speciation: An Efficient Maximum-Likelihood Method for the Isolation-with-Initial-Migration Model.

The isolation-with-migration (IM) model is commonly used to make inferences about gene flow during speciation, using polymorphism data. However, it has been reported that the parameter estimates obtained by fitting the IM model are very sensitive to the model's assumptions-including the assumption of constant gene flow until the present. This article is concerned with the isolation-with-initial-migration (IIM) model, which drops precisely this assumption. In the IIM model, one ancestral population divides into two descendant subpopulations, between which there is an initial period of gene flow and a subsequent period of isolation. We derive a very fast method of fitting an extended version of the IIM model, which also allows for asymmetric gene flow and unequal population sizes. This is a maximum-likelihood method, applicable to data on the number of segregating sites between pairs of DNA sequences from a large number of independent loci. In addition to obtaining parameter estimates, our method can also be used, by means of likelihood-ratio tests, to distinguish between alternative models representing the following divergence scenarios: (a) divergence with potentially asymmetric gene flow until the present, (b) divergence with potentially asymmetric gene flow until some point in the past and in isolation since then, and (c) divergence in complete isolation. We illustrate the procedure on pairs of Drosophila sequences from ∼30,000 loci. The computing time needed to fit the most complex version of the model to this data set is only a couple of minutes. The R code to fit the IIM model can be found in the supplementary files of this article.

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.

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 tau 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.

A stochastic model for head lice infections.

We investigate the dynamics of head lice infections in schools, by considering a model for endemic infection based on a stochastic SIS (susceptible-infected-susceptible) epidemic model, with the addition of an external source of infection. We deduce a range of properties of our model, including the length of a single outbreak of infection. We use the stationary distribution of the number of infected individuals, in conjunction with data from a recent study carried out in Welsh schools on the prevalence of head lice infections, and employ maximum likelihood methods to obtain estimates of the model parameters. A complication is that, for each school, only a sample of the pupils was checked for infection. Our likelihood function takes account of the missing data by incorporating a hypergeometric sampling element. We arrive at estimates of the ratios of the "within school" and "external source" transmission rates to the recovery rate and use these to obtain estimates for various quantities of interest.

The effect of unequal migration rates on FST.

Using the structured coalescent model, it is shown that unequal migration rates between different pairs of subpopulations can increase the value of Wright's coefficient F(ST) and its dependence on the mutation rate, and decrease the effective level of gene flow. Two specific models of population structure are considered: (i) an 'island model with barrier' where migration rates between subpopulations on the same side of the barrier are higher than migration rates between subpopulations on opposite sides of the barrier, and (ii) the two-dimensional stepping-stone model with unequal migration rates in the two dimensions of the model.

Allelic histories: positive selection on a HIV-resistance allele.

The CCR5-Delta32 allele crucially determines the course of HIV infection and appears to be highly protective against the disease. Population genetic studies suggest that the allele has been under positive selection in Europe in the past. In a recent paper, Alison Galvani and Montgomery Slatkin collate the available evidence and use a mathematical model to strongly suggest that smallpox could have exerted sufficient selection pressure to explain the distribution of the allele across Europe. This is a beautiful example of the power of mathematical models in evolutionary genetics.