Maximum likelihood estimation of a migration matrix and effective population sizes in n subpopulations by using a coalescent approach

A maximum likelihood estimator based on the coalescent for unequal migration rates and different subpopulation sizes is developed. The method uses a Markov chain Monte Carlo approach to investigate possible genealogies with branch lengths and with migration events. Properties of the new method are shown by using simulated data from a four-population n-island model and a source–sink population model. Our estimation method as coded in migrate is tested against genetree; both programs deliver a very similar likelihood surface. The algorithm converges to the estimates fairly quickly, even when the Markov chain is started from unfavorable parameters. The method was used to estimate gene flow in the Nile valley by using mtDNA data from three human populations.

Geographical structuring in the mtDNA of Italians.

Geographical patterns of mtDNA variation were studied in 12 Italian samples (1072 individuals) by two different spatial autocorrelation methods. Separate analyses of the frequencies of 12 restriction morphs show North-South clines, differences between Sardinia and the mainland populations, and the effects of isolation by distance. A recently developed autocorrelation statistic summarizing molecular similarity at all sites (AIDA; autocorrelation index for DNA analysis) confirms the presence of a clinical pattern; differences between random pairs of haplotypes tend to increase with their geographical distance. The partition of gene diversity, however, reveals that most variability occurs within populations, whereas differences between populations are minor (GST = 0.057). When the data from the 12 samples are pooled, two descriptors of genetic variability (number of polymorphic sites and average sequence difference between pairs of individuals) do not behave as expected under neutrality. The presence of clinal patterns, Tajima's tests, and a simulation experiment agree in suggesting that population sizes increased rapidly in Italy and Sicily but not necessarily so in Sardinia. The distribution of pairwise sequence differences in the Italian peninsula (excluding Sardinia) permits a tentative location of the demographic increase between 8000 and 20,500 years ago. These dates are consistent with archaeological estimates of two distinct expansion processes, occurring, respectively, in the Neolithic and after the last glacial maximum in the Paleolithic. Conversely, there is no genetic evidence that such processes have had a major impact on the Sardinian population.

Using rare mutations to estimate population divergence times: A maximum likelihood approach

In this paper we propose a method to estimate by maximum likelihood the divergence time between two populations, specifically designed for the analysis of nonrecurrent rare mutations. Given the rapidly growing amount of data, rare disease mutations affecting humans seem the most suitable candidates for this method. The estimator RD, and its conditional version RDc, were derived, assuming that the population dynamics of rare alleles can be described by using a birth–death process approximation and that each mutation arose before the split of a common ancestral population into the two diverging populations. The RD estimator seems more suitable for large sample sizes and few alleles, whose age can be approximated, whereas the RDc estimator appears preferable when this is not the case. When applied to three cystic fibrosis mutations, the estimator RD could not exclude a very recent time of divergence among three Mediterranean populations. On the other hand, the divergence time between these populations and the Danish population was estimated to be, on the average, 4,500 or 15,000 years, assuming or not a selective advantage for cystic fibrosis carriers, respectively. Confidence intervals are large, however, and can probably be reduced only by analyzing more alleles or loci.