We shall extend Kingman's coalescent to the geographically structured population model with migration among colonies. It is described by a continuous-time Markov chain, which is proved to be a dual process of the diffusion process of stepping-stone model. We shall derive a system of equations for the spatial distribution of a common ancestor of sampled genes from colonies and the mean time to getting to one common ancestor. These equations are solved in three particular models; a two-population model, the island model and the one-dimensional stepping-stone model with symmetric nearest-neighbour migration.

In this article we assume that the entire population is subdivided into a finite number of panmictic colonies, each of which consists of a respective number of haploid individuals. We also assume that random genetic drift occurs in each colony and migration among colonies, which is independent of time and ergodic. We study the genealogical process of sampled genes from geographically structured populations. We prove that if the actual total population number is replaced by the effective population number, the mean coalescence time converges to that in a panmictic population in the strong migration limit. We also obtain the geographical distribution of the common ancestor.

Subterminal satellite (StSat) repeats, consisting of 32-bp-long AT-rich units (GATATTTCCATGTT(T/C)ATACAGATAGCGGTGTA), were first found in chimpanzee and gorilla (African great apes) as one of the major components of heterochromatic regions located proximal to telomeres of chromosomes. StSat repeats have not been found in orangutan (Asian great ape) or human. This patchy distribution among species suggested that the StSat repeats were present in the common ancestor of African great apes and subsequently lost in the lineage leading to human. An alternative explanation is that the StSat repeats in chimpanzee and gorilla have different origins and the repeats did not occur in human. The purpose of the present study was quantitative evaluation of the above alternative possibilities by analyzing the nucleotide variation contained in the repeats. We collected large numbers of sequences of repeat units from genome sequence databases of chimpanzee and gorilla, and also bonobo (an African great ape phylogenetically closer to chimpanzee). We then compared the base composition of the repeat units among the 3 species, and found statistically significant similarities in the base composition. These results support the view that the StSat repeats had already formed multiple arrays in the common ancestor of African great apes. It is thus suggested that humans lost StSat repeats which had once grown to multiple arrays.

Results of twin studies have shown that autism spectrum disorders (ASDs) are attributable to complex multigenic interactions rather than to a single susceptibility gene. However, the growing number of distinct, individually rare genetic causes of ASDs, mostly copy number variations (CNVs), favors an alternative to the polygenic hypothesis, the two-component model, which suggests that ASDs are caused either by de novo mutation or by dominant inheritance from asymptomatic carriers of such a mutation. To verify this hypothesis, we estimated the distribution of ASD-risk among both catchment area-based families and multiplex families. Our results suggest that the models with more than three risk components are preferable to the twocomponent model. Our results also suggest that the largest proportion of ASD cases is caused by dominant inheritance. We additionally show that Supplementary information regarding prevalence has a crucial role in analyzing proband-ascertained data.

The distribution of the number of segregating sites among randomly sampled DNA sequences from a geographically structured population is studied. We assume the infinitely-many-sites model of neutral genes and no recombination. Employing the genealogical process, we derive an equation for the generating function of the distribution of the number of segregating sites. First we study the strong-migration limit and prove that the distribution converges to that for a panmictic population. We also study the case of two sampled DNA sequences in the d-dimensional torus model with homogeneous migration.