Sample genealogies and genetic variation in populations of variable size

We consider neutral evolution of a large population subject to changes in its population size. For a population with a time-variable carrying capacity we have computed the distributions of the total branch lengths of its sample genealogies. Within the coalescent approximation we have obtained a general expression, Eq. (27), for the moments of these distributions for an arbitrary smooth dependence of the population size on time. We investigate how the frequency of population-size variations alters the distributions. This allows us to discuss their influence on the distribution of the number of mutations, and on the population homozygosity in populations with variable size.Comment: 19 pages, 8 figures, 1 tabl

An accurate model for genetic hitch-hiking

We suggest a simple deterministic approximation for the growth of the favoured-allele frequency during a selective sweep. Using this approximation we introduce an accurate model for genetic hitch-hiking. Only when Ns < 10 (N is the population size and s denotes the selection coefficient), are discrepancies between our approximation and direct numerical simulations of a Moran model noticeable. Our model describes the gene genealogies of a contiguous segment of neutral loci close to the selected one, and it does not assume that the selective sweep happens instantaneously. This enables us to compute SNP distributions on the neutral segment without bias.Comment: 12 pages, 10 figure

Linkage disequilibrium under recurrent bottlenecks

Understanding patterns of selectively neutral genetic variation is essential in order to model deviations from neutrality, caused for example by different forms of selection. Best understood is neutral genetic variation at a single locus, but additional insights can be gained by investigating genetic variation at multiple loci. The corresponding patterns of variation reflect linkage disequilibrium and provide information about the underlying multi-locus gene genealogies. The statistical properties of two-locus genealogies have been intensively studied for populations of constant census size, as well as for simple demographic histories such as exponential population growth, and single bottlenecks. By contrast, the combined effect of recombination and sustained demographic fluctuations is poorly understood. Addressing this issue, we study a two-locus Wright-Fisher model of a population subject to recurrent bottlenecks. We derive coalescent approximations for the covariance of the times to the most recent common ancestor at two loci. We find, first, that an effective population-size approximation describes the numerically observed linkage disequilibrium provided that recombination occurs either much faster or much more slowly than the population size changes. Second, when recombination occurs frequently between bottlenecks but rarely within bottlenecks, we observe long-range linkage disequilibrium. Third, we show that in the latter case, a commonly used measure of linkage disequilibrium, sigma_d^2 (closely related to r^2), fails to capture long-range linkage disequilibrium because constituent terms, each reflecting long-range linkage disequilibrium, cancel. Fourth, we analyse a limiting case in which long-range linkage disequilibrium can be described in terms of a Xi-coalescent process allowing for simultaneous multiple mergers of ancestral lines.Comment: 34 pages, 7 figure

The effect of multiple paternity on genetic diversity during and after colonisation

In metapopulations, genetic variation of local populations is influenced by the genetic content of the founders, and of migrants following establishment. We analyse the effect of multiple paternity on genetic diversity using a model in which the highly promiscuous marine snail Littorina saxatilis expands from a mainland to colonise initially empty islands of an archipelago. Migrant females carry a large number of eggs fertilised by 1 - 10 mates. We quantify the genetic diversity of the population in terms of its heterozygosity: initially during the transient colonisation process, and at long times when the population has reached an equilibrium state with migration. During colonisation, multiple paternity increases the heterozygosity by 10 - 300 % in comparison with the case of single paternity. The equilibrium state, by contrast, is less strongly affected: multiple paternity gives rise to 10 - 50 % higher heterozygosity compared with single paternity. Further we find that far from the mainland, new mutations spreading from the mainland cause bursts of high genetic diversity separated by long periods of low diversity. This effect is boosted by multiple paternity. We conclude that multiple paternity facilitates colonisation and maintenance of small populations, whether or not this is the main cause for the evolution of extreme promiscuity in Littorina saxatilis.Comment: 7 pages, 5 figures, electronic supplementary materia

Gene-history correlation and population structure

Correlation of gene histories in the human genome determines the patterns of genetic variation (haplotype structure) and is crucial to understanding genetic factors in common diseases. We derive closed analytical expressions for the correlation of gene histories in established demographic models for genetic evolution and show how to extend the analysis to more realistic (but more complicated) models of demographic structure. We identify two contributions to the correlation of gene histories in divergent populations: linkage disequilibrium, and differences in the demographic history of individuals in the sample. These two factors contribute to correlations at different length scales: the former at small, and the latter at large scales. We show that recent mixing events in divergent populations limit the range of correlations and compare our findings to empirical results on the correlation of gene histories in the human genome.Comment: Revised and extended version: 26 pages, 5 figures, 1 tabl