53 research outputs found
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
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