# The fixation time of a strongly beneficial allele in a structured population

@article{Greven2014TheFT, title={The fixation time of a strongly beneficial allele in a structured population}, author={Andreas Greven and Peter Pfaffelhuber and Cornelia Pokalyuk and A. Wakolbinger}, journal={arXiv: Probability}, year={2014} }

For a beneficial allele which enters a large unstructured population and eventually goes to fixation, it is known that the time to fixation is approximately $2\log(\alpha)/\alpha$ for a large selection coefficient $\alpha$. For a population that is distributed over finitely many colonies, with migration between these colonies, we detect various regimes of the migration rate $\mu$ for which the fixation times have different asymptotics as $\alpha \to \infty$. If $\mu$ is of order $\alpha$, the…

## 6 Citations

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## References

SHOWING 1-10 OF 32 REFERENCES

A framework for estimating the fixation time of an advantageous allele in stepping‐stone models

- EconomicsJournal of evolutionary biology
- 2012

A framework for calculating the fixation time of a positively selected allele in a subdivided population, as a function of the number of demes present, the migration rate between them and the manner in which they are connected is laid out.

Fixation probability and time in subdivided populations.

- BiologyGenetics
- 2003

This article allows for an arbitrary distribution among demes of reproductive success, both beneficial and deleterious effects, and arbitrary dominance, and verified by simulation for a broad range of population structures, including the island model, the stepping-stone model, and a model with extinction and recolonization.

FIXATION PROBABILITIES AND FIXATION TIMES IN A SUBDIVIDED POPULATION

- MathematicsEvolution; international journal of organic evolution
- 1981

The approach taken in this paper to the problem of finding the probabilities of fixation and times to fixation in a subdivided population is necessarily indirect and there is no way to solve the complete multi-dimensional diffusion equation and obtain the required quantities.

An approximate sampling formula under genetic hitchhiking

- Biology
- 2006

A sampling formula is derived which shows that, with this order of accuracy, in a sample of fixed size there are at most two nonsingleton families of individuals which are identical by descent at the neutral locus from the beginning of the sweep.

The hitch-hiking effect of a favourable gene.

- BiologyGenetical research
- 1974

If the selective coefficients at the linked locus are small compared to those at the substituted locus, it is shown that the probability of complete fixation at thelinked locus is approximately exp (— Nc), where c is the recombinant fraction and N the population size.

The conditional ancestral selection graph with strong balancing selection.

- BiologyTheoretical population biology
- 2009

The ancestral selection graph under strong directional selection.

- BiologyTheoretical population biology
- 2013

Duality, ancestral and diffusion processes in models with selection.

- BiologyTheoretical population biology
- 2009

Random partitions approximating the coalescence of lineages during a selective sweep

- Biology
- 2004

Two approximations for the selective sweep of a selective sweep are introduced, one of which is related to Kingman’s paintbox construction, replaces the coin flips by integer-valued random variables and leads to very accurate results.

Hitchhiking Effect of a Beneficial Mutation Spreading in a Subdivided Population

- BiologyGenetics
- 2011

The results indicate that the overall strength of genetic hitchhiking—the degree to which expected heterozygosity decreases—is diminished by population subdivision, mainly because opportunity for the breakdown of Hitchhiking by recombination increases as the spread of the beneficial mutation across demes is delayed when migration rate is much smaller than the strength of selection.