# Statistical properties of the site-frequency spectrum associated with Lambda-coalescents

@article{Birkner2013StatisticalPO, title={Statistical properties of the site-frequency spectrum associated with Lambda-coalescents}, author={Matthias C. F. Birkner and Jochen Blath and Bjarki Eldon}, journal={arXiv: Populations and Evolution}, year={2013} }

Statistical properties of the site frequency spectrum associated with Lambda-coalescents are our objects of study. In particular, we derive recursions for the expected value, variance, and covariance of the spectrum, extending earlier results of Fu (1995) for the classical Kingman coalescent. Estimating coalescent parameters introduced by certain Lambda-coalescents for datasets too large for full likelihood methods is our focus. The recursions for the expected values we obtain can be used to…

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## 15 Citations

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## References

SHOWING 1-10 OF 19 REFERENCES

### A coalescent process with simultaneous multiple mergers for approximating the gene genealogies of many marine organisms.

- BiologyTheoretical population biology
- 2008

### On Asymptotics of the Beta Coalescents

- MathematicsAdvances in Applied Probability
- 2014

We show that the total number of collisions in the exchangeable coalescent process driven by the beta (1, b) measure converges in distribution to a 1-stable law, as the initial number of particles…

### Coalescent processes derived from some compound Poisson population models

- Mathematics
- 2011

A particular subclass of compound Poisson population models is analyzed. The models in the domain of attraction of the Kingman coalescent are characterized and it is shown that these models are never…

### Patterns of Neutral Diversity Under General Models of Selective Sweeps

- BiologyGenetics
- 2012

A general model of recurrent selective sweeps in a coalescent framework is developed, one that generalizes the recurrent full-sweep model to the case where selected alleles do not sweep to fixation and shows that in a large population, only the initial rapid increase of a selected allele affects the genealogy at partially linked sites.

### The asymptotic distribution of the length of Beta-coalescent trees

- Mathematics
- 2012

We derive the asymptotic distribution of the total length $L_n$ of a $\operatorname {Beta}(2-\alpha,\alpha)$-coalescent tree for $1<\alpha<2$, starting from $n$ individuals. There are two regimes: If…

### Population growth of human Y chromosomes: a study of Y chromosome microsatellites.

- Biology, EconomicsMolecular biology and evolution
- 1999

The finding of a recent common ancestor (probably in the last 120,000 years), coupled with a strong signal of demographic expansion in all populations, suggests either a recent human expansion from a small ancestral population, or natural selection acting on the Y chromosome.

### On the number of segregating sites in genetical models without recombination.

- EconomicsTheoretical population biology
- 1975

### Coalescents with Simultaneous Multiple Collisions

- Mathematics
- 2000

We study a family of coalescent processes that undergo ``simultaneous multiple collisions,'' meaning that many clusters of particles can merge into a single cluster at one time, and many such mergers…

### Testing for Neutrality in Samples With Sequencing Errors

- BiologyGenetics
- 2008

It is shown that even with a moderate number of sequencing errors, neutrality tests based on the frequency spectrum reject neutrality, which implies that analyses of data sets with such errors will systematically lead to wrong inferences of evolutionary scenarios.

### The Total External Branch Length of Beta-Coalescents†

- PhysicsCombinatorics, Probability and Computing
- 2014

It turns out that the fluctuations of the external branch length follow those of τn2−α over the entire parameter regime, where τn denotes the random number of coalescences that bring the n lineages down to one.