# Statistical Properties of the Site-Frequency Spectrum Associated with Λ-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={Genetics}, year={2013}, volume={195}, pages={1037 - 1053} }

Statistical properties of the site-frequency spectrum associated with Λ-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 Λ-coalescents for data sets too large for full-likelihood methods is our focus. The recursions for the expected values we obtain can be used to find the…

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## References

SHOWING 1-10 OF 76 REFERENCES

### Computing likelihoods for coalescents with multiple collisions in the infinitely many sites model

- MathematicsJournal of mathematical biology
- 2008

It is argued that within the (vast) family of Λ-coalescents, the parametrisable sub-family of Beta(2 − α, α)-coalesCents, where α ∈ (1, 2], are of particular relevance and obtained a method to compute (approximate) likelihood surfaces for the observed type probabilities of a given sample.

### Experiments with the Site Frequency Spectrum

- Computer Science, MathematicsBulletin of mathematical biology
- 2011

This work uses a controlled lumped Markov chain and computational commutative algebraic methods to compute the exact likelihood of the SFS and many classical linear combinations of it at a non-recombining locus that is neutrally evolving under the infinitely-many-sites mutation model.

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

- BiologyTheoretical population biology
- 2008

### Importance sampling for Lambda-coalescents in the infinitely many sites model.

- MathematicsTheoretical population biology
- 2011

### Coalescent Processes When the Distribution of Offspring Number Among Individuals Is Highly Skewed

- BiologyGenetics
- 2006

A complex set of scaling relationships between mutation and reproduction in a simple model of a population suggests the presence of rare reproduction events in which ∼8% of the population is replaced by the offspring of a single individual.

### Estimation of parameters in large offspring number models and ratios of coalescence times.

- BiologyTheoretical population biology
- 2011

### Analysis of DNA sequence variation within marine species using Beta-coalescents.

- BiologyTheoretical population biology
- 2013

### A coalescent model for the effect of advantageous mutations on the genealogy of a population

- Mathematics
- 2004

### CONVERGENCE TO THE COALESCENT WITH SIMULTANEOUS MULTIPLE MERGERS

- Mathematics
- 2003

The general coalescent process with simultaneous multiple mergers of ancestral lines was initially characterized by Mohle and Sagitov (2001) in terms of a sequence of measures defined on the…