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… 

Multi-locus data distinguishes between population growth and multiple merger coalescents

  • Jere Koskela
  • Computer Science
    Statistical applications in genetics and molecular biology
  • 2018
Abstract We introduce a low dimensional function of the site frequency spectrum that is tailor-made for distinguishing coalescent models with multiple mergers from Kingman coalescent models with

Quantifying uncertainty in the inference of generalized coalescents

TLDR
It is shown that useful inferences may be made from non-singleton data alone if singletons are suspect due to sequencing or data-cleaning errors, although the data requirements are greatly increased.

The site-frequency spectrum associated with Ξ-coalescents

TLDR
Recursions for the expected site-frequency spectrum associated with so-called Xi-coalescents, that is exchangeable coalescents which admit simultaneous multiple mergers of ancestral lineages, are given, and it is suggested that for autosomal population genetic data from diploid or polyploid highly fecund populations who may have skewed offspring distributions, one should not apply Lambda-coaledents, but Xi-cents.

The Site Frequency Spectrum for General Coalescents

TLDR
This work derives a new formula for the expected SFS for general Λ- and Ξ-coalescents, which leads to an efficient algorithm and obtains general theoretical results for the identifiability of the Λ measure when ζ is a constant function, as well as for the identity of the function ζ under a fixed Ξ measure.

Phase-type distributions in population genetics.

Phase-type distributions in population genetics

Probability modelling for DNA sequence evolution is well established and provides a rich framework for understanding genetic variation between samples of individuals from one or more populations. We

The multifurcating skyline plot

TLDR
This work applies the multifurcating skyline plot to a molecular clock phylogeny of 1,610 Ebola virus sequences from the 2014-2016 West African outbreak and shows that variance in the reproductive success of the pathogen through time can be estimated by combining the skyline plot with epidemiological case count data.

The expected neutral frequency spectrum of linked sites

We present an exact, closed expression for the expected neutral Site Frequency Spectrum for two neutral sites, 2-SFS, without recombination. This spectrum is the immediate extension of the well known

Inferring Demography and Selection in Organisms Characterized by Skewed Offspring Distributions

TLDR
A novel method for the joint inference of demography and selection under the Ψ-coalescent model, termed Multiple-Merger Coalescent Approximate Bayesian Computation, or MMC-ABC is proposed, which first demonstrates mis-inference under the Kingman, and exhibits the superior performance of M MC-ABC under conditions of skewed offspring distributions.

References

SHOWING 1-10 OF 76 REFERENCES

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

TLDR
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

TLDR
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.

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

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

TLDR
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.

  • B. Eldon
  • Biology
    Theoretical population biology
  • 2011

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

CONVERGENCE TO THE COALESCENT WITH SIMULTANEOUS MULTIPLE MERGERS

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
...