# Multiple-merger genealogies: Models, consequences, inference

@article{Freund2020MultiplemergerGM,
title={Multiple-merger genealogies: Models, consequences, inference},
author={Fabian Freund},
journal={arXiv: Probability},
year={2020}
}
• F. Freund
• Published 23 October 2020
• Biology
• arXiv: Probability
Trees corresponding to $\Lambda$- and $\Xi$-$n$-coalescents can be both quite similar and fundamentally different compared to bifurcating tree models based on Kingman's $n$-coalescent. This has consequences for inference of a well-fitting gene genealogy as well as for assessing biological properties of species having such sample genealogies. Here, mathematical properties concerning clade sizes in the tree as well as changes of the tree when the samples are enlargened are highlighted. To be used…
4 Citations

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## References

SHOWING 1-10 OF 57 REFERENCES
Cannings models, population size changes and multiple-merger coalescents
• F. Freund
• Mathematics
Journal of mathematical biology
• 2020
This article gives a more general construction of time-changed Λ - n -coalescents as limits of specific Cannings models with rather arbitrary time changes.
Distinguishing multiple-merger from Kingman coalescence using two-site frequency spectra
• Biology
• 2018
A new method is presented based on the pointwise mutual information of the two-site frequency spectrum for pairs of linked sites that can detect when the genome-wide genetic diversity is inconsistent with the Kingman coalescent, rather than detecting outlier regions, as in selection scan methods.
Rigorous results for a population model with selection II: genealogy of the population
We consider a model of a population of fixed size $N$ undergoing selection. Each individual acquires beneficial mutations at rate $\mu_N$, and each beneficial mutation increases the individual's
Genealogies in simple models of evolution
• Biology
• 2012
It is discussed how coalescence times which grow logarithmically with the size of the population in contrast with the linear growth of the neutral case are modified in a simple way of introducing selection.
Genealogical Properties of Subsamples in Highly Fecund Populations
• Mathematics
bioRxiv
• 2017
The results indicate how ’informative’ a subsample is about the properties of the larger complete sample, how much information is gained by increasing the sample size, and how the ‘informativeness’ of the subsample varies between different coalescent processes.
Can the Site-Frequency Spectrum Distinguish Exponential Population Growth from Multiple-Merger Coalescents?
• Physics
Genetics
• 2015
Estimates of statistical power indicate that exponential and algebraic growth can indeed be distinguished from multiple-merger coalescents, even for moderate sample sizes, if the number of segregating sites is high enough.
On the genealogy of nested subsamples from a haploid population
• Biology