Multiple-merger genealogies -- models, consequences, inference

TL;DR

This paper explores complex multiple-merger coalescent models, analyzing their properties and implications for biological inference, and discusses extensions for variable population sizes.

Contribution

It provides mathematical insights into clade sizes and tree changes in multiple-merger coalescents, and extends models to account for changing population sizes.

Findings

Analysis of clade size distributions in multiple-merger trees

Impact of sample size changes on tree structure

Extension of models to variable population sizes

Abstract

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 as realistic genealogy models for real populations, an extension for changing population sizes is discussed.