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.
- Pub Date:
- October 2020
- Mathematics - Probability;
- Quantitative Biology - Populations and Evolution;
- 60_02 (Primary) 60J90;
- 92D25 (Secondary)
- This is a review of my project within the DFG Priority Programme 1590 "Probabilistic Structures in Evolution". It will appear in "Probabilistic Structures in Evolution", ed. by E. Baake and A. Wakolbinger, EMS Publishing House, Zurich