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2020 Distributional analysis of the extra-clustering model with uniformly generated phylogenetic trees
Michael Fuchs, Chih-Hong Lee, Ariel R. Paningbatan
Electron. Commun. Probab. 25: 1-13 (2020). DOI: 10.1214/20-ECP291


The extra-clustering model for the group formation process of social animals was introduced by Durand, Blum and François. The model uses the relatedness of the animals, which is described by phylogenetic trees. If these trees are drawn from the Yule-Harding model, it was analyzed in recent work. Here, we analyze it for the uniform model, which is the other widely-studied model on phylogenetics trees. More precisely, we derive moments and limit laws for the number of groups, the number of groups of fixed size and the largest group size. Our results show that, independent of the probability of extra-clustering, there is on average only a finite number of groups, one of which is very large whereas all others are small. This behavior considerably differs from the Yule-Harding case, where the finiteness of the number of groups is dependent on the extra-clustering probability.


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Michael Fuchs. Chih-Hong Lee. Ariel R. Paningbatan. "Distributional analysis of the extra-clustering model with uniformly generated phylogenetic trees." Electron. Commun. Probab. 25 1 - 13, 2020.


Received: 24 July 2019; Accepted: 21 January 2020; Published: 2020
First available in Project Euclid: 8 February 2020

zbMATH: 1443.92129
MathSciNet: MR4069733
Digital Object Identifier: 10.1214/20-ECP291

Primary: 05A16 , 60F05 , 92B05

Keywords: animal grouping , convergence of moments , extra-cluster model , largest group size , limit laws , moments , negative binomial distribution , number of groups , PDA model , phylogenetic tree


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