A Beta-splitting model for evolutionary trees.
In this article, we construct a generalization of the Blum-François Beta-splitting model for evolutionary trees, which was itself inspired by Aldous' Beta-splitting model on cladograms. The novelty of our approach allows for asymmetric shares of diversification rates (or diversification 'potential') between two sister species in an evolutionarily interpretable manner, as well as the addition of extinction to the model in a natural way. We describe the incremental evolutionary construction of a tree with n leaves by splitting or freezing extant lineages through the generating, organizing and deleting processes. We then give the probability of any (binary rooted) tree under this model with no extinction, at several resolutions: ranked planar trees giving asymmetric roles to the first and second offspring species of a given species and keeping track of the order of the speciation events occurring during the creation of the tree, unranked planar trees, ranked non-planar trees and finally (unranked non-planar) trees. We also describe a continuous-time equivalent of the generating, organizing and deleting processes where tree topology and branch lengths are jointly modelled and provide code in SageMath/Python for these algorithms.
School of Mathematics and Statistics , University of Canterbury , Private Bag 4800, Christchurch 8041 , New Zealand.
Raazesh
R
Sainudiin
CMAP-CNRS, Ecole Polytechnique, 91128 Palaiseau Cedex , France.
Amandine
0000-0003-4464-015X
A
Véber
Beta-splitting model(s); binary search trees; random evolutionary trees; speciation and extinction model