Abstract
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.
Highlights
In the last couple of decades, many models of random evolutionary trees have been introduced and studied, as reviewed by Mooers & Heard [1] and Morlon [2]
Most of them are formulated in terms of individual species diversification rates mirroring the influence of particular features such as species age, trait, available niche space, etc
We propose a continuous-time process of leaf splitting and freezing such that the shape of the tree obtained after N events has the same distribution as that obtained through the generating, organizing and deleting processes after N steps
Summary
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 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
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