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The shape of phylogenies under phase-type distributed times to speciation and extinction


Soewongsono, AC and Holland, BR and O'Reilly, MM, The shape of phylogenies under phase-type distributed times to speciation and extinction, Bulletin of Mathematical Biology, 84 Article 118. ISSN 0092-8240 (2022) [Refereed Article]

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DOI: doi:10.1007/s11538-022-01072-w


Phylogenetic trees describe relationships between extant species, but beyond that their shape and their relative branch lengths can provide information on broader evolutionary processes of speciation and extinction. However, currently many of the most widely used macro-evolutionary models make predictions about the shapes of phylogenetic trees that differ considerably from what is observed in empirical phylogenies. Here, we propose a flexible and biologically plausible macroevolutionary model for phylogenetic trees where times to speciation or extinction events are drawn from a Coxian phase-type (PH) distribution. First, we show that different choices of parameters in our model lead to a range of tree balances as measured by Aldous’ β statistic. In particular, we demonstrate that it is possible to find parameters that correspond well to empirical tree balance. Next, we provide a natural extension of the β statistic to sets of trees. This extension produces less biased estimates of β compared to using the median β values from individual trees. Furthermore, we derive a likelihood expression for the probability of observing an edge-weighted tree under a model with speciation but no extinction. Finally, we illustrate the application of our model by performing both absolute and relative goodness-of-fit tests for two large empirical phylogenies (squamates and angiosperms) that compare models with Coxian PH distributed times to speciation with models that assume exponential or Weibull distributed waiting times. In our numerical analysis, we found that, in most cases, models assuming a Coxian PH distribution provided the best fit.

Item Details

Item Type:Refereed Article
Keywords:macro-evolutionary model, diversification, tree balance , phase-type distribution
Research Division:Mathematical Sciences
Research Group:Statistics
Research Field:Stochastic analysis and modelling
Objective Division:Expanding Knowledge
Objective Group:Expanding knowledge
Objective Field:Expanding knowledge in the mathematical sciences
UTAS Author:Soewongsono, AC (Mr Albert Soewongsono)
UTAS Author:Holland, BR (Professor Barbara Holland)
UTAS Author:O'Reilly, MM (Associate Professor Malgorzata O'Reilly)
ID Code:154588
Year Published:2022
Funding Support:Australian Research Council (DP180100352)
Deposited By:Mathematics
Deposited On:2022-12-13
Last Modified:2023-01-10

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