Journal of Mathematical Biology

, Volume 57, Issue 5, pp 713–735 | Cite as

Stochastic properties of generalised Yule models, with biodiversity applications

  • Tanja Gernhard
  • Klaas Hartmann
  • Mike Steel


The Yule model is a widely used speciation model in evolutionary biology. Despite its simplicity many aspects of the Yule model have not been explored mathematically. In this paper, we formalise two analytic approaches for obtaining probability densities of individual branch lengths of phylogenetic trees generated by the Yule model. These methods are flexible and permit various aspects of the trees produced by Yule models to be investigated. One of our methods is applicable to a broader class of evolutionary processes, namely the Bellman–Harris models. Our methods have many practical applications including biodiversity and conservation related problems. In this setting the methods can be used to characterise the expected rate of biodiversity loss for Yule trees, as well as the expected gain of including the phylogeny in conservation management. We briefly explore these applications.


Yule Phylogenetic diversity Tree Null model Biodiversity Extinction Bellman Harris 

Mathematics Subject Classification (2000)

92-08 60J80 05C05 


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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Kombinatorische GeometrieTechnische Universität MünchenMünchenGermany
  2. 2.Biomathematics Research CentreUniversity of CanterburyChristchurchNew Zealand
  3. 3.ICT Centre, CSIROHobartAustralia
  4. 4.Allan Wilson Centre for Molecular Ecology and Evolution, Biomathematics Research CentreUniversity of CanterburyChristchurchNew Zealand

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