Stochastic properties of generalised Yule models, with biodiversity applications
- 177 Downloads
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.
KeywordsYule Phylogenetic diversity Tree Null model Biodiversity Extinction Bellman Harris
Mathematics Subject Classification (2000)92-08 60J80 05C05
Unable to display preview. Download preview PDF.
- 7.Gernhard, T.: Stochastic models of speciation events in phylogenetic trees. Diplom Thesis, Technical University of Munich, Germany (2006)Google Scholar
- 8.Gernhard, T.: The conditioned reconstructed process. J. Theor. Biol. (2008, in press)Google Scholar
- 9.Gernhard T., Ford D., Vos R., Steel M.: Estimating the relative order of speciation or coalescence events on a given phylogeny. Evol. Bioinform. Online 2, 309–317 (2006)Google Scholar
- 11.Hartmann, K., Mooers, A.O.: When should phylogenies guide conservation management? (in preparation)Google Scholar
- 12.Hartmann K., Steel M.: Phylogenetic diversity: from combinatorics to ecology. In: Gascuel, O., Steel, M.(eds) Reconstructing Evolution—New Mathematical and Computational Advances, Oxford University Press, New York (2007)Google Scholar
- 13.Hartmann, K., Gernhard, T., Wong, D.: Sampling trees from evolutionary models. Systematic Biology (submitted)Google Scholar
- 17.Mooers A.O., Heard S.B., Chrostowski E.: Evolutionary heritage as a metric for conservation. In: Purvis, A., Brooks, T., Gittleman, J.(eds) Phylogeny and Conservation, pp. 120–138. Cambridge University Press, Cambridge (2005)Google Scholar
- 22.Steel M.: Tools to construct and study big trees: A mathematical perspective. In: Hodkinson T.R., Parnell J.A. (eds.) Reconstructing the Tree of Life: Taxonomy and Systematics of Species Rich Taxa. CRC Press, USA (2006)Google Scholar
- 24.Walters C.J.: Adaptive Management of Renewable Resources. Macmillan, New York (1986)Google Scholar