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A critical branching process model for biodiversity | | David J. Aldous
; Lea Popovic
; | | Date: |
18 Oct 2004 | | Subject: | Probability; Populations and Evolution MSC-class: 60J85; 92D15 | math.PR q-bio.PE | | Abstract: | Motivated as a null model for comparison with data, we study the following model for a phylogenetic tree on $n$ extant species. The origin of the clade is a random time in the past, whose (improper) distribution is uniform on $(0,infty)$. After that origin, the process of extinctions and speciations is a continuous-time critical branching process of constant rate, conditioned on having the prescribed number $n$ of species at the present time. We study various mathematical properties of this model as $n o infty$ limits: time of origin and of most recent common ancestor; pattern of divergence times within lineage trees; time series of numbers of species; number of extinct species in total, or ancestral to extant species; and "local" structure of the tree itself. We emphasize several mathematical techniques: associating walks with trees, a point process representation of lineage trees, and Brownian limits. | | Source: | arXiv, math.PR/0410402 | | Services: | Forum | Review | PDF | Favorites | |
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