A critical branching process model for biodiversity
By David J. Aldous, Lea Popovic. Advances in Applied Probability, 2004
109 citations recorded by the source corpus.
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,∞); thereafter, the process of extinctions and speciations is a continuous-time critical branching process of constant rate, conditioned on there being the prescribed number n of species at the present time. We study various mathematical properties of this model as n→∞: namely the time of origin and of the most recent common ancestor, the pattern of divergence times within lineage trees, the time series of the number of species, the total number of extinct species, the total number of species ancestral to the extant ones, and the ‘local’ structure of the tree itself. We emphasize several mathematical techniques: the association of walks with trees; a point process representation of lineage trees; and Brownian limits.
Subfields: Genetics, Mathematical Physics, Sociology and Political Science
View Paper: https://www.semanticscholar.org/paper/ae898bb4a891275a7ce782c95d62bcd70f3fd3d9
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Citations in the corpus
- The conditioned reconstructed process. (2008, background): “Special cases of the birth-death process are the Yule model (Yule, 1924) where µ = 0 and the critical branching process (Aldous and Popovic, 2005; Popovic, 2004) where µ = λ.”
- The coalescent structure of continuous-time Galton–Watson trees (2017, methodology): “[19] Lambert, A. and Popovic, L. (2013).”