A critical branching process model for biodiversity
| dc.creator | Aldous, David J. | |
| dc.creator | Popovic, Lea | |
| dc.date | 2004-10-18 | |
| dc.date.accessioned | 2026-07-07T05:13:23Z | |
| dc.date.available | 2026-07-07T05:13:23Z | |
| dc.description | 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 $n \to \infty$ 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. | |
| dc.description | 31 pages, 7 figures | |
| dc.identifier | https://arxiv.org/abs/math/0410402 | |
| dc.identifier | http://arxiv.org/abs/math/0410402 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72927 | |
| dc.subject | Probability | |
| dc.subject | Populations and Evolution | |
| dc.subject | 60J85; 92D15 | |
| dc.title | A critical branching process model for biodiversity | |
| dc.type | text |