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Supercritical multitype branching processes: the ancestral types of typical individuals | | Hans-Otto Georgii
; Ellen Baake
; | | Date: |
5 Feb 2003 | | Journal: | Adv. Appl. Prob. 35 (2003), 1090-1110 | | Subject: | Probability; Populations and Evolution MSC-class: 60J80; 60F10 | math.PR q-bio.PE | | Abstract: | For supercritical multitype branching processes in continuous time, we investigate the evolution of types along those lineages that survive up to some time t. We establish almost-sure convergence theorems for both time and population averages of ancestral types (conditioned on non-extinction), and identify the mutation process describing the type evolution along typical lineages. An important tool is a representation of the family tree in terms of a suitable size-biased tree with trunk. As a by-product, this representation allows a `conceptual proof’ (in the sense of Kurtz, Lyons, Pemantle, Peres 1997) of the continuous-time version of the Kesten-Stigum theorem. | | Source: | arXiv, math.PR/0302049 | | Services: | Forum | Review | PDF | Favorites | |
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