2003/02/28 by Hans-Otto Georgii, Ellen Baake
Mathematics · Biochemistry, Genetics and Molecular Biology · #math.PR #q-bio.PE #msc:60J80 #msc:60F10
published as Adv. Appl. Prob. 35 (2003), 1090-1110 · 23 pages, 1 figure; minor additions, added references
arxiv created 2003/06/10 · arxiv updated 2009/11/30
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.