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Skeletons of near-critical Bienaymé-Galton-Watson branching processes

Serik Sagitov (Institutionen för matematiska vetenskaper, matematisk statistik) ; Maria Conceicao Serra
Advances in Applied Probability (0001-8678). Vol. 47 (2015), 2, p. 530-544.
[Artikel, refereegranskad vetenskaplig]

Skeletons of branching processes are defined as trees of lineages characterized by an appropriate signature of future reproduction success. In the supercritical case a natural choice is to look for the lineages that survive forever (O'Connell (1993)). In the critical case it was suggested that the particles with the total number of descendants exceeding a certain threshold could be distinguished (see Sagitov (1997)). These two definitions lead to asymptotic representations of the skeletons as either pure birth process (in the slightly supercritical case) or critical birth death processes (in the critical case conditioned on the total number of particles exceeding a high threshold value). The limit skeletons reveal typical survival scenarios for the underlying branching processes. In this paper we consider near-critical Bienayme-Galton-Watson processes and define their skeletons using marking of particles. If marking is rare, such skeletons are approximated by birth and death processes, which can be subcritical, critical, or supercritical. We obtain the limit skeleton for a sequential mutation model (Sagitov and Serra (2009)) and compute the density distribution function for the time to escape from extinction.

Nyckelord: Bienayme-Galton-Watson process, birth and death process, Decomposable Multitype Branching, Evolutionary Dynamics



Denna post skapades 2015-07-29. Senast ändrad 2016-07-07.
CPL Pubid: 220043

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematisk statistik (2005-2016)

Ämnesområden

Matematisk statistik

Chalmers infrastruktur

 


Projekt

Denna publikation är ett resultat av följande projekt:


Stochastic models of gene and species trees (VR//2010-5623)