Skeletons of near-critical Bienaymé-Galton-Watson branching processes
Journal article, 2015

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.

Decomposable Multitype Branching

Bienayme-Galton-Watson process

Evolutionary Dynamics

birth and death process


Serik Sagitov

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematical Statistics

Maria Conceicao Serra

Advances in Applied Probability

0001-8678 (ISSN) 1475-6064 (eISSN)

Vol. 47 2 530-544

Stochastic models of gene and species trees

Swedish Research Council (VR) (2010-5623), 2011-01-01 -- 2013-12-31.

Subject Categories

Probability Theory and Statistics



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