Splitting trees with neutral Poissonian mutations. I: Small families

DOI10.1016/j.spa.2011.11.002zbMath1255.60153arXiv1009.0680OpenAlexW2110421859MaRDI QIDQ765886

Nicolas Champagnat, Amaury Lambert

Publication date: 22 March 2012

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1009.0680

zbMATH Keywords

branching processLévy processscale functionPoisson point processregenerative setcoalescent point processCrump-Mode-Jagers processlinear birth-death processsplitting treerandom characteristic

Mathematics Subject Classification ID

Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80) Genetics and epigenetics (92D10)

Related Items (13)

Mutations on a random binary tree with measured boundary ⋮ Mutational pattern of a sample from a critical branching population ⋮ Central limit theorem for supercritical binary homogeneous Crump-Mode-Jagers processes ⋮ Birth and death processes with neutral mutations ⋮ Random ultrametric trees and applications ⋮ Species abundance distributions in neutral models with immigration or mutation and general lifetimes ⋮ Genetic composition of an exponentially growing cell population ⋮ Approximation of the allelic frequency spectrum in general supercritical branching populations ⋮ Splitting Trees Stopped when the First Clock Rings and Vervaat's Transformation ⋮ Some properties of the conditioned reconstructed process with Bernoulli sampling ⋮ Further properties of a random graph with duplications and deletions ⋮ Splitting trees with neutral mutations at birth ⋮ Asymptotic Degree Distribution of a Duplication–Deletion Random Graph Model

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Asymptotic regimes for the partition into colonies of a branching process with emigration
• Limit theorems for sums determined by branching and other exponentially growing processes
• The structure of the allelic partition of the total population for Galton-Watson processes with neutral mutations
• A limit theorem for trees of alleles in branching processes with rare neutral mutations
• Size-biased and conditioned random splitting trees
• Evolution of resistance and progression to disease during clonal expansion of cancer
• Asymptotic genealogy of a critical branching process
• Splitting trees with neutral Poissonian mutations. II: Largest and oldest families
• The contour of splitting trees is a Lévy process
• The growth and composition of branching populations
• Multitype Bienaymé–Galton–Watson processes escaping extinction
• The allelic partition for coalescent point processes
• An infinite-alleles version of the simple branching process
• On the convergence of supercritical general (C-M-J) branching processes
• Convergence of general branching processes and functionals thereof
• A critical branching process model for biodiversity

This page was built for publication: Splitting trees with neutral Poissonian mutations. I: Small families