We're sorry but this page doesn't work properly without JavaScript enabled. Please enable it to continue.
Feedback

Genealogies for stochastic population models

Formal Metadata

Title
Genealogies for stochastic population models
Title of Series
Number of Parts
19
Author
License
CC Attribution - NonCommercial - NoDerivatives 4.0 International:
You are free to use, copy, distribute and transmit the work or content in unchanged form for any legal and non-commercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor.
Identifiers
Publisher
Release Date
Language

Content Metadata

Subject Area
Genre
Abstract
Stochastic models of populations have a long history beginning with branching processes and continuing with models in population genetics and models of the spatial distribution of populations. At the same time, models of population genealogies were developed in the population genetics literature. Work with Peter Donnelly (1999) showed how to simultaneously construct models that include both the forward in time evolution of the population distribution and the backward in time genealogy starting at any time point in the forward in time evolution. These "lookdown" constructions were essentially restricted to neutral models, that is, models in which birth rates, offspring distributions, and death rates do not depend on the types or locations of the individuals in the population. Following some earlier preliminary results, work with Eliane Rodrigues (2011) gave lookdown constructions for general Markov branching processes in which the birth rates, offspring distributions, and death rates can depend on the location/type of the individual. Extension of these lookdown/genealogical constructions to very general Markov population models, to appear in a forthcoming paper with Alison Etheridge, will be discussed.