Poisson random forests and coalescents in expanding populations

Stochastic Analysis Seminar Series

Let (V, ≥) be a finite, partially ordered set. Say a directed forest on V is a set of directed edges [x,y> with x ≤ y such that no vertex has indegree greater than one.

Thus for a finite measure μ on some partially ordered measurable space D we may define a Poisson random forest by choosing a set of  vertices V according to a Poisson point process weighted by the number of directed forests on V, and selecting a directed forest uniformly.

We give a necessary and sufficient condition for such a process to exist and show that the process may be expressed as a multi-type branching process with type space D.

We build on this observation, together with a construction of the simple birth death process due to Kurtz and Rodrigues [2011] to develop a coalescent theory for rapidly expanding populations.

Location:
Speaker(s):

Sam Finch (University of Copenhagen)

Date:
Monday, February 25, 2013 - 14:15
to 15:15