Format

Send to

Choose Destination
J Math Biol. 2008 Mar;56(3):391-412. Epub 2007 Sep 14.

Counting labeled transitions in continuous-time Markov models of evolution.

Author information

1
Department of Biomathematics, David Geffen School of Medicine at UCLA, Los Angeles, CA 90095, USA. vminin@stat.washington.edu

Abstract

Counting processes that keep track of labeled changes to discrete evolutionary traits play critical roles in evolutionary hypothesis testing. If we assume that trait evolution can be described by a continuous-time Markov chain, then it suffices to study the process that counts labeled transitions of the chain. For a binary trait, we demonstrate that it is possible to obtain closed-form analytic solutions for the probability mass and probability generating functions of this evolutionary counting process. In the general, multi-state case we show how to compute moments of the counting process using an eigen decomposition of the infinitesimal generator, provided the latter is a diagonalizable matrix. We conclude with two examples that demonstrate the utility of our results.

PMID:
17874105
DOI:
10.1007/s00285-007-0120-8
[Indexed for MEDLINE]

Supplemental Content

Full text links

Icon for Springer
Loading ...
Support Center