Critical case stochastic phylogenetic tree model via the laplace transform
Journal article, 2014

Birth-and-death models are now a common mathematical tool to describe branching patterns observed in real-world phylogenetic trees. Liggett and Schinazi (2009) is one such example. The authors propose a simple birth-and-death model that is compatible with phylogenetic trees of both influenza and HIV, depending on the birth rate parameter. An interesting special case of this model is the critical case where the birth rate equals the death rate. This is a non-trivial situation and to study its asymptotic behaviour we employed the Laplace transform. With this, we correct the proof of Liggett and Schinazi (2009) in the critical case.

Phylogenetic tree

Tauberian theory

Stochastic model

Author

Krzysztof Bartoszek

Chalmers, Mathematical Sciences, Mathematical Statistics

University of Gothenburg

M. Krzeminski

Demonstratio Mathematica

0420-1213 (ISSN)

Vol. 47 2 474-481

Subject Categories

Mathematics

DOI

10.2478/dema-2014-0038

More information

Latest update

3/21/2018