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Critical case stochastic phylogenetic tree model via the laplace transform

Krzysztof Bartoszek (Institutionen för matematiska vetenskaper) ; M. Krzeminski
Demonstratio Mathematica (0420-1213). Vol. 47 (2014), 2, p. 474-481.
[Artikel, refereegranskad vetenskaplig]

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.

Nyckelord: Phylogenetic tree, Stochastic model, Tauberian theory



Denna post skapades 2015-03-24. Senast ändrad 2016-04-15.
CPL Pubid: 214208

 

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