Birth and Death Processes with Neutral Mutations

Nicolas Champagnat, Amaury Lambert and Mathieu Richard

International Journal of Stochastic Analysis, 2012, vol. 2012, 1-20

Abstract:

We review recent results of ours concerning branching processes with general lifetimes and neutral mutations, under the infinitely many alleles model, where mutations can occur either at the birth of particles or at a constant rate during their lives. In both models, we study the allelic partition of the population at time . We give closed-form formulae for the expected frequency spectrum at and prove a pathwise convergence to an explicit limit, as , of the relative numbers of types younger than some given age and carried by a given number of particles (small families). We also provide the convergences in distribution of the sizes or ages of the largest families and of the oldest families. In the case of exponential lifetimes, population dynamics are given by linear birth and death processes, and we can most of the time provide general formulations of our results unifying both models.

Date: 2012
References: Add references at CitEc
Citations: View citations in EconPapers (4)

Downloads: (external link)
http://downloads.hindawi.com/journals/IJSA/2012/569081.pdf (application/pdf)
http://downloads.hindawi.com/journals/IJSA/2012/569081.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijsa:569081

DOI: 10.1155/2012/569081

Access Statistics for this article

More articles in International Journal of Stochastic Analysis from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().