Coalescence and sampling distributions for Feller diffusions

Conrad J. Burden and Robert C. Griffiths

Theoretical Population Biology, 2024, vol. 155, issue C, 67-76

Abstract: Consider the diffusion process defined by the forward equation ut(t,x)=12{xu(t,x)}xx−α{xu(t,x)}x for t,x≥0 and −∞<α<∞, with an initial condition u(0,x)=δ(x−x0). This equation was introduced and solved by Feller to model the growth of a population of independently reproducing individuals. We explore important coalescent processes related to Feller’s solution. For any α and x0>0 we calculate the distribution of the random variable An(s;t), defined as the finite number of ancestors at a time s in the past of a sample of size n taken from the infinite population of a Feller diffusion at a time t since its initiation. In a subcritical diffusion we find the distribution of population and sample coalescent trees from time t back, conditional on non-extinction as t→∞. In a supercritical diffusion we construct a coalescent tree which has a single founder and derive the distribution of coalescent times.

Keywords: Coalescent; Diffusion process; Branching process; Feller diffusion; Sampling distributions (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S004058092300076X
Full text for ScienceDirect subscribers only

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:eee:thpobi:v:155:y:2024:i:c:p:67-76

DOI: 10.1016/j.tpb.2023.12.001

Access Statistics for this article

Theoretical Population Biology is currently edited by Jeremy Van Cleve

More articles in Theoretical Population Biology from Elsevier
Bibliographic data for series maintained by Catherine Liu ().