Coalescence and sampling distributions for Feller diffusions

Conrad J. Burden*, Robert C. Griffiths

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    Abstract

    Consider the diffusion process defined by the forward equation [Formula presented] 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.

    Original languageEnglish
    Pages (from-to)67-76
    Number of pages10
    JournalTheoretical Population Biology
    Volume155
    DOIs
    Publication statusPublished - Feb 2024

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