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- W4386118869 abstract "The Yule branching process is a classical model for the random generation of gene tree topologies in population genetics. It generates binary ranked trees -also called histories- with a finite number $n$ of leaves. We study the lengths $ell_1 > ell_2 > cdots > ell_k > cdots$ of the external branches of a Yule generated random history of size $n$, where the length of an external branch is defined as the rank of its parent node. When $n rightarrow infty$, we show that the random variable $ell_k$, once rescaled as $frac{n-ell_k}{sqrt{n/2}}$, follows a $chi$-distribution with $2k$ degrees of freedom, with mean $mathbb E(ell_k) sim n$ and variance $mathbb V(ell_k) sim n big(k-frac{pi k^2}{16^k} binom{2k}{k}^2big)$. Our results contribute to the study of the combinatorial features of Yule generated gene trees, in which external branches are associated with singleton mutations affecting individual gene copies." @default.
- W4386118869 created "2023-08-25" @default.
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- W4386118869 date "2023-08-25" @default.
- W4386118869 modified "2023-09-27" @default.
- W4386118869 title "Distribution of External Branch Lengths in Yule Histories" @default.
- W4386118869 doi "https://doi.org/10.37236/11438" @default.
- W4386118869 hasPublicationYear "2023" @default.
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