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Tree shape in population genetics and phylogeny

Michael G B Blum 1
1 TIMB
TIMC - Techniques de l'Ingénierie Médicale et de la Complexité - Informatique, Mathématiques et Applications, Grenoble - UMR 5525, ESE - Ecologie Systématique et Evolution
Abstract : The main part of this manuscript focuses on tree balance in phylogeny and population genetics. The binary tree structure is central in these fields. In phylogeny, trees represent the genealogies of species. In population genetics, trees represent the genealogies of genes and it is called the coalescent. A genealogy is said to be unbalanced when most of the internal nodes split the genealogy in two subtrees of different sizes. The most classical models of random phylogenies are the Yule model, which assumes that all species are equally likely to speciate, and the uniform model, which assumes that all phylogenies are equally likely. In both models we find the means and the variances, as well as the limiting distributions of tree balance measures widely used by biologists. In population genetics, the balance of coalescent trees reveals powerful at detecting a specific departure from the neutral rm model: fertility inheritance. When fertility is inherited, individuals whose parents had many children are more likely to have numerous offspring. We reconstruct the genealogies of human populations from samples of mitochondrial DNA. Genealogies from hunter-gatherer populations are the most unbalanced, suggesting a high fertility inheritance in these populations. In a last part, we apply coalescence theory to spatial genetics. We propose three methods to estimate a parameter of spatial dispersion. These methods are applied to estimate the rate of spatial dispersion of Scandinavian brown bears.
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https://tel.archives-ouvertes.fr/tel-00011156
Contributor : Michael Gb Blum <>
Submitted on : Tuesday, December 6, 2005 - 9:59:15 PM
Last modification on : Thursday, November 19, 2020 - 3:56:09 PM
Long-term archiving on: : Friday, April 2, 2010 - 11:22:11 PM

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  • HAL Id : tel-00011156, version 1

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Michael G B Blum. Tree shape in population genetics and phylogeny. Mathematics [math]. Institut National Polytechnique de Grenoble - INPG, 2005. English. ⟨tel-00011156⟩

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