Maximum Likelihood Estimation for Unrooted 3-Leaf Trees: An Analytic Solution for the CFN Model.
Bull Math Biol
; 86(9): 106, 2024 Jul 12.
Article
em En
| MEDLINE
| ID: mdl-38995457
ABSTRACT
Maximum likelihood estimation is among the most widely-used methods for inferring phylogenetic trees from sequence data. This paper solves the problem of computing solutions to the maximum likelihood problem for 3-leaf trees under the 2-state symmetric mutation model (CFN model). Our main result is a closed-form solution to the maximum likelihood problem for unrooted 3-leaf trees, given generic data; this result characterizes all of the ways that a maximum likelihood estimate can fail to exist for generic data and provides theoretical validation for predictions made in Parks and Goldman (Syst Biol 63(5)798-811, 2014). Our proof makes use of both classical tools for studying group-based phylogenetic models such as Hadamard conjugation and reparameterization in terms of Fourier coordinates, as well as more recent results concerning the semi-algebraic constraints of the CFN model. To be able to put these into practice, we also give a complete characterization to test genericity.
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Texto completo:
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Base de dados:
MEDLINE
Assunto principal:
Filogenia
/
Conceitos Matemáticos
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Modelos Genéticos
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Mutação
Idioma:
En
Ano de publicação:
2024
Tipo de documento:
Article
País de afiliação:
Estados Unidos