Multilinear algebra for phylogenetic reconstruction
Phylogenetic reconstruction tries to recover the ancestral relationships among a group of contemporary species and represent them in a phylogenetic tree. To do it, it is useful to model evolution adopting a parametric statistic model. Using these models one is able to deduce polynomial relationships...
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| Tipo de recurso: | tesis de maestría |
| Fecha de publicación: | 2015 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/77124 |
| Acceso en línea: | https://hdl.handle.net/2117/77124 |
| Access Level: | acceso abierto |
| Palabra clave: | PENDENT Genetics Population dynamics Phylogenetic tree Phylogenetic invariants General Markov model Joint distribution Tensor Dinàmica de poblacions Genètica Classificació AMS::92 Biology and other natural sciences::92D Genetics and population dynamics Àrees temàtiques de la UPC::Matemàtiques i estadística |
| Sumario: | Phylogenetic reconstruction tries to recover the ancestral relationships among a group of contemporary species and represent them in a phylogenetic tree. To do it, it is useful to model evolution adopting a parametric statistic model. Using these models one is able to deduce polynomial relationships between the observed probabilities, known as phylogenetic invariants. Mathematicians have recently begun to be interested in the study of these polynomials and have developed techniques from algebraic geometry that have already been used in the study of phylogenetics. Nowadays there exist some phylogenetic reconstruction methods based in these phylogenetic invariants. In this project we study some theoretical results on stochasticity conditions of the parameters of the model and we analyze whether they give some new information to these reconstruction methods. We implement the conditions and analyze the results comparing them with the results provided by the reconstruction method Erik+2. Finally we propose a new reconstruction method based in the same ideas, with different implementation, and with very good results on simulated data. |
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