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Probabilistic Graphical Model Representation in Phylogenetics
Stockholm University, Faculty of Science, Department of Mathematics.
University of California, Berkeley.
University of California, Berkeley .
University of California, Berkeley .
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(English)Manuscript (preprint) (Other academic)
Abstract [en]

Recent years have seen a rapid expansion of the model space explored in statistical phylogenetics, emphasizing the need for new approaches to model representation and software development. Clear communication and representation of the chosen model is crucial for: (1) reproducibility of an analysis, (2) model development and (3) software design. Moreover, a unified, clear and understandable framework formodel representation lowers the barrier for beginning scientists and non-specialists to grasp the model including the assumptions and parameter/variable dependencies.

Graphical models is such a unifying framework that has gained in popularity in the statistical literature in recent years. The core idea isto break complex models into conditionally independent distributions and the strength lies in, amongst others: comprehensibility, flexibility, adaptability and computational algorithms. Graphical models can be used to teach statistical models, to facilitate communication among phylogeneticists and in the development of generic software for simulation and statistical inference.

Here, we provide an introduction to graphical models for phylogeneticists and extend the standard graphical model representation to the realm of phylogenetics. We introduce a new graphical model component, tree plates, to capture the changing structure of the subgraph corresponding to a phylogenetic tree. We describe a range of phylogenetic models using the graphical model framework and built these into separate, interchangeable modules. Phylogenetic model graphs can be readily used in simulation, maximum likelihood inference, and Bayesian inference using either Metropolis-Hastings or Gibbs sampling of the posterior distribution.

National Category
Evolutionary Biology Mathematics
Research subject
Mathematical Statistics
Identifiers
URN: urn:nbn:se:su:diva-95360OAI: oai:DiVA.org:su-95360DiVA: diva2:659509
Available from: 2013-10-25 Created: 2013-10-25 Last updated: 2013-10-28Bibliographically approved
In thesis
1. Bayesian Phylogenetic Inference: Estimating Diversification Rates from Reconstructed Phylogenies
Open this publication in new window or tab >>Bayesian Phylogenetic Inference: Estimating Diversification Rates from Reconstructed Phylogenies
2013 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Phylogenetics is the study of the evolutionary relationship between species. Inference of phylogeny relies heavily on statistical models that have been extended and refined tremendously over the past years into very complex hierarchical models. Paper I introduces probabilistic graphical models to statistical phylogenetics and elaborates on the potential advantages a unified graphical model representation could have for the community, e.g., by facilitating communication and improving reproducibility of statistical analyses of phylogeny and evolution.

Once the phylogeny is reconstructed it is possible to infer the rates of diversification (speciation and extinction). In this thesis I extend the birth-death process model, so that it can be applied to incompletely sampled phylogenies, that is, phylogenies of only a subsample of the presently living species from one group. Previous work only considered the case when every species had the same probability to be included and here I examine two alternative sampling schemes: diversified taxon sampling and cluster sampling. Paper II introduces these sampling schemes under a constant rate birth-death process and gives the probability density for reconstructed phylogenies. These models are extended in Paper IV to time-dependent diversification rates, again, under different sampling schemes and applied to empirical phylogenies. Paper III focuses on fast and unbiased simulations of reconstructed phylogenies. The efficiency is achieved by deriving the analytical distribution and density function of the speciation times in the reconstructed phylogeny.

Place, publisher, year, edition, pages
Stockholm: Department of Mathematics, Stockholm University, 2013. 26 p.
Keyword
Phylogenetics, Bayesian inference, Graphical Models, Birth-Death Process, Diversification
National Category
Evolutionary Biology Mathematics
Research subject
Mathematical Statistics
Identifiers
urn:nbn:se:su:diva-95361 (URN)978-91-7447-771-9 (ISBN)
Public defence
2013-11-29, sal 14, hus 5, Kräftriket, Roslagsvägen 101, Stockholm, 10:00 (English)
Opponent
Supervisors
Note

At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 1: Manuscript. Paper 4: Accepted.

Available from: 2013-11-07 Created: 2013-10-25 Last updated: 2015-03-10Bibliographically approved

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