Developing and applying supertree methods in Phylogenomics and Macroevolution

Supertrees can be used to combine partially overalapping trees and generate more inclusive phylogenies. It has been proposed that Maximum Likelihood (ML) supertrees method (SM) could be developed using an exponential probability distribution to model errors in the input trees (given a proposed supertree). When the tree-­‐to-­‐tree distances used in the ML computation are symmetric differences, the ML SM has been shown to be equivalent to a Majority-­‐Rule consensus SM, and hence, exactly as the latter, it has the desirable property of being a median tree (with reference to the set of input trees). The ability to estimate the likelihood of supertrees, allows implementing Bayesian (MCMC) approaches, which have the advantage to allow the support for the clades in a supertree to be properly estimated. I present here the L.U.St software package; it contains the first implementation of a ML SM and allows for the first time statistical tests on supertrees. I also characterized the first implementation of the Bayesian (MCMC) SM. Both the ML and the Bayesian (MCMC) SMs have been tested for and found to be immune to biases. The Bayesian (MCMC) SM is applied to the reanalyses of a variety of datasets (i.e. the datasets for the Metazoa and the Carnivora), and I have also recovered the first Bayesian supertree-­‐based phylogeny of the Eubacteria and the Archaebacteria. These new SMs are discussed, with reference to other, well-­‐ known SMs like Matrix Representation with Parsimony. Both the ML and Bayesian SM offer multiple attractive advantages over current alternatives

Developing and applying supertree methods in Phylogenomics and Macroevolution

Supertrees can be used to combine partially overalapping trees and generate more inclusive phylogenies. It has been proposed that Maximum Likelihood (ML) supertrees method (SM) could be developed using an exponential probability distribution to model errors in the input trees (given a proposed supertree). When the tree-­‐to-­‐tree distances used in the ML computation are symmetric differences, the ML SM has been shown to be equivalent to a Majority-­‐Rule consensus SM, and hence, exactly as the latter, it has the desirable property of being a median tree (with reference to the set of input trees). The ability to estimate the likelihood of supertrees, allows implementing Bayesian (MCMC) approaches, which have the advantage to allow the support for the clades in a supertree to be properly estimated. I present here the L.U.St software package; it contains the first implementation of a ML SM and allows for the first time statistical tests on supertrees. I also characterized the first implementation of the Bayesian (MCMC) SM. Both the ML and the Bayesian (MCMC) SMs have been tested for and found to be immune to biases. The Bayesian (MCMC) SM is applied to the reanalyses of a variety of datasets (i.e. the datasets for the Metazoa and the Carnivora), and I have also recovered the first Bayesian supertree-­‐based phylogeny of the Eubacteria and the Archaebacteria. These new SMs are discussed, with reference to other, well-­‐ known SMs like Matrix Representation with Parsimony. Both the ML and Bayesian SM offer multiple attractive advantages over current alternatives

The matroid structure of representative triple sets and triple-closure computation

The closure cl (R) of a consistent set R of triples (rooted binary trees on three leaves) provides essential information about tree-like relations that are shown by any supertree that displays all triples in . In this contribution, we are concerned with representative triple sets, that is, subsets R' of R with cl (R') = cl . In this case, R' still contains all information on the tree structure implied by R, although R' might be significantly smaller. We show that representative triple sets that are minimal w.r.t. inclusion form the basis of a matroid. This in turn implies that minimal representative triple sets also have minimum cardinality. In particular, the matroid structure can be used to show that minimum representative triple sets can be computed in polynomial time with a simple greedy approach. For a given triple set R that “identifies” a tree, we provide an exact value for the cardinality of its minimum representative triple sets. In addition, we utilize the latter results to provide a novel and efficient method to compute the closure cl (R) of a consistent triple set R that improves the time complexity (R Lr 4) of the currently fastest known method proposed by Bryant and Steel (1995). In particular, if a minimum representative triple set for R is given, it can be shown that the time complexity to compute cl (R) can be improved by a factor up to R Lr . As it turns out, collections of quartets (unrooted binary trees on four leaves) do not provide a matroid structure, in general

Polynomial supertree methods in phylogenomics: algorithms, simulations and software

One of the objectives in modern biology, especially phylogenetics, is to build larger clades of the Tree of Life. Large-scale phylogenetic analysis involves several serious challenges. The aim of this thesis is to contribute to some of the open problems in this context. In computational phylogenetics, supertree methods provide a way to reconstruct larger clades of the Tree of Life. We present a novel polynomial time approach for the computation of supertrees called FlipCut supertree. Our method combines the computation of minimum cuts from graph-based methods with a matrix representation method, namely Minimum Flip Supertrees. Here, the input trees are encoded in a 0/1/?-matrix. We present a heuristic to search for a minimum set of 0/1-flips such that the resulting matrix admits a directed perfect phylogeny. In contrast to other polynomial time approaches, our results can be interpreted in the sense that we try to minimize a global objective function, namely the number of flips in the input matrix. We extend our approach by using edge weights to weight the columns of the 0/1/?-matrix. In order to compare our new FlipCut supertree method with other recent polynomial supertree methods and matrix representation methods, we present a large scale simulation study using two different data sets. Our findings illustrate the trade-off between accuracy and running time in supertree construction, as well as the pros and cons of different supertree approaches. Furthermore, we present EPoS, a modular software framework for phylogenetic analysis and visualization. It fills the gap between command line-based algorithmic packages and visual tools without sufficient support for computational methods. By combining a powerful graphical user interface with a plugin system that allows simple integration of new algorithms, visualizations and data structures, we created a framework that is easy to use, to extend and that covers all important steps of a phylogenetic analysis