Computing a smallest multilabeled phylogenetic tree from rooted triplets.

We investigate the computational complexity of inferring a smallest possible multilabeled phylogenetic tree (MUL tree) which is consistent with each of the rooted triplets in a given set. This problem has not been studied previously in the literature. We prove that even the very restricted case of determining if there exists a MUL tree consistent with the input and having just one leaf duplication is an NP-hard problem.

Robustness of phylogenetic inference based on minimum evolution.

Minimum evolution is the guiding principle of an important class of distance-based phylogeny reconstruction methods, including neighbor-joining (NJ), which is the most cited tree inference algorithm to date. The minimum evolution principle involves searching for the tree with minimum length, where the length is estimated using various least-squares criteria. Since evolutionary distances cannot be known precisely but only estimated, it is important to investigate the robustness of phylogenetic reconstruction to imprecise estimates for these distances.

Fixed-parameter tractability of the maximum agreement supertree problem.

Given a set L of labels and a collection of rooted trees whose leaves are bijectively labeled by some elements of L, the Maximum Agreement Supertree (SMAST) problem is given as follows: find a tree T on a largest label set L(') is included in L that homeomorphically contains every input tree restricted to L('). The problem has phylogenetic applications to infer supertrees and perform tree congruence analyses. In this paper, we focus on the parameterized complexity of this NP-hard problem, considering different combinations of parameters as well as particular cases.

PhySIC: a veto supertree method with desirable properties.

This paper focuses on veto supertree methods; i.e., methods that aim at producing a conservative synthesis of the relationships agreed upon by all source trees.