Inferring polyploid phylogenies from multiply-labeled gene trees

Abstract

Background: Gene trees that arise in the context of reconstructing the evolutionary history of polyploid species are often multiply-labeled, that is, the same leaf label can occur several times in a single tree. This property considerably complicates the task of forming a consensus of a collection of such trees compared to usual phylogenetic trees.

Polynomial-Time Algorithms for Building a Consensus MUL-Tree

“…In this article, we have shown that the problem of building a consensus MUL-tree can be solved in polynomial time for certain types of consensus MUL-trees, thus significantly improving on the previously existing, exponential-time methods of Huber et al (2012) and Lott et al (2009b). We have also presented a number of negative results regarding the existence, uniqueness, and time complexity of consensus MULtrees.…”

“…For some examples, see Figures 2,3,4,5,6, and 8. MUL-trees have a number of applications in different research fields, such as biogeography (see, e.g., Ganapathy et al, 2006;Minaka, 1990; and Chapter 6 of Nelson and Platnick, 1981); the study of host-parasite cospeciation (Page, 1993); gene evolution studies (Fellows et al, 2003;Lott et al, 2009b;Page, 1994;Scornavacca et al, 2011), and computer science (see the references in Huber et al, 2011).…”

“…It was first addressed by Lott et al (2009b). Their motivation came from a more general problem related to reconstructing complex evolutionary scenarios involving so-called polyploid species.…”

“…Lott et al (2009a) suggested that rather than inferring a phylogenetic network directly, it may be easier to first reconcile the input into a single MUL-tree and then apply an algorithm from Huber et al (2006) that is guaranteed to output a network with the minimum number of non tree nodes. For this purpose, Lott et al (2009b) presented a method for constructing a greedy kind of consensus MUL-tree that uses the same basic strategy as the well-known greedy consensus tree method (Bryant, 2003;Sung, 2010) for single-labeled phylogenetic trees. A serious disadvantage of their method is that its running time is exponential in the size of the input, and indeed, according to the discussion in Lott et al (2009a), the method probably needs to be improved to deal with datasets from new sequencing technologies in the near future.…”

“…It is an important open problem to identify alternative types of (informative) consensus MUL-trees that can be computed more efficiently than Huber et al (2012) and Lott et al (2009b). In this article, we investigate the computational complexity of inferring three types of consensus MUL-trees, which we call the strict consensus MUL-tree, the majority rule consensus MUL-tree, and the singular majority rule consensus MUL-tree, and derive a number of positive and negative results.…”