Inferring Optimal Species Trees Under Gene Duplication and Loss

Abstract

Species tree estimation from multiple markers is complicated by the fact that gene trees can differ from each other (and from the true species tree) due to several biological processes, one of which is gene duplication and loss. Local search heuristics for two NP-hard optimization problems -minimize gene duplications (MGD) and minimize gene duplications and losses (MGDL) -are popular techniques for estimating species trees in the presence of gene duplication and loss. In this paper, we present an alternative approach to solving MGD and MGDL from rooted gene trees. First, we characterize each tree in terms of its "subtree-bipartitions" (a concept we introduce). Then we show that the MGD species tree is defined by a maximum weight clique in a vertex-weighted graph that can be computed from the subtree-bipartitions of the input gene trees, and the MGDL species tree is defined by a minimum weight clique in a similarly constructed graph. We also show that these optimal cliques can be found in polynomial time in the number of vertices of the graph using a dynamic programming algorithm (similar to that of Hallett and Lagergren 1 ), because of the special structure of the graphs. Finally, we show that a constrained version of these problems, where the subtree-bipartitions of the species tree are drawn from the subtree-bipartitions of the input gene trees, can be solved in time that is polynomial in the number of gene trees and taxa. We have implemented our dynamic programming algorithm in a publicly available software tool, available at

Computational approaches to species phylogeny inference and gene tree reconciliation

“…Than and Rosenberg proved that this parsimony criterion of minimizing the number of extra lineages is in fact statistically inconsistent (that is, inference under this criterion might converge on the wrong species tree, even as the number of gene trees used in the inference increases) [18]. Bayzid et al devised exact algorithms for inferring a species tree that minimizes the number of duplications and losses [19]. …”

STELAR: a statistically consistent coalescent-based species tree estimation method by maximizing triplet consistency

“…Each internal node u in a tree T divides the set of taxa present in the subtree rooted at u into two distinct sets. We call this a subtree-bipartition, denoted by SBP T (u), which was originally defined in [35]. We denote by T u the subtree under node u of tree T. We denote the leaves in T by L(T), an arbitrary set of three species {a, b, c} ⊂ X by r, and a rooted topology on r by t r .…”

STELAR: A statistically consistent coalescent-based species tree estimation method by maximizing triplet consistency

“…Each internal node u in a tree T divides the set of taxa present in the subtree rooted at u into two distinct sets. We call this a subtree-bipartition, denoted by SBP T (u), which was originally defined in [35]. We denote by T u the subtree under node u of tree T .…”

“…The algorithmic design (and corresponding theoretical results) in STELAR is structurally similar to ASTRAL. This sort of DP-based approach, which implicitly finds a maximum or minimum clique in a graph modelled from the input gene trees, was first used by [39] and later was used in Phylonet [40,41], DynaDup [35,42] and AS-TRAL. The key idea in STELAR is to find an equation for computing the number of triplets in the gene trees that agree with a given subtree in the species tree, which ultimately enables us to design a dynamic programming algorithm for estimating a species tree by maximizing the triplet agreement.…”