Supertrees based on the subtree prune-and-regraft distance

Abstract

Supertree methods reconcile a set of phylogenetic trees into a single structure that is often interpreted as a branching history of species. A key challenge is combining conflicting evolutionary histories that are due to artifacts of phylogenetic reconstruction and phenomena such as lateral gene transfer (LGT). Although they often work well in practice, existing supertree approaches use optimality criteria that do not reflect underlying processes, have known biases and may be unduly influenced by LGT. We present the first method to construct supertrees by using the subtree prune-and-regraft (SPR) distance as an optimality criterion. Although calculating the rooted SPR distance between a pair of trees is NP-hard, our new maximum agreement forest-based methods can reconcile trees with hundreds of taxa and > 50 transfers in fractions of a second, which enables repeated calculations during the course of an iterative search. Our approach can accommodate trees in which uncertain relationships have been collapsed to multifurcating nodes. Using a series of simulated benchmark datasets, we show that SPR supertrees are more similar to correct species histories under plausible rates of LGT than supertrees based on parsimony or Robinson-Foulds distance criteria. We successfully constructed an SPR supertree from a phylogenomic dataset of 40,631 gene trees that covered 244 genomes representing several major bacterial phyla. Our SPR-based approach also allowed direct inference of highways of gene transfer between bacterial classes and genera; a small number of these highways connect genera in different phyla and can highlight specific genes implicated in long-distance LGT.

Problems with supertrees based on the subtree prune‐and‐regraft distance, with comments on majority rule supertrees

“…This justification can only be assessed in practice through simulations, and is always tied to the specific conditions of the simulations performed. A recent example of such an approach to justifying a supertree method is by Whidden et al (2014), who proposed supertrees based on the subtree pruneand-regraft (SPR) distances (Hein et al, 1996). The SPR supertree is the binary tree with the minimum sum of SPR distances to the source trees (the source trees can have polytomies).…”

“…The program SPRSupertrees (written by C. Whidden) implements the method and is available at http://kiwi.cs.dal.ca/Software. Whidden et al (2014) defended their method on the grounds that, when using it to combine source trees representing different genes with simulated lateral gene transfers (LGTs), it produces supertrees closer to the model tree than matrix representation with parsimony (MRP; Baum, 1992;Ragan, 1992;Baum and Ragan, 1993) and Robinson-Foulds (RF) supertrees (Bansal et al, 2010). We do not dispute the results of Whidden et al's simulations-it may well be true that under the specific conditions of LGT they simulated, SPR supertrees are more likely than MRP of RF supertrees to return the true tree.…”

“…Because minimizing the sum of SPR distances to the source trees has no special meaning in terms of the groupings, the SPR supertree can also display clades not present in any of the source trees, and contradict groups present in the majority of the source treesboth of which were explicitly considered by Whidden et al (2014) as problematic in the case of MRP. Whidden et al (2014) did not discuss whether SPR supertrees could have this behaviour, but Figs 2 and 3 show examples of these two problems.…”

“…The default value of 0.5 precludes cases like those in Figs 2 and 3, but at the expense of not allowing full minimization of the SPR distances to source trees. In other words, while the default 0.5 produces more reasonable results, it sets a limit on the degree to which the criterion proposed by Whidden et al (2014) can be optimized. Thus, unrestricted optimization of the criterion-SPR distances to the source trees-leads to results that are hard to defend.…”

“…An additional problem with SPR supertrees concerns a point that, on first approach, seems merely technical, but in fact also concerns unsolved methodological issues. The SPR supertree is defined by Whidden et al (2014) as the binary tree that minimizes the sum of SPR distances; computations are much easier on binary trees. Of course there may be multiple equally optimal binary trees, or a single optimal supertree but supported only weakly, for example in the case of conflicting input trees (as in the examples presented here), and then a less resolved supertree may be desirable.…”