Fast FPT Algorithms for Computing Rooted Agreement Forests: Theory and Experiments

Whidden, Chris; Beiko, Robert G.; Zeh, Norbert

doi:10.1007/978-3-642-13193-6_13

Cited by 44 publications

(55 citation statements)

References 18 publications

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“…Our published MAF algorithm (Whidden et al 2010; 2013) operates in a bottom-up fashion in the first tree, denoted T 1 , and reduces the second tree to a forest, denoted F 2 . During the algorithm, we identify subtrees that are identical in T 1 and F 2 and, in particular, pairs of such trees that are siblings in T 1 (sibling pairs).…”

Section: Methodsmentioning

confidence: 99%

Supertrees Based on the Subtree Prune-and-Regraft Distance

2014

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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). Many 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 benchmark datasets simulated under plausible rates of LGT, we show that SPR supertrees are more similar to correct species histories 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. [Lateral gene transfer; matrix representation with parsimony; phylogenomics; prokaryotic phylogeny; Robinson–Foulds; subtree prune-and-regraft; supertrees.]

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Section: Methodsmentioning

confidence: 99%

Supertrees Based on the Subtree Prune-and-Regraft Distance

2014

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“…Although the SPR distance (rooted and unrooted) is NP-hard to compute [3,12], it is fixed-parameter tractable with respect to the distance in the rooted case [3]. In particular, one can determine in O(n)-time whether two rooted phylogenetic trees are adjacent in the rSPR graph (O(n 2 )-time for unrooted trees) using the algorithms of Whidden et al [42][43][44]46]. We applied this method comparing each of the m trees pairwise to identify adjacencies, requiring a total of O(m 2 n)-time (O(m 2 n 2 )-time in the unrooted case).…”

Section: Preliminariesmentioning

confidence: 99%

Ricci-Ollivier Curvature of the Rooted Phylogenetic Subtree-Prune-Regraft Graph

Whidden

Matsen

2015

2016 Proceedings of the Thirteenth Workshop on Analytic Algorithmics and Combinatorics (ANALCO)

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Statistical phylogenetic inference methods use tree rearrangement operations such as subtree-prune-regraft (SPR) to perform Markov chain Monte Carlo (MCMC) across tree topologies. These methods are known to mix quickly when sampling from the simple uniform distribution of trees but may become stuck in the local optima of multi-modal posterior distributions for real data induced by non-uniform likelihoods. The structure of the graph induced by tree rearrangement operations is an important determinant of the mixing properties of MCMC, motivating study of the underlying rSPR graph in greater detail.In this paper, we investigate the rSPR graph in a new way: by calculating Ricci-Ollivier curvature with respect to uniform and Metropolis-Hastings random walks. We confirm using simulation that mean access time distributions depend on distance, degree, and curvature, showing the relevance of these curvature results to stochastic tree search. These calculations require fast new algorithms for constructing and sampling these graphs, reducing the time required to compute an rSPR graph from O(m 2 n)-time to O(mn 3 ), where m is the (often large) number of trees in the graph and n their number of leaves, and reducing the time required to select an SPR neighbor of a tree uniformly at random to O(n) time. We then develop a closed form solution to characterize how the number of SPR neighbors of a tree changes after an SPR operation is applied to that tree. This gives bounds on the curvature, as well as a flatness-in-the-limit theorem indicating that paths of small topology changes are easy to traverse. However, we find that large topology changes (i.e. moving a large subtree) gives pairs of trees with negative curvature. Although these pairs of trees with negative curvature do not impede mixing in this simple well-connected space, they may manifest as bottlenecks in the much smaller * This work was funded by National Science Foundation award 1223057. Chris Whidden is a Simons Foundation Fellow of the Life Sciences Research Foundation.† Program in Computational Biology, Fred Hutchinson Cancer Research Center, Seattle, WA, USA 98109. {cwhidden,matsen}@fredhutch.org credible sets induced by phylogenetic posteriors with a likelihood function. This work extends our knowledge of the rSPR graph, in particular properties that are relevant for investigation of sampling the rSPR graph.

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“…; T k . Note that our definition of an AAF is the same as those in [4], [18] but is different from that in [16]. With respect to an AF F of T 1 ; .…”

Section: Agreement Forests (Afs)mentioning

confidence: 99%

“…We omit the details of computing one MAAF, one MAF, or all MAFs, because they are similar to the computation of all MAAFs. Whidden et al [16] give an algorithm for computing an MAF of two given phylogenetic trees T 1 and T 2 on the same set X of species in Oð3 disconnectivity of an MAF of T 1 and T 2 . The basic idea behind their algorithm is as follows: initially, we set F 1 ¼ T 1 and F 2 ¼ T 2 .…”

Section: Computing Mafs Maafs and Optimal Type-i Networkmentioning

confidence: 99%

Algorithms for Reticulate Networks of Multiple Phylogenetic Trees

Chen

Wang

2012

IEEE/ACM Trans. Comput. Biol. and Bioinf.

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Abstract-A reticulate network N of multiple phylogenetic trees may have nodes with two or more parents (called reticulation nodes). There are two ways to define the reticulation number of N. One way is to define it as the number of reticulation nodes in N [13]; in this case, a reticulate network with the smallest reticulation number is called an optimal type-I reticulate network of the trees. The better way is to define it as the total number of parents of reticulation nodes in N minus the number of reticulation nodes in N [18]; in this case, a reticulate network with the smallest reticulation number is called an optimal type-II reticulate network of the trees. In this paper, we first present a fast fixed-parameter algorithm for constructing one or all optimal type-I reticulate networks of multiple phylogenetic trees. We then use the algorithm together with other ideas to obtain an algorithm for estimating a lower bound on the reticulation number of an optimal type-II reticulate network of the input trees. To our knowledge, these are the first fixed-parameter algorithms for the problems. We have implemented the algorithms in ANSI C, obtaining programs CMPT and MaafB. Our experimental data show that CMPT can construct optimal type-I reticulate networks rapidly and MaafB can compute better lower bounds for optimal type-II reticulate networks within shorter time than the previously best program PIRN designed by Wu [18].

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Fast FPT Algorithms for Computing Rooted Agreement Forests: Theory and Experiments

Cited by 44 publications

References 18 publications

Supertrees Based on the Subtree Prune-and-Regraft Distance

Supertrees Based on the Subtree Prune-and-Regraft Distance

Ricci-Ollivier Curvature of the Rooted Phylogenetic Subtree-Prune-Regraft Graph

Algorithms for Reticulate Networks of Multiple Phylogenetic Trees

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