Bounding the Number of Hybridisation Events for a Consistent Evolutionary History

Baroni, Mihaela; Grünewald, Stefan; Moulton, Vincent; Semple, Charles

doi:10.1007/s00285-005-0315-9

Cited by 92 publications

(128 citation statements)

References 18 publications

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“…Such forests are frequently used to model reticulate evolution for when two rooted binary phylogenetic trees T and T are given (see for example Baroni et al 2005;Hein et al 1996). Our analysis centers around a new algorithm, called TemporalHybrid, which reconstructs a temporal hybridization network for T and T if one exists.…”

Section: Constructing Temporal Hybridization Network For Two Treesmentioning

confidence: 99%

“…The minimum number h(T , T ) of hybridization events and the size of a maximum-acyclic-agreement forest of T and T are related through the following theorem (Baroni et al 2005). …”

Section: Agreement Forestsmentioning

confidence: 99%

“…Although not explicitly stated in Baroni et al (2005), one direction of Theorem 4.1 is essentially established by proving that, if N is a hybridization network on X that displays T and T , then there is an acyclic-agreement forest F for T and T such that |F| ≤ h(N ) + 1. Intuitively, one takes N and iteratively cuts off rooted subtrees by deleting hybridization vertices and their three incident arcs.…”

Section: Theorem 41 Let T and T Be Two Rooted Binary Phylogenetic X mentioning

confidence: 99%

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Analyzing and reconstructing reticulation networks under timing constraints

2009

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Reticulation networks are now frequently used to model the history of life for various groups of species whose evolutionary past is likely to include reticulation events such as horizontal gene transfer or hybridization. However, the reconstructed networks are rarely guaranteed to be temporal. If a reticulation network is temporal, then it satisfies the two biologically motivated timing constraints of instantaneously occurring reticulation events and successively occurring speciation events. On the other hand, if a reticulation network is not temporal, it is always possible to make it temporal by adding a number of additional unsampled or extinct taxa. In the first half of the paper, we show that deciding whether a given number of additional taxa is sufficient to transform a non-temporal reticulation network into a temporal one is an NP-complete problem. As one is often given a set of gene trees instead of a network in the context of hybridization, this motivates the second half of the paper which provides an algorithm, called TemporalHybrid, for reconstructing a temporal hybridization network that simultaneously explains the ancestral history of two trees or indicates that no such network exists. We further derive two methods to decide whether or not a temporal hybridization network exists for two given trees and illustrate one of the methods on a grass data set.All authors contributed equally to this work.

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Section: Constructing Temporal Hybridization Network For Two Treesmentioning

confidence: 99%

“…The minimum number h(T , T ) of hybridization events and the size of a maximum-acyclic-agreement forest of T and T are related through the following theorem (Baroni et al 2005). …”

Section: Agreement Forestsmentioning

confidence: 99%

Section: Theorem 41 Let T and T Be Two Rooted Binary Phylogenetic X mentioning

confidence: 99%

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Analyzing and reconstructing reticulation networks under timing constraints

2009

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“…Note that the hybridization number of two trees is always bigger than their rSPR distance [2], and so Lemma 2 and Corollary 2 imply the following:…”

Section: Theorem 4 (Theorem 22 Of [16])mentioning

confidence: 99%

“…This question, along with the closely related problems of determining the minimum number of subtree prune and regraft, respectively tree bisection and reconnection, operations required to transform one phylogenetic tree into another (the rSPR Distance and TBR Distance problem, respectively) has been considered in a number of papers [1,2,3,5,10,12,17,18]. Key theoretical developments have shown that each of these three problems is NPhard even in the restricted case that the input consists of two binary phylogenetic trees [4,6,12], but also that they are all fixed-parameter tractable in their respective natural parameters [1,4,5].…”

Section: Introductionmentioning

confidence: 99%

On the fixed parameter tractability of agreement-based phylogenetic distances

et al. 2016

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International audienceThree important and related measures for summarizing the dissimilarity in phylogenetic trees are the minimum number of hybridization events required to fit two phylogenetic trees onto a single phylogenetic network (the hybridization number), the (rooted) subtree prune and regraft distance (the rSPR distance) and the tree bisection and reconnection distance (the TBR distance) between two phylogenetic trees. The respective problems of computing these measures are known to be NP-hard, but also fixed-parameter tractable in their respective natural parameters. This means that, while they are hard to compute in general, for cases in which a parameter (here the hybridization number and rSPR/TBR distance, respectively) is small, the problem can be solved efficiently even for large input trees. Here, we present new analyses showing that the use of the “cluster reduction” rule—already defined for the hybridization number and the rSPR distance and introduced here for the TBR distance—can transform any O(f(p)⋅n) -time algorithm for any of these problems into an O(f(k)⋅n) -time one, where n is the number of leaves of the phylogenetic trees, p is the natural parameter and k is a much stronger (that is, smaller) parameter: the minimum level of a phylogenetic network displaying both trees

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