A mathematical foundation for the analysis of cladistic character compatibility

Estabrook, George F.; Johnson, C. S.; McMorris, F. R.

doi:10.1016/0025-5564(76)90035-3

Cited by 120 publications

(53 citation statements)

References 7 publications

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“…In perfect phylogeny [19,20,23], the phylogenetic tree is constructed according to the divergence of different characters of the objects. Specifically, there are only two states for each characters: zero, where the character is absent; and one, where it is present (i.e.…”

Section: Perfect Phylogenymentioning

confidence: 99%

“…In character-based models, the phylogenetic tree is constructed according to the presence or absence of the characters observed from the species. Perfect phylogeny [19,20] is one of the classical characterbased models. In this model, there are only two states for each character: zero, where the character is absent; and one, where it is present.…”

Section: Introductionmentioning

confidence: 99%

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A new phylogenetic tree model for fuzzy characters

Auyeung

2005

International Conference on Information Technology: Coding and Computing (ITCC'05) - Volume II

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Section: Perfect Phylogenymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A new phylogenetic tree model for fuzzy characters

Auyeung

2005

International Conference on Information Technology: Coding and Computing (ITCC'05) - Volume II

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“…A classical problem in this area is the tree compatibility problem (also called the cladistic character compatibility problem) [10,11,12]. The tree compatibility problem says that the set T of trees is compatible if a tree T exists such that C(T ) = ∪ Ti∈T C(T i ).…”

Section: Rv-iiimentioning

confidence: 99%

“…These methods include maximum agreement subtrees [16,19,13,24,14], strict consensus trees [4,9], median trees (also known as majority trees) [5], compatibility trees [10,11,12], the Nelson tree [22], and the Adams consensus [1].…”

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confidence: 99%

Computing the Local Consensus of Trees

1998

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Abstract. The inference of consensus from a set of evolutionary trees is a fundamental problem in a number of fields such as biology and historical linguistics, and many models for inferring this consensus have been proposed. In this paper we present a model for deriving what we call a local consensus tree T from a set of trees T . The model we propose presumes a function f , called a total local consensus function, which determines for every triple A of species, the form that the local consensus tree should take on A. We show that all local consensus trees, when they exist, can be constructed in polynomial time and that many fundamental problems can be solved in linear time. We also consider partial local consensus functions and study optimization problems under this model. We present linear time algorithms for several variations. Finally we point out that the local consensus approach ties together many previous approaches to constructing consensus trees.Key words. algorithms, graphs, evolutionary trees AMS subject classifications. 05C05, 68Q25, 92-08, 92B05PII. S0097539795287642 1.Introduction. An evolutionary tree (also called a phylogeny or phylogenetic tree) for a species set S is a rooted tree with |S| = n leaves labeled by distinct elements in S. Because evolutionary history is difficult to determine (it is both computationally difficult as most optimization problems in this area are NP-hard and scientifically difficult as well since a range of approaches appropriate to different types of data exist), a common approach to solving this problem is to apply many different algorithms to a given data set, or to different data sets representing the same species set, and then look for common elements from the set of trees which are returned.There is extensive literature about inferring consensus from ordered sets of trees, with much attention paid to the properties of the rules for inferring the consensus. In this paper, we will make an explicit assumption that the consensus rule be independent of the ordering of the trees in the input; i.e., we will presume that the input to the consensus problem is an unordered multiset of evolutionary trees, each leaf-labelled by the elements in S. We call this input a profile, noting that in this paper the terminology is restricted in meaning as we have indicated.Several consensus methods are described in the literature for deriving one tree from a profile of evolutionary trees. These methods include maximum agreement subtrees [16,19,13,24,14], strict consensus trees [4,9], median trees (also known as majority trees) [5], compatibility trees [10,11,12], the Nelson tree [22], and the Adams consensus [1].The algorithms for some of these are implemented in standard packages and are in use; most common, perhaps, are strict and majority consensus tree approaches.

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“…Compatibility analysis was developed in the late 1960s and 1970s as part of the explosion of interest in computerized phylogenetic analysis. Estabrook, who died in 2011, was one of the major contributors to the theory, methods, and algorithms used to identify compatible characters and the socalled "convex" groups that share them (10)(11)(12). Compatible characters are best understood as those character combinations that do not logically require homoplasy to explain them.…”

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confidence: 99%

Trait-based extinction catches the Red Queen napping during the Cambrian

Polly¹

2014

Proc. Natl. Acad. Sci. U.S.A.

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A mathematical foundation for the analysis of cladistic character compatibility

Cited by 120 publications

References 7 publications

A new phylogenetic tree model for fuzzy characters

A new phylogenetic tree model for fuzzy characters

Computing the Local Consensus of Trees

Trait-based extinction catches the Red Queen napping during the Cambrian

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