J. Comput. Biol. - Exactly computing the parsimony scores on phylogenetic networks using dynamic programming.

Tópicos

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Resumo

Scoring a given phylogenetic network is the first step that is required in searching for the best evolutionary framework for a given dataset. Using the principle of maximum parsimony, we can score phylogenetic networks based on the minimum number of state changes across a subset of edges of the network for each character that are required for a given set of characters to realize the input states at the leaves of the networks. Two such subsets of edges of networks are interesting in light of studying evolutionary histories of datasets: (i) the set of all edges of the network, and (ii) the set of all edges of a spanning tree that minimizes the score. The problems of finding the parsimony scores under these two criteria define slightly different mathematical problems that are both NP-hard. In this article, we show that both problems, with scores generalized to adding substitution costs between states on the endpoints of the edges, can be solved exactly using dynamic programming. We show that our algorithms require O(m(p)k) storage at each vertex (per character), where k is the number of states the character can take, p is the number of reticulate vertices in the network, m=k for the problem with edge set (i), and m=2 for the problem with edge set (ii). This establishes an O(nm(p)k(2)) algorithm for both the problems (n is the number of leaves in the network), which are extensions of Sankoff's algorithm for finding the parsimony scores for phylogenetic trees. We will discuss improvements in the complexities and show that for phylogenetic networks whose underlying undirected graphs have disjoint cycles, the storage at each vertex can be reduced to O(mk), thus making the algorithm polynomial for this class of networks. We will present some properties of the two approaches and guidance on choosing between the criteria, as well as traverse through the network space using either of the definitions. We show that our methodology provides an effective means to study a wide variety of datasets.

Resumo Limpo

score given phylogenet network first step requir search best evolutionari framework given dataset use principl maximum parsimoni can score phylogenet network base minimum number state chang across subset edg network charact requir given set charact realiz input state leav network two subset edg network interest light studi evolutionari histori dataset set edg network ii set edg span tree minim score problem find parsimoni score two criteria defin slight differ mathemat problem nphard articl show problem score general ad substitut cost state endpoint edg can solv exact use dynam program show algorithm requir ompk storag vertex per charact k number state charact can take p number reticul vertic network mk problem edg set m problem edg set ii establish onmpk algorithm problem n number leav network extens sankoff algorithm find parsimoni score phylogenet tree will discuss improv complex show phylogenet network whose under undirect graph disjoint cycl storag vertex can reduc omk thus make algorithm polynomi class network will present properti two approach guidanc choos criteria well travers network space use either definit show methodolog provid effect mean studi wide varieti dataset

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