An ILP solution for the gene duplication problem

Chang, Wen-Chieh; Burleigh, Gordon; Fernández-Baca, David; Eulenstein, Oliver

doi:10.1186/1471-2105-12-s1-s14

Cited by 28 publications

(37 citation statements)

References 47 publications

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“…The entries M αp serve as ILP variables. In contrast to the work of [35], we allow trivial columns in M in which all entries are 0. Minimizing the number of non-trivial columns then yields a least resolved tree.…”

Section: Ilp Formulationmentioning

confidence: 99%

“…To this end, we determine the maximum consistent subset S * in the set S of species triples induced by those triples of (T, t) that have a speciation vertex as their root. The hard part in the ILP formulation for this problem is to enforce consistency of a set of triples [35]. This step can be simplified considerably using the fact that for every consistent triple set S * there is a strictly dense consistent triple set S ′ that contains S * (Lemma 7).…”

Section: Ilp Formulationmentioning

confidence: 99%

“…Thus S is the tree with the minimal number of (inner) vertices that displays S * . Our ILP formulation uses ideas from the work of [35] to construct S in the form of an equivalent partial hierarchy. 9.1.…”

Section: Ilp Formulationmentioning

confidence: 99%

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Phylogenomics with paralogs

Hellmuth

Wieseke

Lechner

et al. 2015

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

115

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Phylogenomics heavily relies on well-curated sequence data sets that comprise, for each gene, exclusively 1:1 orthologos. Paralogs are treated as a dangerous nuisance that has to be detected and removed. We show here that this severe restriction of the data sets is not necessary. Building upon recent advances in mathematical phylogenetics, we demonstrate that gene duplications convey meaningful phylogenetic information and allow the inference of plausible phylogenetic trees, provided orthologs and paralogs can be distinguished with a degree of certainty. Starting from tree-free estimates of orthology, cograph editing can sufficiently reduce the noise to find correct event-annotated gene trees. The information of gene trees can then directly be translated into constraints on the species trees. Although the resolution is very poor for individual gene families, we show that genomewide data sets are sufficient to generate fully resolved phylogenetic trees, even in the presence of horizontal gene transfer.orthology | paralogy | gene tree | species tree | cograph M olecular phylogenetics is primarily concerned with the reconstruction of evolutionary relationships between species based on sequence information. To this end, alignments of protein or DNA sequences are used, whose evolutionary history is believed to be congruent to that of the respective species. This property can be ensured most easily in the absence of gene duplications and horizontal gene transfer (HGT). Phylogenetic studies judiciously select families of genes that rarely exhibit duplications (such as rRNAs, most ribosomal proteins, and many of the housekeeping enzymes). In phylogenomics, elaborate automatic pipelines such as HaMStR (1), are used to filter genomewide data sets to at least deplete sequences with detectable paralogs (homologs in the same species).In the presence of gene duplications, however, it becomes necessary to distinguish between the evolutionary history of genes (gene trees) and the evolutionary history of the species (species trees) in which these genes reside. Leaves of a gene tree represent genes. Their inner nodes represent two kinds of evolutionary events, namely the duplication of genes within a genome-giving rise to paralogs-and speciations, in which the ancestral gene complement is transmitted to two daughter lineages. Two genes are (co)orthologous if their last common ancestor in the gene tree represents a speciation event, whereas they are paralogous if their last common ancestor is a duplication event; see refs. 2 and 3 for a more recent discussion on orthology and paralogy relationships. Speciation events, in turn, define the inner vertices of a species tree. However, they depend on both the gene and the species phylogeny, as well as the reconciliation between the two. The latter identifies speciation vertices in the gene tree with a particular speciation event in the species tree and places the gene duplication events on the edges of the species tree. Intriguingly, it is nevertheless possible in practice to distinguis...

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Section: Ilp Formulationmentioning

confidence: 99%

Section: Ilp Formulationmentioning

confidence: 99%

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Phylogenomics with paralogs

Hellmuth

Wieseke

Lechner

et al. 2015

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

115

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show abstract

“…Therefore, different heuristics and Integer Linear Programs have been developed [25,26,9,27]. Recently, the Minimum Duplication Bipartite problem has been introduced to tackle the Minimum Duplication problem [28].…”

Section: Known Resultsmentioning

confidence: 99%

Complexity Insights of the Minimum Duplication Problem

Blin

Bonizzoni

Dondi

et al. 2012

SOFSEM 2012: Theory and Practice of Computer Science

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The Minimum Duplication problem is a well-known problem in phylogenetics and comparative genomics. Given a set of gene trees, the Minimum Duplication problem asks for a species tree that induces the minimum number of gene duplications in the input gene trees. Recently, a variant of the Minimum Duplication problem, called Minimum Duplication Bipartite, has been introduced, where the goal is to find all pre-duplications, that is duplications that in the evolution precede the first speciation with respect to a species tree. In this paper, we investigate the complexity of both Minimum Duplication and Minimum Duplication Bipartite. First of all, we prove that the Minimum Duplication problem is APX-hard, even when the input consists of five uniquely leaf-labeled gene trees (improving upon known results on the complexity of the problem). Then, we show that the Minimum Duplication Bipartite problem can be solved efficiently with a randomized algorithm when the input gene trees have bounded depth. An extended abstract of this paper appeared in SOFSEM 2012 [1].

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“…13 These local search strategies are effective for relatively small numbers of taxa, but their utility for very large numbers of taxa has not been explored. In addition to local search techniques, exact solutions 14,15 and fixed-parameter tractable algorithms 1,16 have been proposed for addressing MGD and MGDL; however, to date these approaches have not been used as widely as the heuristic searches.…”

Section: Introductionmentioning

confidence: 99%

Inferring Optimal Species Trees Under Gene Duplication and Loss

2012

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Species tree estimation from multiple markers is complicated by the fact that gene trees can differ from each other (and from the true species tree) due to several biological processes, one of which is gene duplication and loss. Local search heuristics for two NP-hard optimization problems -minimize gene duplications (MGD) and minimize gene duplications and losses (MGDL) -are popular techniques for estimating species trees in the presence of gene duplication and loss. In this paper, we present an alternative approach to solving MGD and MGDL from rooted gene trees. First, we characterize each tree in terms of its "subtree-bipartitions" (a concept we introduce). Then we show that the MGD species tree is defined by a maximum weight clique in a vertex-weighted graph that can be computed from the subtree-bipartitions of the input gene trees, and the MGDL species tree is defined by a minimum weight clique in a similarly constructed graph. We also show that these optimal cliques can be found in polynomial time in the number of vertices of the graph using a dynamic programming algorithm (similar to that of Hallett and Lagergren 1 ), because of the special structure of the graphs. Finally, we show that a constrained version of these problems, where the subtree-bipartitions of the species tree are drawn from the subtree-bipartitions of the input gene trees, can be solved in time that is polynomial in the number of gene trees and taxa. We have implemented our dynamic programming algorithm in a publicly available software tool, available at

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An ILP solution for the gene duplication problem

Cited by 28 publications

References 47 publications

Phylogenomics with paralogs

Phylogenomics with paralogs

Complexity Insights of the Minimum Duplication Problem

Inferring Optimal Species Trees Under Gene Duplication and Loss

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