scholarly journals Collecting reliable clades using the Greedy Strict Consensus Merger

PeerJ ◽  
2016 ◽  
Vol 4 ◽  
pp. e2172 ◽  
Author(s):  
Markus Fleischauer ◽  
Sebastian Böcker
Keyword(s):  
Computational Complexity ◽  
Phylogenetic Trees ◽  
Optimization Problems ◽  
Matrix Representation ◽  
Phylogenetic Inference ◽  
Scoring Functions ◽  
True Positive ◽  
Worst Case ◽  
Inference Methods ◽  
Supertree Methods

Supertree methods combine a set of phylogenetic trees into a single supertree. Similar to supermatrix methods, these methods provide a way to reconstruct larger parts of the Tree of Life, potentially evading the computational complexity of phylogenetic inference methods such as maximum likelihood. The supertree problem can be formalized in different ways, to cope with contradictory information in the input. Many supertree methods have been developed. Some of them solve NP-hard optimization problems like the well-known Matrix Representation with Parsimony, while others have polynomial worst-case running time but work in a greedy fashion (FlipCut). Both can profit from a set of clades that are already known to be part of the supertree. The Superfine approach shows how the Greedy Strict Consensus Merger (GSCM) can be used as preprocessing to find these clades. We introduce different scoring functions for the GSCM, a randomization, as well as a combination thereof to improve the GSCM to find more clades. This helps, in turn, to improve the resolution of the GSCM supertree. We find this modifications to increase the number of true positive clades by 18% compared to the currently used Overlap scoring.

scholarly journals Collecting reliable clades using the Greedy Strict Consensus Merger

2015 ◽  
Author(s):  
Markus Fleischauer ◽  
Sebastian Böcker
Keyword(s):  
Computational Complexity ◽  
Phylogenetic Trees ◽  
Optimization Problems ◽  
Matrix Representation ◽  
Phylogenetic Inference ◽  
Scoring Functions ◽  
True Positive ◽  
Worst Case ◽  
Inference Methods ◽  
Supertree Methods

Supertree methods combine a set of phylogenetic trees into a single supertree. Similar to supermatrix methods, these methods provide a way to reconstruct larger parts of the Tree of Life, potentially evading the computational complexity of phylogenetic inference methods such as maximum likelihood. The supertree problem can be formalized in different ways, to cope with contradictory information in the input. Many supertree methods have been developed. Some of them solve NP-hard optimization problems like the well known Matrix Representation with Parsimony, others have polynomial worst-case running time but work in a greedy fashion (FlipCut). Both can profit from a set of clades that are already known to be part of the supertree. The Superfine approach shows how the Greedy Strict Consensus Merger (GSCM) can be used as preprocessing to find these clades. We introduce different scoring functions for the GSCM, a randomization, as well as a combination thereof to improve the GSCM to find more clades. This helps, in turn, to improve the resolution of the final supertree. We find this modifications to increase the number of true positive clades by 16% while decreasing the number of false positive clades by 3% compared to the currently used Overlap scoring.

scholarly journals Collecting reliable clades using the Greedy Strict Consensus Merger

2015 ◽  
Author(s):  
Markus Fleischauer ◽  
Sebastian Böcker
Keyword(s):  
Computational Complexity ◽  
Phylogenetic Trees ◽  
Optimization Problems ◽  
Matrix Representation ◽  
Phylogenetic Inference ◽  
Scoring Functions ◽  
True Positive ◽  
Worst Case ◽  
Inference Methods ◽  
Supertree Methods

Supertree methods combine a set of phylogenetic trees into a single supertree. Similar to supermatrix methods, these methods provide a way to reconstruct larger parts of the Tree of Life, potentially evading the computational complexity of phylogenetic inference methods such as maximum likelihood. The supertree problem can be formalized in different ways, to cope with contradictory information in the input. Many supertree methods have been developed. Some of them solve NP-hard optimization problems like the well known Matrix Representation with Parsimony, others have polynomial worst-case running time but work in a greedy fashion (FlipCut). Both can profit from a set of clades that are already known to be part of the supertree. The Superfine approach shows how the Greedy Strict Consensus Merger (GSCM) can be used as preprocessing to find these clades. We introduce different scoring functions for the GSCM, a randomization, as well as a combination thereof to improve the GSCM to find more clades. This helps, in turn, to improve the resolution of the final supertree. We find this modifications to increase the number of true positive clades by 16% while decreasing the number of false positive clades by 3% compared to the currently used Overlap scoring.

scholarly journals Collecting reliable clades using the Greedy Strict Consensus Merger

2015 ◽  
Author(s):  
Markus Fleischauer ◽  
Sebastian Böcker
Keyword(s):  
Computational Complexity ◽  
Phylogenetic Trees ◽  
Optimization Problems ◽  
Matrix Representation ◽  
Phylogenetic Inference ◽  
Scoring Functions ◽  
True Positive ◽  
Worst Case ◽  
Inference Methods ◽  
Supertree Methods

Supertree methods combine a set of phylogenetic trees into a single supertree. Similar to supermatrix methods, these methods provide a way to reconstruct larger parts of the Tree of Life, potentially evading the computational complexity of phylogenetic inference methods such as maximum likelihood. The supertree problem can be formalized in different ways, to cope with contradictory information in the input. Many supertree methods have been developed. Some of them solve NP-hard optimization problems like the well known Matrix Representation with Parsimony, others have polynomial worst-case running time but work in a greedy fashion (FlipCut). Both can profit from a set of clades that are already known to be part of the supertree. The Superfine approach shows how the Greedy Strict Consensus Merger (GSCM) can be used as preprocessing to find these clades. We introduce different scoring functions for the GSCM, a randomization, as well as a combination thereof to improve the GSCM to find more clades. This helps, in turn, to improve the resolution of the final supertree. We find this modifications to increase the number of true positive clades by 16% while decreasing the number of false positive clades by 3% compared to the currently used Overlap scoring.

scholarly journals Collecting reliable clades using the Greedy Strict Consensus Merger

2015 ◽  
Author(s):  
Markus Fleischauer ◽  
Sebastian Böcker
Keyword(s):  
Computational Complexity ◽  
Phylogenetic Trees ◽  
Optimization Problems ◽  
Matrix Representation ◽  
Phylogenetic Inference ◽  
Scoring Functions ◽  
True Positive ◽  
Worst Case ◽  
Inference Methods ◽  
Supertree Methods

Supertree methods combine a set of phylogenetic trees into a single supertree. Similar to supermatrix methods, these methods provide a way to reconstruct larger parts of the Tree of Life, potentially evading the computational complexity of phylogenetic inference methods such as maximum likelihood. The supertree problem can be formalized in different ways, to cope with contradictory information in the input. Many supertree methods have been developed. Some of them solve NP-hard optimization problems like the well known Matrix Representation with Parsimony, others have polynomial worst-case running time but work in a greedy fashion (FlipCut). Both can profit from a set of clades that are already known to be part of the supertree. The Superfine approach shows how the Greedy Strict Consensus Merger (GSCM) can be used as preprocessing to find these clades. We introduce different scoring functions for the GSCM, a randomization, as well as a combination thereof to improve the GSCM to find more clades. This helps, in turn, to improve the resolution of the final supertree. We find this modifications to increase the number of true positive clades by 16% while decreasing the number of false positive clades by 3% compared to the currently used Overlap scoring.

scholarly journals Polynomial Supertree Methods Revisited

2011 ◽  
Vol 2011 ◽  
pp. 1-21 ◽  
Author(s):  
Malte Brinkmeyer ◽  
Thasso Griebel ◽  
Sebastian Böcker
Keyword(s):  
Simulation Study ◽  
Phylogenetic Trees ◽  
Optimization Problem ◽  
Matrix Representation ◽  
Distance Matrix ◽  
Extensive Simulation ◽  
Supertree Method ◽  
Pros And Cons ◽  
To Come ◽  
Supertree Methods

Supertree methods allow to reconstruct large phylogenetic trees by combining smaller trees with overlapping leaf sets into one, more comprehensive supertree. The most commonly used supertree method, matrix representation with parsimony (MRP), produces accurate supertrees but is rather slow due to the underlying hard optimization problem. In this paper, we present an extensive simulation study comparing the performance of MRP and the polynomial supertree methods MinCut Supertree, Modified MinCut Supertree, Build-with-distances, PhySIC, PhySIC_IST, and super distance matrix. We consider both quality and resolution of the reconstructed supertrees. Our findings illustrate the tradeoff between accuracy and running time in supertree construction, as well as the pros and cons of voting- and veto-based supertree approaches. Based on our results, we make some general suggestions for supertree methods yet to come.

scholarly journals BCD Beam Search: considering suboptimal partial solutions in Bad Clade Deletion supertrees

PeerJ ◽  
2018 ◽  
Vol 6 ◽  
pp. e4987
Author(s):  
Markus Fleischauer ◽  
Sebastian Böcker
Keyword(s):  
Matrix Representation ◽  
Search Algorithm ◽  
Simulated Data ◽  
Biological Data ◽  
Beam Search ◽  
Worst Case ◽  
Running Time ◽  
Minimum Cuts ◽  
Supertree Methods

Supertree methods enable the reconstruction of large phylogenies. The supertree problem can be formalized in different ways in order to cope with contradictory information in the input. Some supertree methods are based on encoding the input trees in a matrix; other methods try to find minimum cuts in some graph. Recently, we introduced Bad Clade Deletion (BCD) supertrees which combines the graph-based computation of minimum cuts with optimizing a global objective function on the matrix representation of the input trees. The BCD supertree method has guaranteed polynomial running time and is very swift in practice. The quality of reconstructed supertrees was superior to matrix representation with parsimony (MRP) and usually on par with SuperFine for simulated data; but particularly for biological data, quality of BCD supertrees could not keep up with SuperFine supertrees. Here, we present a beam search extension for the BCD algorithm that keeps alive a constant number of partial solutions in each top-down iteration phase. The guaranteed worst-case running time of the new algorithm is still polynomial in the size of the input. We present an exact and a randomized subroutine to generate suboptimal partial solutions. Both beam search approaches consistently improve supertree quality on all evaluated datasets when keeping 25 suboptimal solutions alive. Supertree quality of the BCD Beam Search algorithm is on par with MRP and SuperFine even for biological data. This is the best performance of a polynomial-time supertree algorithm reported so far.

scholarly journals A New Phylogenetic Inference Based on Genetic Attribute Reduction for Morphological Data

Entropy ◽  
2019 ◽  
Vol 21 (3) ◽  
pp. 313
Author(s):  
Jun Feng ◽  
Zeyun Liu ◽  
Hongwei Feng ◽  
Richard Sutcliffe ◽  
Jianni Liu ◽  
...  
Keyword(s):  
Phylogenetic Tree ◽  
Phylogenetic Trees ◽  
Missing Values ◽  
Attribute Reduction ◽  
Evaluation Criteria ◽  
Phylogenetic Inference ◽  
Morphological Data ◽  
Matching Algorithm ◽  
Inference Methods ◽  
Degree Of Similarity

To address the instability of phylogenetic trees in morphological datasets caused by missing values, we present a phylogenetic inference method based on a concept decision tree (CDT) in conjunction with attribute reduction. First, a reliable initial phylogenetic seed tree is created using a few species with relatively complete morphological information by using biologists’ prior knowledge or by applying existing tools such as MrBayes. Second, using a top-down data processing approach, we construct concept-sample templates by performing attribute reduction at each node in the initial phylogenetic seed tree. In this way, each node is turned into a decision point with multiple concept-sample templates, providing decision-making functions for grafting. Third, we apply a novel matching algorithm to evaluate the degree of similarity between the species’ attributes and their concept-sample templates and to determine the location of the species in the initial phylogenetic seed tree. In this manner, the phylogenetic tree is established step by step. We apply our algorithm to several datasets and compare it with the maximum parsimony, maximum likelihood, and Bayesian inference methods using the two evaluation criteria of accuracy and stability. The experimental results indicate that as the proportion of missing data increases, the accuracy of the CDT method remains at 86.5%, outperforming all other methods and producing a reliable phylogenetic tree.

scholarly journals Computing nearest neighbour interchange distances between ranked phylogenetic trees

2021 ◽  
Vol 82 (1-2) ◽  
Author(s):  
Lena Collienne ◽  
Alex Gavryushkin
Keyword(s):  
Cancer Research ◽  
Computational Complexity ◽  
Phylogenetic Tree ◽  
Shortest Path ◽  
Phylogenetic Trees ◽  
Shortest Paths ◽  
Nearest Neighbour ◽  
Tree Inference ◽  
Subtree Prune And Regraft ◽  
Comparison Algorithms

AbstractMany popular algorithms for searching the space of leaf-labelled (phylogenetic) trees are based on tree rearrangement operations. Under any such operation, the problem is reduced to searching a graph where vertices are trees and (undirected) edges are given by pairs of trees connected by one rearrangement operation (sometimes called a move). Most popular are the classical nearest neighbour interchange, subtree prune and regraft, and tree bisection and reconnection moves. The problem of computing distances, however, is $${\mathbf {N}}{\mathbf {P}}$$ N P -hard in each of these graphs, making tree inference and comparison algorithms challenging to design in practice. Although anked phylogenetic trees are one of the central objects of interest in applications such as cancer research, immunology, and epidemiology, the computational complexity of the shortest path problem for these trees remained unsolved for decades. In this paper, we settle this problem for the ranked nearest neighbour interchange operation by establishing that the complexity depends on the weight difference between the two types of tree rearrangements (rank moves and edge moves), and varies from quadratic, which is the lowest possible complexity for this problem, to $${\mathbf {N}}{\mathbf {P}}$$ N P -hard, which is the highest. In particular, our result provides the first example of a phylogenetic tree rearrangement operation for which shortest paths, and hence the distance, can be computed efficiently. Specifically, our algorithm scales to trees with tens of thousands of leaves (and likely hundreds of thousands if implemented efficiently).

scholarly journals The trouble with the second quantifier

4OR ◽  
2021 ◽  
Author(s):  
Gerhard J. Woeginger
Keyword(s):  
Computational Complexity ◽  
Robust Optimization ◽  
Complexity Theory ◽  
Operational Research ◽  
Optimization Problems ◽  
Bilevel Optimization ◽  
Theoretical Background ◽  
Research Community ◽  
Universal Quantifier ◽  
Computational Complexity Theory

AbstractWe survey optimization problems that allow natural simple formulations with one existential and one universal quantifier. We summarize the theoretical background from computational complexity theory, and we present a multitude of illustrating examples. We discuss the connections to robust optimization and to bilevel optimization, and we explain the reasons why the operational research community should be interested in the theoretical aspects of this area.

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