scholarly journals Ranking top-k trees in tree-based phylogenetic networks

2019 ◽  
Author(s):  
Momoko Hayamizu ◽  
Kazuhisa Makino
Keyword(s):  
Optimal Algorithm ◽  
Linear Time ◽  
Fundamental Problem ◽  
Phylogenetic Network ◽  
Reticulate Evolution ◽  
Interesting Property ◽  
Biological Data ◽  
Phylogenetic Networks ◽  
Linear Delay ◽  
Algorithmic Problems

Abstract 'Tree-based' phylogenetic networks provide a mathematically-tractable model for representing reticulate evolution in biology. Such networks consist of an underlying 'support tree' together with arcs between the edges of this tree. However, a tree-based network can have several such support trees, and this leads to a variety of algorithmic problems that are relevant to the analysis of biological data. Recently, Hayamizu (arXiv:1811.05849 [math.CO]) proved a structure theorem for tree-based phylogenetic networks and obtained linear-time and linear-delay algorithms for many basic problems on support trees, such as counting, optimisation, and enumeration. In the present paper, we consider the following fundamental problem in statistical data analysis: given a tree-based phylogenetic network $N$ whose arcs are associated with probability, create the top-$k$ support tree ranking for $N$ by their likelihood values. We provide a linear-delay (and hence optimal) algorithm for the problem and thus reveal the interesting property of tree-based phylogenetic networks that ranking top-$k$ support trees is as computationally easy as picking $k$ arbitrary support trees.

scholarly journals A Divide-and-Conquer Method for Scalable Phylogenetic Network Inference from Multi-locus Data

2019 ◽  
Author(s):  
Jiafan Zhu ◽  
Xinhao Liu ◽  
Huw A. Ogilvie ◽  
Luay K. Nakhleh
Keyword(s):  
Large Scale ◽  
Network Inference ◽  
Incomplete Lineage Sorting ◽  
Phylogenetic Network ◽  
Biological Data ◽  
Phylogenetic Networks ◽  
Divide And Conquer ◽  
Lineage Sorting ◽  
Step Method ◽  
Sequence Alignments

AbstractReticulate evolutionary histories, such as those arising in the presence of hybridization, are best modeled as phylogenetic networks. Recently developed methods allow for statistical inference of phylogenetic networks while also accounting for other processes, such as incomplete lineage sorting (ILS). However, these methods can only handle a small number of loci from a handful of genomes.In this paper, we introduce a novel two-step method for scalable inference of phylogenetic networks from the sequence alignments of multiple, unlinked loci. The method infers networks on subproblems and then merges them into a network on the full set of taxa. To reduce the number of trinets to infer, we formulate a Hitting Set version of the problem of finding a small number of subsets, and implement a simple heuristic to solve it. We studied their performance, in terms of both running time and accuracy, on simulated as well as on biological data sets. The two-step method accurately infers phylogenetic networks at a scale that is infeasible with existing methods. The results are a significant and promising step towards accurate, large-scale phylogenetic network inference.We implemented the algorithms in the publicly available software package PhyloNet (https://bioinfocs.rice.edu/PhyloNet)[email protected]

scholarly journals Maximum Parsimony Inference of Phylogenetic Networks in the Presence of Polyploid Complexes

2020 ◽  
Author(s):  
Zhi Yan ◽  
Zhen Cao ◽  
Yushu Liu ◽  
Luay Nakhleh
Keyword(s):  
Network Inference ◽  
Incomplete Lineage Sorting ◽  
Phylogenetic Network ◽  
Biological Data ◽  
Phylogenetic Networks ◽  
Data Sets ◽  
Gene Trees ◽  
Polyploid Species ◽  
Lineage Sorting ◽  
Work Done

AbstractPhylogenetic networks provide a powerful framework for modeling and analyzing reticulate evolutionary histories. While polyploidy has been shown to be prevalent not only in plants but also in other groups of eukaryotic species, most work done thus far on phylogenetic network inference assumes diploid hybridization. These inference methods have been applied, with varying degrees of success, to data sets with polyploid species, even though polyploidy violates the mathematical assumptions underlying these methods. Statistical methods were developed recently for handling specific types of polyploids and so were parsimony methods that could handle polyploidy more generally yet while excluding processes such as incomplete lineage sorting. In this paper, we introduce a new method for inferring most parsimonious phylogenetic networks on data that include polyploid species. Taking gene trees as input, the method seeks a phylogenetic network that minimizes deep coalescences while accounting for polyploidy. The method could also infer trees, thus potentially distinguishing between auto- and allo-polyploidy. We demonstrate the performance of the method on both simulated and biological data. The inference method as well as a method for evaluating given phylogenetic networks are implemented and publicly available in the PhyloNet software package.

scholarly journals Maximum Parsimony Inference of Phylogenetic Networks in the Presence of Polyploid Complexes

2021 ◽  
Author(s):  
Zhi Yan ◽  
Zhen Cao ◽  
Yushu Liu ◽  
Huw A Ogilvie ◽  
Luay Nakhleh
Keyword(s):  
Network Inference ◽  
Incomplete Lineage Sorting ◽  
Gene Tree ◽  
Phylogenetic Network ◽  
Biological Data ◽  
Phylogenetic Networks ◽  
Data Sets ◽  
Polyploid Species ◽  
Lineage Sorting ◽  
Work Done

Abstract Phylogenetic networks provide a powerful framework for modeling and analyzing reticulate evolutionary histories. While polyploidy has been shown to be prevalent not only in plants but also in other groups of eukaryotic species, most work done thus far on phylogenetic network inference assumes diploid hybridization. These inference methods have been applied, with varying degrees of success, to data sets with polyploid species, even though polyploidy violates the mathematical assumptions underlying these methods. Statistical methods were developed recently for handling specific types of polyploids and so were parsimony methods that could handle polyploidy more generally yet while excluding processes such as incomplete lineage sorting. In this paper, we introduce a new method for inferring most parsimonious phylogenetic networks on data that include polyploid species. Taking gene tree topologies as input, the method seeks a phylogenetic network that minimizes deep coalescences while accounting for polyploidy. We demonstrate the performance of the method on both simulated and biological data. The inference method as well as a method for evaluating evolutionary hypotheses in the form of phylogenetic networks are implemented and publicly available in the PhyloNet software package.

scholarly journals Unifying Gene Duplication, Loss, and Coalescence on Phylogenetic Networks

2019 ◽  
Author(s):  
Peng Du ◽  
Huw A. Ogilvie ◽  
Luay Nakhleh
Keyword(s):  
Gene Duplication ◽  
Incomplete Lineage Sorting ◽  
Gene Tree ◽  
Phylogenetic Network ◽  
Biological Data ◽  
Phylogenetic Networks ◽  
Lineage Sorting ◽  
Evolutionary Processes ◽  
Domains Of Life ◽  
Gene Duplication And Loss

AbstractStatistical methods were recently introduced for inferring phylogenetic networks under the multispecies network coalescent, thus accounting for both reticulation and incomplete lineage sorting. Two evolutionary processes that are ubiquitous across all three domains of life, but are not accounted for by those methods, are gene duplication and loss (GDL).In this work, we devise a three-piece model—phylogenetic network, locus network, and gene tree—that unifies all the aforementioned processes into a single model of how genes evolve in the presence of ILS, GDL, and introgression within the branches of a phylogenetic network. To illustrate the power of this model, we develop an algorithm for estimating the parameters of a phylogenetic network topology under this unified model. The algorithm consists of a set of moves that allow for stochastic search through the parameter space. The challenges with developing such moves stem from the intricate dependencies among the three pieces of the model. We demonstrate the application of the model and the accuracy of the algorithm on simulated as well as biological data.Our work adds to the biologist’s toolbox of methods for phylogenomic inference by accounting for more complex evolutionary processes.

scholarly journals Inference of Species Phylogenies from Bi-allelic Markers Using Pseudo-likelihood

2018 ◽  
Author(s):  
Jiafan Zhu ◽  
Luay Nakhleh
Keyword(s):  
Network Inference ◽  
Sequence Data ◽  
Phylogenetic Network ◽  
Simulated Data ◽  
Biological Data ◽  
Phylogenetic Networks ◽  
Gene Trees ◽  
Multispecies Coalescent ◽  
Pseudo Likelihood ◽  
Computational Bottleneck

AbstractMotivationPhylogenetic networks represent reticulate evolutionary histories. Statistical methods for their inference under the multispecies coalescent have recently been developed. A particularly powerful approach uses data that consist of bi-allelic markers (e.g., single nucleotide polymorphism data) and allows for exact likelihood computations of phylogenetic networks while numerically integrating over all possible gene trees per marker. While the approach has good accuracy in terms of estimating the network and its parameters, likelihood computations remain a major computational bottleneck and limit the method’s applicability.ResultsIn this paper, we first demonstrate why likelihood computations of networks take orders of magnitude more time when compared to trees. We then propose an approach for inference of phylo-genetic networks based on pseudo-likelihood using bi-allelic markers. We demonstrate the scalability and accuracy of phylogenetic network inference via pseudo-likelihood computations on simulated data. Furthermore, we demonstrate aspects of robustness of the method to violations in the underlying assumptions of the employed statistical model. Finally, we demonstrate the application of the method to biological data. The proposed method allows for analyzing larger data sets in terms of the numbers of taxa and reticulation events. While pseudo-likelihood had been proposed before for data consisting of gene trees, the work here uses sequence data directly, offering several advantages as we discuss.AvailabilityThe methods have been implemented in PhyloNet (http://bioinfocs.rice.edu/phylonet)[email protected], [email protected]

scholarly journals Minimum Common String Partition Problem: Hardness and Approximations

10.37236/1947 ◽  
2005 ◽  
Vol 12 (1) ◽  
Author(s):  
Avraham Goldstein ◽  
Petr Kolman ◽  
Jie Zheng
Keyword(s):  
Genome Rearrangement ◽  
Linear Time ◽  
Fundamental Problem ◽  
Text Processing ◽  
Partition Problem ◽  
Sorting By Reversals ◽  
String Comparison ◽  
Minimum Number ◽  
Tight Connection ◽  
Minimum Common String Partition

String comparison is a fundamental problem in computer science, with applications in areas such as computational biology, text processing and compression. In this paper we address the minimum common string partition problem, a string comparison problem with tight connection to the problem of sorting by reversals with duplicates, a key problem in genome rearrangement. A partition of a string $A$ is a sequence ${\cal P} = (P_1,P_2,\dots,P_m)$ of strings, called the blocks, whose concatenation is equal to $A$. Given a partition ${\cal P}$ of a string $A$ and a partition ${\cal Q}$ of a string $B$, we say that the pair $\langle{{\cal P},{\cal Q}}\rangle$ is a common partition of $A$ and $B$ if ${\cal Q}$ is a permutation of ${\cal P}$. The minimum common string partition problem (MCSP) is to find a common partition of two strings $A$ and $B$ with the minimum number of blocks. The restricted version of MCSP where each letter occurs at most $k$ times in each input string, is denoted by $k$-MCSP. In this paper, we show that $2$-MCSP (and therefore MCSP) is NP-hard and, moreover, even APX-hard. We describe a $1.1037$-approximation for $2$-MCSP and a linear time $4$-approximation algorithm for $3$-MCSP. We are not aware of any better approximations.

scholarly journals A Contraction-based Ratio-cut Partitioning Algorithm

VLSI Design ◽  
2002 ◽  
Vol 15 (2) ◽  
pp. 485-489
Author(s):  
Youssef Saab
Keyword(s):  
Linear Time ◽  
Fundamental Problem ◽  
Cluster Formation ◽  
Vlsi Circuits ◽  
Iterative Improvement ◽  
Partitioning Algorithm ◽  
Partitioning Algorithms ◽  
Simple Ratio ◽  
Iterative Partitioning

Partitioning is a fundamental problem in the design of VLSI circuits. In recent years, ratio-cut partitioning has received attention due to its tendency to partition circuits into their natural clusters. Node contraction has also been shown to enhance the performance of iterative partitioning algorithms. This paper describes a new simple ratio-cut partitioning algorithm using node contraction. This new algorithm combines iterative improvement with progressive cluster formation. Under suitably mild assumptions, the new algorithm runs in linear time. It is also shown that the new algorithm compares favorably with previous approaches.

Efficient Web Mining for Traversal Path Patterns

Web Mining ◽  
2011 ◽  
pp. 322-338 ◽  
Author(s):  
Zhixiang Chen ◽  
Richard H. Fowler ◽  
Ada Wai-Chee Fu ◽  
Chunyue Wang
Keyword(s):  
Web Mining ◽  
Linear Time ◽  
Fundamental Problem ◽  
A Priori ◽  
Web Pages ◽  
Suffix Trees ◽  
Web Logs ◽  
Large Alphabet ◽  
Optimal Linear ◽  
Linear Time Algorithms

A maximal forward reference of a Web user is a longest consecutive sequence of Web pages visited by the user in a session without revisiting some previously visited page in the sequence. Efficient mining of frequent traversal path patterns, that is, large reference sequences of maximal forward references, from very large Web logs is a fundamental problem in Web mining. This chapter aims at designing algorithms for this problem with the best possible efficiency. First, two optimal linear time algorithms are designed for finding maximal forward references from Web logs. Second, two algorithms for mining frequent traversal path patterns are devised with the help of a fast construction of shallow generalized suffix trees over a very large alphabet. These two algorithms have respectively provable linear and sublinear time complexity, and their performances are analyzed in comparison with the a priori-like algorithms and the Ukkonen algorithm. It is shown that these two new algorithms are substantially more efficient than the a priori-like algorithms and the Ukkonen algorithm.

scholarly journals Implementing Large Genomic Single Nucleotide Polymorphism Data Sets in Phylogenetic Network Reconstructions: A Case Study of Particularly Rapid Radiations of Cichlid Fish

2020 ◽  
Vol 69 (5) ◽  
pp. 848-862 ◽  
Author(s):  
Melisa Olave ◽  
Axel Meyer
Keyword(s):  
Single Nucleotide Polymorphism ◽  
Gene Flow ◽  
Genetic Material ◽  
Cichlid Fish ◽  
Phylogenetic Network ◽  
Phylogenetic Networks ◽  
Nucleotide Polymorphism ◽  
Rapid Radiation ◽  
Data Set ◽  
Single Nucleotide

Abstract The Midas cichlids of the Amphilophus citrinellus spp. species complex from Nicaragua (13 species) are an extraordinary example of adaptive and rapid radiation ($<$24,000 years old). These cichlids are a very challenging group to infer its evolutionary history in phylogenetic analyses, due to the apparent prevalence of incomplete lineage sorting (ILS), as well as past and current gene flow. Assuming solely a vertical transfer of genetic material from an ancestral lineage to new lineages is not appropriate in many cases of genes transferred horizontally in nature. Recently developed methods to infer phylogenetic networks under such circumstances might be able to circumvent these problems. These models accommodate not just ILS, but also gene flow, under the multispecies network coalescent (MSNC) model, processes that are at work in young, hybridizing, and/or rapidly diversifying lineages. There are currently only a few programs available that implement MSNC for estimating phylogenetic networks. Here, we present a novel way to incorporate single nucleotide polymorphism (SNP) data into the currently available PhyloNetworks program. Based on simulations, we demonstrate that SNPs can provide enough power to recover the true phylogenetic network. We also show that it can accurately infer the true network more often than other similar SNP-based programs (PhyloNet and HyDe). Moreover, our approach results in a faster algorithm compared to the original pipeline in PhyloNetworks, without losing power. We also applied our new approach to infer the phylogenetic network of Midas cichlid radiation. We implemented the most comprehensive genomic data set to date (RADseq data set of 679 individuals and $>$37K SNPs from 19 ingroup lineages) and present estimated phylogenetic networks for this extremely young and fast-evolving radiation of cichlid fish. We demonstrate that the MSNC is more appropriate than the multispecies coalescent alone for the analysis of this rapid radiation. [Genomics; multispecies network coalescent; phylogenetic networks; phylogenomics; RADseq; SNPs.]

scholarly journals Phylogenetic network analysis of SARS-CoV-2 genomes

2020 ◽  
Vol 117 (17) ◽  
pp. 9241-9243 ◽  
Author(s):  
Peter Forster ◽  
Lucy Forster ◽  
Colin Renfrew ◽  
Michael Forster
Keyword(s):  
Amino Acid ◽  
Network Analysis ◽  
East Asia ◽  
Phylogenetic Network ◽  
Common Type ◽  
Phylogenetic Networks ◽  
Ancestral Genome ◽  
Founder Effects ◽  
Environmental Resistance ◽  
Ancestral Type

In a phylogenetic network analysis of 160 complete human severe acute respiratory syndrome coronavirus 2 (SARS-Cov-2) genomes, we find three central variants distinguished by amino acid changes, which we have named A, B, and C, with A being the ancestral type according to the bat outgroup coronavirus. The A and C types are found in significant proportions outside East Asia, that is, in Europeans and Americans. In contrast, the B type is the most common type in East Asia, and its ancestral genome appears not to have spread outside East Asia without first mutating into derived B types, pointing to founder effects or immunological or environmental resistance against this type outside Asia. The network faithfully traces routes of infections for documented coronavirus disease 2019 (COVID-19) cases, indicating that phylogenetic networks can likewise be successfully used to help trace undocumented COVID-19 infection sources, which can then be quarantined to prevent recurrent spread of the disease worldwide.

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