A Polynomial-Time Algorithm for Minimizing the Deep Coalescence Cost for Level-1 Species Networks

Lemay, Matthew A.; Libeskind-Hadas, Ran; Wu, Yi-Chieh

doi:10.1109/tcbb.2021.3105922

Cited by 6 publications

(5 citation statements)

References 38 publications

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“…Work towards characterizing and understanding the identifiability of level-1 networks (Solís-Lemus and Ané 2016; Solis-Lemus et al 2020; Gross et al 2021; Allman et al 2022) has led to many reticulate inference methods assuming an underlying level-1 network (Huber et al 2010; Solís-Lemus and Ané 2016; Allman et al 2019; LeMay et al 2021). These methods have surged in popularity recently, largely due to their computational tractability and—for SNaQ (Solís-Lemus and Ané 2016) and NANUQ (Allman et al 2019)— their ability to account for discordance both from gene flow and incomplete lineage sorting.…”

Section: Discussionmentioning

confidence: 99%

Exploring the distribution of phylogenetic networks generated under a birth-death-hybridization process

Justison

Heath

2022

Preprint

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Gene-flow processes such as hybridization and introgression play important roles in shaping diversity across the tree of life. Recent studies extending birth-death models have made it possible to investigate patterns of reticulation in a macroevolutionary context. These models allow for different macroevolutionary patterns of gene flow events that can either add, maintain, or remove lineages, thus creating complex diversification scenarios. Further, many reticulate phylogenetic inference methods assume specific reticulation structures or phylogenies belonging to certain network classes. However, the distributions of phylogenetic networks under reticulate birth-death processes are poorly characterized and it is unknown whether they violate common methodological assumptions. We use a combination of analytical and simulation techniques to explore phylogenetic network space under a birth-death-hybridization process. Specifically, we measured the number of lineages through time and role of hybridization in diversification along with the proportion of phylogenetic networks that belong to commonly used network classes (e.g., tree-child, tree-based, or level-1 networks). We find that the growth of phylogenetic networks and class membership is largely affected by the assumptions about macroevolutionary patterns of gene flow. In accordance with previous studies, a lower proportion of networks belonged to these classes based on type and density of reticulate events. However, under a birth-death-hybridization process, these factors form an antagonistic relationship; the type of reticulation events that cause high membership proportions also lead to the highest reticulation density, consequently lowering the overall proportion of phylogenies in some classes. Further, we observed that genetic distance-dependent gene flow and incomplete sampling increase the proportion of class membership, primarily due to having fewer reticulate events. Our results can inform studies if their biological expectations of gene flow are associated with evolutionary histories that satisfy the assumptions of current methodology and aid in finding phylogenetic classes that are relevant for methods development.

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Section: Discussionmentioning

confidence: 99%

Exploring the distribution of phylogenetic networks generated under a birth-death-hybridization process

Justison

Heath

2022

Preprint

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“…This quantity can be calculated from the known embedding of the gene tree within the network. It is of interest because inference methods may attempt to use this number of extra lineages as a criterion to infer the embedding of gene trees within a species tree or species network (Yu et al, 2013; LeMay et al, 2022; Wawerka et al, 2022).…”

Section: Gene Tree Simulatormentioning

confidence: 99%

PhyloCoalSimulations: A simulator for network multispecies coalescent models, including a new extension for the inheritance of gene flow

Fogg

Allman

Ané

2023

Preprint

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We consider the evolution of phylogenetic gene trees along phylogenetic species networks, according to the network multispecies coalescent process, and introduce a new network coalescent model with correlated inheritance of gene flow. This model generalizes two traditional versions of the network coalescent: with independent or common inheritance. At each reticulation, multiple lineages of a given locus are inherited from parental populations chosen at random, either independently across lineages, or with positive correlation according to a Dirichlet process. This process may account for locus-specific probabilities of inheritance, for example. We implemented the simulation of gene trees under these network coalescent models in the Julia package PhyloCoalSimulations, which depends on PhyloNetworks and its powerful network manipulation tools. Input species phylogenies can be read in extended Newick format, either in numbers of generations or in coalescent units. Simulated gene trees can be written in Newick format, and in a way that preserves information about their embedding within the species network. This embedding can be used for downstream purposes, such as to simulate species-specific processes like rate variation across species, or for other scenarios as illustrated in this note. This package should be useful for simulation studies and simulation-based inference methods. The software is available open source with documentation and a tutorial at https://github.com/cecileane/PhyloCoalSimulations.jl.

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“…Let G and S be any given binary tree and binary network, respectively, and let s : G → S be an embedding. The Incomplete Linear Sorting (ILS) event is an edge e ∈ G entering a pipe t ∈ S provided that at least two edges enter t (see [9]). The locus of an ILS event is the pipe t. The ILS-cost over a pipe t ∈ S entered by k t ≥ 1 edges from G is defined as c t = c•(k t -1), where c is the cost of a single ILS plus the costs of all duplications and all losses in t. The ILS-cost over S is defined as ∑ t∈S↓ c t plus the costs of all duplications and all losses in S, where t runs over pipes t ∈ S entered by at least one edge from G; the latter is denoted as t ∈ S↓.…”

Section: Ils-minimum Embedding Of a Tree Into A Network And Theoremmentioning

confidence: 99%

“…In [9], a construction algorithm was suggested for a minimum (with respect to ILS events only) embedding of a tree into a network of level 1. Additionally, in [9] (section "Conclusion"), a method was outlined to generalize that algorithm to the case of a network of any level k. Our algorithm uses the idea from [9] combined with ideas of the algorithm of Theorem 1.…”

Section: Ils-minimum Embedding Of a Tree Into A Network And Theoremmentioning

confidence: 99%

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Constructing an Evolutionary Tree and Path–Cycle Graph Evolution along It

Gorbunov

Lyubetsky

2023

Mathematics

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The paper solves the problem of constructing an evolutionary tree and the evolution of structures along it. This problem has long been posed and extensively researched; it is formulated and discussed below. As a result, we construct an exact cubic-time algorithm which outputs a tree with the minimum cost of embedding into it and of embedding it into a given network (Theorem 1). We construct an algorithm that outputs a minimum embedding of a tree into a network, taking into account incomplete linear sorting; the algorithm depends linearly on the number of nodes in the network and is exact if the sorting cost is not less than the sum of the duplication cost and the loss cost (Theorem 3). We construct an exact approximately quadratic-time algorithm which, for arbitrary costs of SCJ operations, solves the problem of reconstruction of given structures on any two-star tree (Theorem 4). We construct an exact algorithm which reduced the problem of DCJ reconstruction of given structures on any star to a logarithmic-length sequence of SAT problems, each of them being of approximately quadratic size (Theorem 5). The theorems have rigorous and complete proofs of correctness and complexity of the algorithms, and are accompanied by numerical examples and numerous explanatory illustrations, including flowcharts.

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A Polynomial-Time Algorithm for Minimizing the Deep Coalescence Cost for Level-1 Species Networks

Cited by 6 publications

References 38 publications

Exploring the distribution of phylogenetic networks generated under a birth-death-hybridization process

Exploring the distribution of phylogenetic networks generated under a birth-death-hybridization process

PhyloCoalSimulations: A simulator for network multispecies coalescent models, including a new extension for the inheritance of gene flow

Constructing an Evolutionary Tree and Path–Cycle Graph Evolution along It

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