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Joanna L. Davies,
Frantisek Simancík,
Rune Lyngsø,
Thomas Mailund and
Jotun Hein. On Recombination-Induced Multiple and Simultaneous Coalescent Events. In GEN, Vol. 177:2151-2160, 2007.
Keywords: coalescent, phylogenetic network, phylogeny, recombination, statistical model.
Note: http://dx.doi.org/10.1534/genetics.107.071126.
Toggle abstract
"Coalescent theory deals with the dynamics of how sampled genetic material has spread through a population from a single ancestor over many generations and is ubiquitous in contemporary molecular population genetics. Inherent in most applications is a continuous-time approximation that is derived under the assumption that sample size is small relative to the actual population size. In effect, this precludes multiple and simultaneous coalescent events that take place in the history of large samples. If sequences do not recombine, the number of sequences ancestral to a large sample is reduced sufficiently after relatively few generations such that use of the continuous-time approximation is justified. However, in tracing the history of large chromosomal segments, a large recombination rate per generation will consistently maintain a large number of ancestors. This can create a major disparity between discrete-time and continuous-time models and we analyze its importance, illustrated with model parameters typical of the human genome. The presence of gene conversion exacerbates the disparity and could seriously undermine applications of coalescent theory to complete genomes. However, we show that multiple and simultaneous coalescent events influence global quantities, such as total number of ancestors, but have negligible effect on local quantities, such as linkage disequilibrium. Reassuringly, most applications of the coalescent model with recombination (including association mapping) focus on local quantities. Copyright © 2007 by the Genetics Society of America."
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Sagi Snir and
Tamir Tuller. The NET-HMM approach: Phylogenetic Network Inference by Combining Maximum Likelihood and Hidden Markov Models. In JBCB, Vol. 7(4):625-644, 2009.
Keywords: explicit network, from sequences, HMM, lateral gene transfer, likelihood, phylogenetic network, phylogeny, statistical model.
Note: http://research.haifa.ac.il/~ssagi/published%20papers/Snir-NET-HMM-JBCB-2009.pdf.
Toggle abstract
"Horizontal gene transfer (HGT) is the event of transferring genetic material from one lineage in the evolutionary tree to a different lineage. HGT plays a major role in bacterial genome diversification and is a significant mechanism by which bacteria develop resistance to antibiotics. Although the prevailing assumption is of complete HGT, cases of partial HGT (which are also named chimeric HGT) where only part of a gene is horizontally transferred, have also been reported, albeit less frequently. In this work we suggest a new probabilistic model, the NET-HMM, for analyzing and modeling phylogenetic networks. This new model captures the biologically realistic assumption that neighboring sites of DNA or amino acid sequences are not independent, which increases the accuracy of the inference. The model describes the phylogenetic network as a Hidden Markov Model (HMM), where each hidden state is related to one of the network's trees. One of the advantages of the NET-HMM is its ability to infer partial HGT as well as complete HGT. We describe the properties of the NET-HMM, devise efficient algorithms for solving a set of problems related to it, and implement them in software. We also provide a novel complementary significance test for evaluating the fitness of a model (NET-HMM) to a given dataset. Using NET-HMM, we are able to answer interesting biological questions, such as inferring the length of partial HGT's and the affected nucleotides in the genomic sequences, as well as inferring the exact location of HGT events along the tree branches. These advantages are demonstrated through the analysis of synthetical inputs and three different biological inputs. © 2009 Imperial College Press."
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Joel Velasco and
Elliott Sober. Testing for Treeness: Lateral Gene Transfer, Phylogenetic Inference, and Model Selection. In Biology and Philosophy, Vol. 25(4):675-687, 2010.
Keywords: explicit network, model selection, phylogenetic network, phylogeny, reconstruction, statistical model.
Note: http://joelvelasco.net/Papers/velascosober-testingfortreeness.pdf.
Toggle abstract
"A phylogeny that allows for lateral gene transfer (LGT) can be thought of as a strictly branching tree (all of whose branches are vertical) to which lateral branches have been added. Given that the goal of phylogenetics is to depict evolutionary history, we should look for the best supported phylogenetic network and not restrict ourselves to considering trees. However, the obvious extensions of popular tree-based methods such as maximum parsimony and maximum likelihood face a serious problem-if we judge networks by fit to data alone, networks that have lateral branches will always fit the data at least as well as any network that restricts itself to vertical branches. This is analogous to the well-studied problem of overfitting data in the curve-fitting problem. Analogous problems often have analogous solutions and we propose to treat network inference as a case of model selection and use the Akaike Information Criterion (AIC). Strictly tree-like networks are more parsimonious than those that postulate lateral as well as vertical branches. This leads to the conclusion that we should not always infer LGT events whenever it would improve our fit-to-data, but should do so only when the improved fit is larger than the penalty for adding extra lateral branches. © 2010 Springer Science+Business Media B.V."
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Laura S. Kubatko. Identifying Hybridization Events in the Presence of Coalescence via Model Selection. In Systematic Biology, Vol. 58(5):478-488, 2009.
Keywords: AIC, BIC, branch length, coalescent, explicit network, from rooted trees, from species tree, hybridization, lineage sorting, model selection, phylogenetic network, phylogeny, statistical model.
Note: http://dx.doi.org/10.1093/sysbio/syp055.
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Tao Sang and
Yang Zhong. Testing Hybridization Hypotheses Based on Incongruent Gene Trees. In Systematic Biology, Vol. 49(3):422-434, 2000.
Keywords: bootstrap, from rooted trees, hybridization, lateral gene transfer, lineage sorting, phylogenetic network, phylogeny, reconstruction, statistical model.
Note: http://dx.doi.org/10.1080/10635159950127321.
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Chen Meng and
Laura S. Kubatko. Detecting hybrid speciation in the presence of incomplete lineage sorting using gene tree incongruence: A model. In Theoretical Population Biology, Vol. 75(1):35-45, 2009.
Keywords: bayesian, coalescent, from network, from rooted trees, hybridization, likelihood, lineage sorting, phylogenetic network, phylogeny, statistical model.
Note: http://dx.doi.org/10.1016/j.tpb.2008.10.004.
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"The application of phylogenetic inference methods, to data for a set of independent genes sampled randomly throughout the genome, often results in substantial incongruence in the single-gene phylogenetic estimates. Among the processes known to produce discord between single-gene phylogenies, two of the best studied in a phylogenetic context are hybridization and incomplete lineage sorting. Much recent attention has focused on the development of methods for estimating species phylogenies in the presence of incomplete lineage sorting, but phylogenetic models that allow for hybridization have been more limited. Here we propose a model that allows incongruence in single-gene phylogenies to be due to both hybridization and incomplete lineage sorting, with the goal of determining the contribution of hybridization to observed gene tree incongruence in the presence of incomplete lineage sorting. Using our model, we propose methods for estimating the extent of the role of hybridization in both a likelihood and a Bayesian framework. The performance of our methods is examined using both simulated and empirical data. © 2008 Elsevier Inc. All rights reserved."
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Nicolas Galtier. A model of horizontal gene transfer and the bacterial phylogeny problem. In Systematic Biology, Vol. 56(4):633-642, 2007.
Keywords: explicit network, generation, lateral gene transfer, phylogenetic network, phylogeny, Program HGT_simul, software, statistical model.
Note: http://dx.doi.org/10.1080/10635150701546231.
Toggle abstract
"How much horizontal gene transfer (HGT) between species influences bacterial phylogenomics is a controversial issue. This debate, however, lacks any quantitative assessment of the impact of HGT on phylogenies and of the ability of tree-building methods to cope with such events. I introduce a Markov model of genome evolution with HGT, accounting for the constraints on time-an HGT event can only occur between concomitantly living species. This model is used to simulate multigene sequence data sets with or without HGT. The consequences of HGT on phylogenomic inference are analyzed and compared to other well-known phylogenetic artefacts. It is found that supertree methods are quite robust to HGT, keeping high levels of performance even when gene trees are largely incongruent with each other. Gene tree incongruence per se is not indicative of HGT. HGT, however, removes the (otherwise observed) positive relationship between sequence length and gene tree congruence to the estimated species tree. Surprisingly, when applied to a bacterial and a eukaryotic multigene data set, this criterion rejects the HGT hypothesis for the former, but not the latter data set. Copyright © Society of Systematic Biologists."
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Mark T. Holder,
Jennifer A. Anderson and
Alisha K. Holloway. Difficulties in Detecting Hybridization. In Systematic Biology, Vol. 50(6):978-982, 2001.
Keywords: bootstrap, from rooted trees, hybridization, lateral gene transfer, lineage sorting, phylogenetic network, phylogeny, reconstruction, statistical model.
Note: http://dx.doi.org/10.1080/106351501753462911.
Toggle abstract
[No abstract available]
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Yun Yu,
Cuong Than,
James H. Degnan and
Luay Nakhleh. Coalescent Histories on Phylogenetic Networks and Detection of Hybridization Despite Incomplete Lineage Sorting. In Systematic Biology, Vol. 60(2):138-149, 2011.
Keywords: coalescent, hybridization, lineage sorting, reconstruction, statistical model.
Note: http://www.cs.rice.edu/~nakhleh/Papers/YuEtAl-SB11.pdf.
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"Analyses of the increasingly available genomic data continue to reveal the extent of hybridization and its role in the evolutionary diversification of various groups of species. We show, through extensive coalescent-based simulations of multilocus data sets on phylogenetic networks, how divergence times before and after hybridization events can result in incomplete lineage sorting with gene tree incongruence signatures identical to those exhibited by hybridization. Evolutionary analysis of such data under the assumption of a species tree model can miss all hybridization events, whereas analysis under the assumption of a species network model would grossly overestimate hybridization events. These issues necessitate a paradigm shift in evolutionary analysis under these scenarios, from a model that assumes a priori a single source of gene tree incongruence to one that integrates multiple sources in a unifying framework. We propose a framework of coalescence within the branches of a phylogenetic network and show how this framework can be used to detect hybridization despite incomplete lineage sorting. We apply the model to simulated data and show that the signature of hybridization can be revealed as long as the interval between the divergence times of the species involved in hybridization is not too small. We reanalyze a data set of 106 loci from 7 in-group Saccharomyces species for which a species tree with no hybridization has been reported in the literature. Our analysis supports the hypothesis that hybridization occurred during the evolution of this group, explaining a large amount of the incongruence in the data. Our findings show that an integrative approach to gene tree incongruence and its reconciliation is needed. Our framework will help in systematically analyzing genomic data for the occurrence of hybridization and elucidating its evolutionary role. [Coalescent history; incomplete lineage sorting; hybridization; phylogenetic network.]. © 2011 The Author(s)."
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Jeremy G. Sumner,
Barbara R. Holland and
Peter D. Jarvis. The algebra of the general Markov model on phylogenetic trees and networks. In BMB, Vol. 74(4):858-880, 2012.
Keywords: abstract network, phylogenetic network, phylogeny, split, split network, statistical model.
Note: http://arxiv.org/abs/1012.5165.
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"It is known that the Kimura 3ST model of sequence evolution on phylogenetic trees can be extended quite naturally to arbitrary split systems. However, this extension relies heavily on mathematical peculiarities of the associated Hadamard transformation, and providing an analogous augmentation of the general Markov model has thus far been elusive. In this paper, we rectify this shortcoming by showing how to extend the general Markov model on trees to include incompatible edges; and even further to more general network models. This is achieved by exploring the algebra of the generators of the continuous-time Markov chain together with the "splitting" operator that generates the branching process on phylogenetic trees. For simplicity, we proceed by discussing the two state case and then show that our results are easily extended to more states with little complication. Intriguingly, upon restriction of the two state general Markov model to the parameter space of the binary symmetric model, our extension is indistinguishable from the Hadamard approach only on trees; as soon as any incompatible splits are introduced the two approaches give rise to differing probability distributions with disparate structure. Through exploration of a simple example, we give an argument that our extension to more general networks has desirable properties that the previous approaches do not share. In particular, our construction allows for convergent evolution of previously divergent lineages; a property that is of significant interest for biological applications. © 2011 Society for Mathematical Biology."
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Gergely J. Szöllösi and
Vincent Daubin. Modeling Gene Family Evolution and Reconciling Phylogenetic Discord. In Evolutionary Genomics, Statistical and Computational Methods, Volume 2, Methods in Molecular Biology, Vol. 856:29-51, Chapter 2, springer, 2011.
Keywords: duplication, from multilabeled tree, lateral gene transfer, likelihood, phylogeny, reconstruction, statistical model.
Note: ArXiv version entitled The pattern and process of gene family evolution.
Toggle abstract
"Large-scale databases are available that contain homologous gene families constructed from hundreds of complete genome sequences from across the three domains of life. Here, we discuss the approaches of increasing complexity aimed at extracting information on the pattern and process of gene family evolution from such datasets. In particular, we consider the models that invoke processes of gene birth (duplication and transfer) and death (loss) to explain the evolution of gene families. First, we review birth-and-death models of family size evolution and their implications in light of the universal features of family size distribution observed across different species and the three domains of life. Subsequently, we proceed to recent developments on models capable of more completely considering information in the sequences of homologous gene families through the probabilistic reconciliation of the phylogenetic histories of individual genes with the phylogenetic history of the genomes in which they have resided. To illustrate the methods and results presented, we use data from the HOGENOM database, demonstrating that the distribution of homologous gene family sizes in the genomes of the eukaryota, archaea, and bacteria exhibits remarkably similar shapes. We show that these distributions are best described by models of gene family size evolution, where for individual genes the death (loss) rate is larger than the birth (duplication and transfer) rate but new families are continually supplied to the genome by a process of origination. Finally, we use probabilistic reconciliation methods to take into consideration additional information from gene phylogenies, and find that, for prokaryotes, the majority of birth events are the result of transfer. © 2012 Springer Science+Business Media, LLC."
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Simon Joly,
Patricia A. McLenachan and
Peter J. Lockhart. A Statistical Approach for Distinguishing Hybridization and Incomplete Lineage Sorting. In The American Naturalist, Vol. 174(2):E54-E70, 2009.
Keywords: hybridization, lineage sorting, phylogenetic network, phylogeny, reconstruction, statistical model.
Note: http://www.plantevolution.org/pdf/Joly&al_2009_AmNat.pdf.
Toggle abstract
"The extent and evolutionary significance of hybridization is difficult to evaluate because of the difficulty in distinguishing hybridization from incomplete lineage sorting. Here we present a novel parametric approach for statistically distinguishing hybridization from incomplete lineage sorting based on minimum genetic distances of a nonrecombining locus. It is based on the idea that the expected minimum genetic distance between sequences from two species is smaller for some hybridization events than for incomplete lineage sorting scenarios. When applied to empirical data sets, distributions can be generated for the minimum interspecies distances expected under incomplete lineage sorting using coalescent simulations. If the observed distance between sequences from two species is smaller than its predicted distribution, incomplete lineage sorting can be rejected and hybridization inferred. We demonstrate the power of the method using simulations and illustrate its application on New Zealand alpine buttercups (Ranunculus). The method is robust and complements existing approaches. Thus it should allow biologists to assess with greater accuracy the importance of hybridization in evolution. © 2009 by The University of Chicago."
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Simon Joly. JML: Testing hybridization from species trees. In Molecular Ecology Ressources, Vol. 12(1):179-184, 2012.
Keywords: from species tree, hybridization, lineage sorting, phylogenetic network, phylogeny, Program JML, statistical model.
Note: http://www.plantevolution.org/pdf/JMLpaper_accepted.pdf.
Toggle abstract
"I introduce the software jml that tests for the presence of hybridization in multispecies sequence data sets by posterior predictive checking following Joly, McLenachan and Lockhart (2009, American Naturalist e54). Although their method could potentially be applied on any data set, the lack of appropriate software made its application difficult. The software jml thus fills a need for an easy application of the method but also includes improvements such as the possibility to incorporate uncertainty in the species tree topology. The jml software uses a posterior distribution of species trees, population sizes and branch lengths to simulate replicate sequence data sets using the coalescent with no migration. A test quantity, defined as the minimum pairwise sequence distance between sequences of two species, is then evaluated on the simulated data sets and compared to the one estimated from the original data. Because the test quantity is a good predictor of hybridization events, departure from the bifurcating species tree model could be interpreted as evidence of hybridization. Software performance in terms of computing time is evaluated for several parameters. I also show an application example of the software for detecting hybridization among native diploid North American roses. © 2011 Blackwell Publishing Ltd."
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Rosalba Radice. A Bayesian Approach to Modelling Reticulation Events with Application to the Ribosomal Protein Gene rps11 of Flowering Plants. In Australian & New Zealand Journal of Statistics, Vol. 54(4):401-426, 2012.
Keywords: bayesian, phylogenetic network, phylogeny, reconstruction, statistical model.
Toggle abstract
"Traditional phylogenetic inference assumes that the history of a set of taxa can be explained by a tree. This assumption is often violated as some biological entities can exchange genetic material giving rise to non-treelike events often called reticulations. Failure to consider these events might result in incorrectly inferred phylogenies. Phylogenetic networks provide a flexible tool which allows researchers to model the evolutionary history of a set of organisms in the presence of reticulation events. In recent years, a number of methods addressing phylogenetic network parameter estimation have been introduced. Some of them are based on the idea that a phylogenetic network can be defined as a directed acyclic graph. Based on this definition, we propose a Bayesian approach to the estimation of phylogenetic network parameters which allows for different phylogenies to be inferred at different parts of a multiple DNA alignment. The algorithm is tested on simulated data and applied to the ribosomal protein gene rps11 data from five flowering plants, where reticulation events are suspected to be present. The proposed approach can be applied to a wide variety of problems which aim at exploring the possibility of reticulation events in the history of a set of taxa. © 2012 Australian Statistical Publishing Association Inc. Published by Wiley Publishing Asia Pty Ltd."
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Yun Yu,
James H. Degnan and
Luay Nakhleh. The probability of a gene tree topology within a phylogenetic network with applications to hybridization detection. In PLoS Genetics, Vol. 8(4):e1002660, 2012.
Keywords: AIC, BIC, explicit network, hybridization, phylogenetic network, phylogeny, statistical model.
Note: http://dx.doi.org/10.1371/journal.pgen.1002660.
Toggle abstract
"Gene tree topologies have proven a powerful data source for various tasks, including species tree inference and species delimitation. Consequently, methods for computing probabilities of gene trees within species trees have been developed and widely used in probabilistic inference frameworks. All these methods assume an underlying multispecies coalescent model. However, when reticulate evolutionary events such as hybridization occur, these methods are inadequate, as they do not account for such events. Methods that account for both hybridization and deep coalescence in computing the probability of a gene tree topology currently exist for very limited cases. However, no such methods exist for general cases, owing primarily to the fact that it is currently unknown how to compute the probability of a gene tree topology within the branches of a phylogenetic network. Here we present a novel method for computing the probability of gene tree topologies on phylogenetic networks and demonstrate its application to the inference of hybridization in the presence of incomplete lineage sorting. We reanalyze a Saccharomyces species data set for which multiple analyses had converged on a species tree candidate. Using our method, though, we show that an evolutionary hypothesis involving hybridization in this group has better support than one of strict divergence. A similar reanalysis on a group of three Drosophila species shows that the data is consistent with hybridization. Further, using extensive simulation studies, we demonstrate the power of gene tree topologies at obtaining accurate estimates of branch lengths and hybridization probabilities of a given phylogenetic network. Finally, we discuss identifiability issues with detecting hybridization, particularly in cases that involve extinction or incomplete sampling of taxa. © 2012 Yu et al."
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Paul Bastide,
Claudia Solís-Lemus,
Ricardo Kriebel,
Kenneth William Sparks and
Cécile Ané. Phylogenetic Comparative Methods on Phylogenetic Networks with Reticulations. In SB, Vol. 67(5):800-820, 2018.
Keywords: ancestral trait reconstruction, from network, likelihood, Program PhyloNetworks SNaQ, software, statistical model, statistical test.
Note: https://doi.org/10.1101/194050.
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Chi Zhang,
Huw A. Ogilvie,
Alexei J. Drummond and
Tanja Stadler. Bayesian Inference of Species Networks from Multilocus Sequence Data. In MBE, Vol. 35(2):504-517, 2018.
Keywords: bayesian, explicit network, from sequences, phylogenetic network, phylogeny, reconstruction, statistical model.
Note: https://dx.doi.org/10.1093/molbev/msx307.
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Rune Lyngsø,
Yun S. Song and
Jotun Hein. Accurate Computation of Likelihoods in the Coalescent with Recombination via Parsimony. In RECOMB08, Vol. 4955:463-477 of LNCS, springer, 2008.
Keywords: coalescent, likelihood, phylogenetic network, phylogeny, recombination, statistical model.
Note: http://dx.doi.org/10.1007/978-3-540-78839-3_41.
Toggle abstract
"Understanding the variation of recombination rates across a given genome is crucial for disease gene mapping and for detecting signatures of selection, to name just a couple of applications. A widely-used method of estimating recombination rates is the maximum likelihood approach, and the problem of accurately computing likelihoods in the coalescent with recombination has received much attention in the past. A variety of sampling and approximation methods have been proposed, but no single method seems to perform consistently better than the rest, and there still is great value in developing better statistical methods for accurately computing likelihoods. So far, with the exception of some two-locus models, it has remained unknown how the true likelihood exactly behaves as a function of model parameters, or how close estimated likelihoods are to the true likelihood. In this paper, we develop a deterministic, parsimony-based method of accurately computing the likelihood for multi-locus input data of moderate size. We first find the set of all ancestral configurations (ACs) that occur in evolutionary histories with at most k crossover recombinations. Then, we compute the likelihood by summing over all evolutionary histories that can be constructed only using the ACs in that set. We allow for an arbitrary number of crossing over, coalescent and mutation events in a history, as long as the transitions stay within that restricted set of ACs. For given parameter values, by gradually increasing the bound k until the likelihood stabilizes, we can obtain an accurate estimate of the likelihood. At least for moderate crossover rates, the algorithm-based method described here opens up a new window of opportunities for testing and fine-tuning statistical methods for computing likelihoods. © 2008 Springer-Verlag Berlin Heidelberg."
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Sagi Snir and
Tamir Tuller. Novel Phylogenetic Network Inference by Combining Maximum Likelihood and Hidden Markov Models. In WABI08, Vol. 5251:354-368 of LNCS, springer, 2008.
Keywords: explicit network, from sequences, HMM, lateral gene transfer, likelihood, phylogenetic network, phylogeny, statistical model.
Note: http://dx.doi.org/10.1007/978-3-540-87361-7_30.
Toggle abstract
"Horizontal Gene Transfer (HGT) is the event of transferring genetic material from one lineage in the evolutionary tree to a different lineage. HGT plays a major role in bacterial genome diversification and is a significant mechanism by which bacteria develop resistance to antibiotics. Although the prevailing assumption is of complete HGT, cases of partial HGT (which are also named chimeric HGT) where only part of a gene is horizontally transferred, have also been reported, albeit less frequently. In this work we suggest a new probabilistic model for analyzing and modeling phylogenetic networks, the NET-HMM. This new model captures the biologically realistic assumption that neighboring sites of DNA or amino acid sequences are not independent, which increases the accuracy of the inference. The model describes the phylogenetic network as a Hidden Markov Model (HMM), where each hidden state is related to one of the network's trees. One of the advantages of the NET-HMM is its ability to infer partial HGT as well as complete HGT. We describe the properties of the NET-HMM, devise efficient algorithms for solving a set of problems related to it, and implement them in software. We also provide a novel complementary significance test for evaluating the fitness of a model (NET-HMM) to a given data set. Using NET-HMM we are able to answer interesting biological questions, such as inferring the length of partial HGT's and the affected nucleotides in the genomic sequences, as well as inferring the exact location of HGT events along the tree branches. These advantages are demonstrated through the analysis of synthetical inputs and two different biological inputs. © 2008 Springer-Verlag Berlin Heidelberg."
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Hyun Jung Park and
Luay Nakhleh. Inference of reticulate evolutionary histories by maximum likelihood:
The performance of information criteria. In RECOMB-CG'12, Vol. 13(suppl 19):S12 of BMCB, 2012.
Keywords: AIC, BIC, explicit network, heuristic, likelihood, phylogenetic network, phylogeny, reconstruction, statistical model.
Note: http://www.biomedcentral.com/1471-2105/13/S19/S12.
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Cayla McBee. Generalizing Fourier Calculus on Evolutionary Trees to Splits Networks. In ISPAN'12, Pages 149-155, 2012.
Keywords: abstract network, from sequences, phylogenetic network, phylogeny, split network, statistical model.
Toggle abstract
"Biologists have been interested in Phylogenetics, the study of evolutionary relatedness among various groups of organisms, for more than 140 years. In spite of this, it has only been in the last 40 years that advances in technology and the availability of DNA sequences have led to statistical, computational and algorithmic work on determining evolutionary relatedness between organisms. One method of determining historical relationships between organisms is to assume a group based evolutionary model and use a discrete Fourier transform. The 1993 paper 'Fourier Calculus on Evolutionary Trees' by L.A. Szekely, M.A. Steel and P.L. Erdos outlines this process. The transform presented in Szekely et al provides an invertible relationship between phylogenetic trees and expected frequencies of nucleotide patterns in nucleotide sequences. This implies that given a set of nucleotide sequences from various organisms it is possible to construct a phylogenetic tree that represents the historical relationships of those organisms. Some scenarios are poorly described by phylogenetic trees and there are biological and statistical reasons for using networks to model phylogenetic relationships. Given this motivation I have generalized Szekely et al's result to apply to a specific type of phylogenetic network known as a splits network. © 2012 IEEE."
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Jiafan Zhu,
Yun Yu and
Luay Nakhleh. In the Light of Deep Coalescence: Revisiting Trees Within Networks. In RECOMB-CG16, Vol. 17(suppl. 14):415.271-282 of BMCB, 2016.
Keywords: branch length, evaluation, explicit network, incomplete lineage sorting, phylogenetic network, phylogeny, statistical model, tree-based network, weakly displaying.
Note: http://arxiv.org/abs/1606.07350.
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- forked on GitHub.