David Bryant
University of Otago, Mathematics and Statistics, Faculty Member
Trees with labelled leaves are useful models for representing evolutionary relationships, particularly in biology (where they are called phylogenetic trees). The wider availability of genetic sequence data, and the use of tree-building... more
Trees with labelled leaves are useful models for representing evolutionary relationships, particularly in biology (where they are called phylogenetic trees). The wider availability of genetic sequence data, and the use of tree-building programs such as Paup, Phylip, and MacClade, has led to a substantial increase in the size and number of phylogenetic trees.
Abstract Consensus methods provide a useful strategy for summarizing information from a collection of gene trees. An important application of consensus methods is to combine gene trees to estimate a species tree. To investigate the... more
Abstract Consensus methods provide a useful strategy for summarizing information from a collection of gene trees. An important application of consensus methods is to combine gene trees to estimate a species tree. To investigate the theoretical properties of consensus trees that would be obtained from large numbers of loci evolving according to a basic evolutionary model, we construct consensus trees from rooted gene trees that occur in proportion to gene-tree probabilities derived from coalescent theory.
Abstract In phylogenetic analyses with combined multigene or multiprotein data sets, accounting for differing evolutionary dynamics at different loci is essential for accurate tree prediction. Existing maximum likelihood (ML) and Bayesian... more
Abstract In phylogenetic analyses with combined multigene or multiprotein data sets, accounting for differing evolutionary dynamics at different loci is essential for accurate tree prediction. Existing maximum likelihood (ML) and Bayesian approaches are computationally intensive. We present an alternative approach that is orders of magnitude faster. The method, Distance Rates (DistR), estimates rates based upon distances derived from gene/protein sequence data.
Abstract The evolutionary history of a set of taxa is usually represented by a phylogenetic tree, and this model has greatly facilitated the discussion and testing of hypotheses. However, it is well known that more complex evolutionary... more
Abstract The evolutionary history of a set of taxa is usually represented by a phylogenetic tree, and this model has greatly facilitated the discussion and testing of hypotheses. However, it is well known that more complex evolutionary scenarios are poorly described by such models.
Abstract Recombination is a powerful evolutionary force that merges historically distinct genotypes. But the extent of recombination within many organisms is unknown, and even determining its presence within a set of homologous sequences... more
Abstract Recombination is a powerful evolutionary force that merges historically distinct genotypes. But the extent of recombination within many organisms is unknown, and even determining its presence within a set of homologous sequences is a difficult question. Here we develop a new statistic, �� w, that can be used to test for recombination.
Abstract The Robinson-Foulds (RF) distance is by far the most widely used measure of dissimilarity between trees. Although the distribution of these distances has been investigated for 20 years, an algorithm that is explicitly polynomial... more
Abstract The Robinson-Foulds (RF) distance is by far the most widely used measure of dissimilarity between trees. Although the distribution of these distances has been investigated for 20 years, an algorithm that is explicitly polynomial time has yet to be described for computing the distribution for trees around a given tree. In this paper, we derive a polynomial-time algorithm for this distribution.
Abstract The tight span, or injective envelope, is an elegant and useful construction that takes a metric space and returns the smallest hyperconvex space into which it can be embedded. The concept has stimulated a large body of theory... more
Abstract The tight span, or injective envelope, is an elegant and useful construction that takes a metric space and returns the smallest hyperconvex space into which it can be embedded. The concept has stimulated a large body of theory and has applications to metric classification and data visualisation.
Abstract Eukaryotes arose from prokaryotes, hence the root in the tree of life resides among the prokaryotic domains. The position of the root is still debated, although pinpointing it would aid our understanding of the early evolution of... more
Abstract Eukaryotes arose from prokaryotes, hence the root in the tree of life resides among the prokaryotic domains. The position of the root is still debated, although pinpointing it would aid our understanding of the early evolution of life. Because prokaryote evolution was long viewed as a tree-like process of lineage bifurcations, efforts to identify the most ancient microbial lineage split have traditionally focused on positioning a root on a phylogenetic tree constructed from one or several genes.
Breakpoint phylogenies methods have been shown to be an effective tool for extracting phylogenetic information from gene order data. Currently, the only practical breakpoint phylogeny algorithms for the analysis of large genomes with... more
Breakpoint phylogenies methods have been shown to be an effective tool for extracting phylogenetic information from gene order data. Currently, the only practical breakpoint phylogeny algorithms for the analysis of large genomes with varied gene content are heuristics with no optimality guarantee. Here we begin to address this lack by deriving lower bounds for the breakpoint median problem and for the more complicated breakpoint phylogeny problem.
Background Phylogenetic reconstruction methods based on gene content often place all the parasitic and endosymbiotic eubacteria (parasites for short) together in a clan. Many other lines of evidence point to this parasites clan being an... more
Background Phylogenetic reconstruction methods based on gene content often place all the parasitic and endosymbiotic eubacteria (parasites for short) together in a clan. Many other lines of evidence point to this parasites clan being an artefact. This artefact could be a consequence of the methods used to construct ortholog databases (due to some unknown bias), the methods used to estimate the phylogeny, or both.
Abstract In this paper we outline two debates about the nature of human cultural history. The first focuses on the extent to which human history is tree-like (its shape), and the second on the unity of that history (its fabric).... more
Abstract In this paper we outline two debates about the nature of human cultural history. The first focuses on the extent to which human history is tree-like (its shape), and the second on the unity of that history (its fabric). Proponents of cultural phylogenetics are often accused of assuming that human history has been both highly tree-like and consisting of tightly linked lineages. Critics have pointed out obvious exceptions to these assumptions.
Abstract We present Neighbor-Net, a distance based method for constructing phylogenetic networks that is based on the Neighbor-Joining (NJ) algorithm of Saitou and Nei. Neighbor-Net provides a snapshot of the data that can guide more... more
Abstract We present Neighbor-Net, a distance based method for constructing phylogenetic networks that is based on the Neighbor-Joining (NJ) algorithm of Saitou and Nei. Neighbor-Net provides a snapshot of the data that can guide more detailed analysis. Unlike split decomposition, Neighbor-Net scales well and can quickly produce detailed and informative networks for several hundred taxa.
Abstract The multispecies coalescent provides an elegant theoretical framework for estimating species trees and species demographics from genetic markers. However, practical applications of the multispecies coalescent model are limited by... more
Abstract The multispecies coalescent provides an elegant theoretical framework for estimating species trees and species demographics from genetic markers. However, practical applications of the multispecies coalescent model are limited by the need to integrate or sample over all gene trees possible for each genetic marker.
Abstract We derive an invertible transform linking two widely used measures of species diversity: phylogenetic diversity and the expected proportions of segregating (non-constant) sites. We assume a bi-allelic (two-state), symmetric,... more
Abstract We derive an invertible transform linking two widely used measures of species diversity: phylogenetic diversity and the expected proportions of segregating (non-constant) sites. We assume a bi-allelic (two-state), symmetric, finite site model of substitution. Like the Hadamard transform of Hendy and Penny, the transform can be expressed independently of the underlying phylogeny. Our results bridge work on diversity from two quite distinct scientific communities.
The idea of inferring phylogenies by selecting trees that minimize the total tree length can be traced back to the 19th century and the mathematician Jakob Steiner. It complies with Occam's principle of scientific inference, which... more
The idea of inferring phylogenies by selecting trees that minimize the total tree length can be traced back to the 19th century and the mathematician Jakob Steiner. It complies with Occam's principle of scientific inference, which essentially maintains that simpler explanations are preferable to more complicated ones and that ad hoc explanations should be avoided. Parsimony methods, which infer phylogenies directly from character data, are a well-known example of this approach.
Traditional methods for estimating rearrangement distances between genomes assume that there is at most one copy of each gene in each genome. In the case that there are multiple genes from the same gene family in a genome, SankofT (1999)... more
Traditional methods for estimating rearrangement distances between genomes assume that there is at most one copy of each gene in each genome. In the case that there are multiple genes from the same gene family in a genome, SankofT (1999) proposes the estimation of true exemplars, a selection of one gene from each gene family in both genomes such that the distance between the resulting exemplar strings is minimized. This is the exemplar distance.
Abstract Genome duplication is an important source of new gene functions and novel physiological pathways. In the course of evolution, the nucleotide sequences of duplicated genes tend to diverge through mutation, so that one copy loses... more
Abstract Genome duplication is an important source of new gene functions and novel physiological pathways. In the course of evolution, the nucleotide sequences of duplicated genes tend to diverge through mutation, so that one copy loses function (and disappears from view) or develops a new function, encoding a distinct but similar product.
Breakpoint phylogenies methods have been shown to be an effective way to extract phylogenetic information from gene order data. Currently, the only practical breakpoint phylogeny algorithms for the analysis of large genomes with varied... more
Breakpoint phylogenies methods have been shown to be an effective way to extract phylogenetic information from gene order data. Currently, the only practical breakpoint phylogeny algorithms for the analysis of large genomes with varied gene content are heuristics with no optimality guarantee. Here we address this shortcoming by describing new bounds for the breakpoint median problem, and for the more complicated breakpoint phylogeny problem.
Sequences that have evolved under recombination have a 'mosaic'structure, with different portions of the alignment having evolved on different trees. In this paper we study the effect of mosaic sequence structure on pairwise distance... more
Sequences that have evolved under recombination have a 'mosaic'structure, with different portions of the alignment having evolved on different trees. In this paper we study the effect of mosaic sequence structure on pairwise distance estimates. If we apply standard distance corrections to sequences that evolved on more than one tree then we are, in effect, correcting according to an incorrect model.
A p hylogenetic tree represents historical evolutionary relationships between different species or organisms. The space of possible phylogenetic trees is both complex and exponentially large. Here we study combinatorial features of... more
A p hylogenetic tree represents historical evolutionary relationships between different species or organisms. The space of possible phylogenetic trees is both complex and exponentially large. Here we study combinatorial features of neighbourhoods within this space, with respect to four standard tree metrics. We focus on the splits of a tree: the bipartitions induced by removing a single edge from the tree.
ABSTRACT. In computational biology, a common way to compare two rooted trees that classify the same set L of labelled leaves is to determine the largest subset of L on which the two trees agree. In this paper we consider the size of this... more
ABSTRACT. In computational biology, a common way to compare two rooted trees that classify the same set L of labelled leaves is to determine the largest subset of L on which the two trees agree. In this paper we consider the size of this quantity if one or both trees are generated randomly, according to two simple null models.
Data from morphology, linguistics, history, and archaeology have all been used to trace the dispersal of chickens from Asian domestication centers to their current global distribution. Each provides a unique perspective which can aid in... more
Data from morphology, linguistics, history, and archaeology have all been used to trace the dispersal of chickens from Asian domestication centers to their current global distribution. Each provides a unique perspective which can aid in the reconstruction of prehistory. This study expands on previous investigations by adding a temporal component from ancient DNA and, in some cases, direct dating of bones of individual chickens from a variety of sites in Europe, the Pacific, and the Americas.
A collection of T1, T2,���, Tk of unrooted, leaf labelled (phylogenetic) trees, all with different leaf sets, is said to be compatible if there exists a tree T such that each tree Ti can be obtained from T by deleting leaves and... more
A collection of T1, T2,���, Tk of unrooted, leaf labelled (phylogenetic) trees, all with different leaf sets, is said to be compatible if there exists a tree T such that each tree Ti can be obtained from T by deleting leaves and contracting edges. Determining compatibility is NP-hard, and the fastest algorithm to date has worst case complexity of around �� (nk) time, n being the number of leaves.
Abstract The Hadamard transform (Hendy and Penny, Syst. Zool. 38 (4): 297���309, 1989; Hendy, Syst. Zool. 38 (4): 310���321, 1989) provides a way to work with stochastic models for sequence evolution without having to deal with the... more
Abstract The Hadamard transform (Hendy and Penny, Syst. Zool. 38 (4): 297���309, 1989; Hendy, Syst. Zool. 38 (4): 310���321, 1989) provides a way to work with stochastic models for sequence evolution without having to deal with the complications of tree space and the graphical structure of trees. Here we demonstrate that the transform can be expressed in terms of the familiar P [��]= e Q [��] formula for Markov chains.
Abstract Analyses of 55 individual and 31 concatenated protein data sets encoded in Reclinomonas americana and Marchantia polymorpha mitochondrial genomes revealed that current methods for constructing phylogenetic trees are... more
Abstract Analyses of 55 individual and 31 concatenated protein data sets encoded in Reclinomonas americana and Marchantia polymorpha mitochondrial genomes revealed that current methods for constructing phylogenetic trees are insufficiently sensitive (or artifact-insensitive) to ascertain the sister of mitochondria among the current sample of eight ��-proteobacterial genomes using mitochondrially-encoded proteins. However, Rhodospirillum rubrum came as close to mitochondria as any ��-proteobacterium investigated.
Abstract: There are many ways to combine rooted phylogenetic trees with overlapping leaf sets into a single" supertree". The most widely used method is MRP (matrix representation with parsimony analysis), but other direct methods have... more
Abstract: There are many ways to combine rooted phylogenetic trees with overlapping leaf sets into a single" supertree". The most widely used method is MRP (matrix representation with parsimony analysis), but other direct methods have been developed recently. However, all these methods utilize typically only the discrete topology of the input trees and ignore other information that might be available.
Background Delimiting species boundaries and reconstructing the evolutionary relationships of late Tertiary and Quaternary species radiations is difficult. One recent approach emphasizes the use of genome-wide molecular markers, such as... more
Background Delimiting species boundaries and reconstructing the evolutionary relationships of late Tertiary and Quaternary species radiations is difficult. One recent approach emphasizes the use of genome-wide molecular markers, such as amplified fragment length polymorphisms (AFLPs) and single nucleotide polymorphisms (SNPs), to identify distinct metapopulation lineages as taxonomic species.
We propose a continuous model for variation in the evolutionary rate across sites and over the phylogenetic tree. We derive exact transition probabilities of substitutions under this model. Changes in rate are modelled using the CIR... more
We propose a continuous model for variation in the evolutionary rate across sites and over the phylogenetic tree. We derive exact transition probabilities of substitutions under this model. Changes in rate are modelled using the CIR process, a diffusion widely used in financial applications. The model directly extends the standard gamma distributed rates across site model, with one additional parameter governing changes in rate down the tree.
Likelihood estimation is central to many areas of the natural and physical sciences and has had a major impact on molecular phylogenetics. In this chapter we provide a concise review of some of the theoretical and computational aspects of... more
Likelihood estimation is central to many areas of the natural and physical sciences and has had a major impact on molecular phylogenetics. In this chapter we provide a concise review of some of the theoretical and computational aspects of likelihood-based phylogenetic inference. We outline the basic probabilistic model and likelihood computation algorithm, as well as extensions to more realistic models and strategies of likelihood optimization.
The exploration and settlement of Polynesia was surely one of the greatest navigational feats in all human history. At a time when Europeans were tentatively edging out into the Mediterranean, Austronesians had colonised half the globe... more
The exploration and settlement of Polynesia was surely one of the greatest navigational feats in all human history. At a time when Europeans were tentatively edging out into the Mediterranean, Austronesians had colonised half the globe [7]. Even more extraordinary is that, at least according to Sharp [11], all of this exploration was carried out in primitive sailing vessels capable only of coastal navigation.
Abstract. We give formulas for calculating in polynomial time the number of ancestral reconstructions for a tree with binary leaf-and root labels for each number of 0 ��� 1 and 1 ��� 0 arcs. For trees of fixed degree, the corresponding... more
Abstract. We give formulas for calculating in polynomial time the number of ancestral reconstructions for a tree with binary leaf-and root labels for each number of 0 ��� 1 and 1 ��� 0 arcs. For trees of fixed degree, the corresponding numbers of 0 ��� 0 and 1 ��� 1 arcs can be deduced. We calculate intervals for the relative cost of 0 ��� 1 and 1 ��� 0 transitions over which the same labelings remain the cheapest.
We present a polynomial time algorithm for computing the refined Buneman tree, thereby making it applicable for tree reconstruction on large data sets. The refined Buneman tree retains many of the desirable properties of its predecessor,... more
We present a polynomial time algorithm for computing the refined Buneman tree, thereby making it applicable for tree reconstruction on large data sets. The refined Buneman tree retains many of the desirable properties of its predecessor, the well-known Buneman tree, but has the practical advantage that it is typically more refined.
The comparison of the gene orders in a set of genomes can be used to infer their phylogenetic relationships and to reconstruct ancestral gene orders. For three genomes this is done by solving the" median problem for breakpoints"; this... more
The comparison of the gene orders in a set of genomes can be used to infer their phylogenetic relationships and to reconstruct ancestral gene orders. For three genomes this is done by solving the" median problem for breakpoints"; this solution can then be incorporated into a routine for estimating optimal gene orders for all the ancestral genomes in a fixed phylogeny.
The growing number of complete genome maps enables the extraction of phylogenetic information from global rearrangements over the whole genome, rather than just local nucleotide or amino acid patterns. As genomes evolve, genes are... more
The growing number of complete genome maps enables the extraction of phylogenetic information from global rearrangements over the whole genome, rather than just local nucleotide or amino acid patterns. As genomes evolve, genes are inserted or deleted, segments of the genome are reversed, or removed and re-inserted at a new position. This leads to different genomes having homologous genes arranged in different orders on their gene maps, and it is these orderings that become the input data for comparative genomics.
Abstract It is now routine for biologists to conduct evolutionary analyses of large DNA and protein sequence datasets. A computational bottleneck in these analyses is the recovery" of the topology of the evolutionary tree for a set of... more
Abstract It is now routine for biologists to conduct evolutionary analyses of large DNA and protein sequence datasets. A computational bottleneck in these analyses is the recovery" of the topology of the evolutionary tree for a set of sequences. This paper presents a practical solution to this challenging problem. In particular, a new technique, called hypercleaning, is presented that can be combined with various tree-building algorithms to efficiently reconstruct from sequence data the best supported edges of the evolutionary tree.
The amalgamation of leaf-labeled trees into a single (super) tree that ���displays��� each of the input trees is an important problem in classification. We discuss various approaches to this problem and show that a simple and well-known... more
The amalgamation of leaf-labeled trees into a single (super) tree that ���displays��� each of the input trees is an important problem in classification. We discuss various approaches to this problem and show that a simple and well-known polynomial-time algorithm can be used to solve this problem whenever the input set of trees contains a minimum size subset that uniquely determines the supertree. Our results exploit a recently established combinatorial property concerning the structure of such collections of trees.
Abstract. Determining an optimal phylogenetic tree using maximum parsimony, also referred to as the Steiner tree problem in phylogenetics, is NP hard. Here we provide a new formulation for this problem which leads to an analytical and... more
Abstract. Determining an optimal phylogenetic tree using maximum parsimony, also referred to as the Steiner tree problem in phylogenetics, is NP hard. Here we provide a new formulation for this problem which leads to an analytical and linear time solution when the dimensionality (sequence length, or number of characters) is at most two. This new formulation of the problem provides a direct link between the maximum parsimony problem and the maximum compatibility problem via the intersection graph.
The Neighbor-Joining (NJ) method of Saitou and Nei is the most widely used distance based method in phylogenetic analysis. Central to the method is the selection criterion, the formula used to choose which pair of objects to amalgamate... more
The Neighbor-Joining (NJ) method of Saitou and Nei is the most widely used distance based method in phylogenetic analysis. Central to the method is the selection criterion, the formula used to choose which pair of objects to amalgamate next. Here we analyze the NJ selection criterion using an axiomatic approach. We show that any selection criterion that is linear, permutation equivariant, statistically consistent and based solely on distance data will give the same trees as those created by NJ.
Abstract Genome phylogenies can be inferred from data on the presence and absence of genes across taxa. Logdet distances may be a good method, because they allow expected genome size to vary across the tree. Recently, Lake and Rivera... more
Abstract Genome phylogenies can be inferred from data on the presence and absence of genes across taxa. Logdet distances may be a good method, because they allow expected genome size to vary across the tree. Recently, Lake and Rivera proposed conditioned genome reconstruction (calculation of logdet distances using only those genes present in a conditioning genome) to deal with unobservable genes that are absent from every taxon of interest.
A cluster A is an Apresjan cluster if every pair of objects within A is more similar than either is to any object outside A. The criterion is intuitive, compelling, but often too restrictive for applications in classification. We... more
A cluster A is an Apresjan cluster if every pair of objects within A is more similar than either is to any object outside A. The criterion is intuitive, compelling, but often too restrictive for applications in classification. We therefore explore extensions of Apresjan clustering to a family of related hierarchical clustering methods. The extensions are shown to be closely connected with the well-known single and average linkage tree constructions. A dual family of methods for classification by splits is also presented.
An important procedure in the mathematics of phylogenetic analysis is to associate, to any collection of weighted splits, the metric given by the corresponding linear combination of split metrics. In this note, we study necessary and... more
An important procedure in the mathematics of phylogenetic analysis is to associate, to any collection of weighted splits, the metric given by the corresponding linear combination of split metrics. In this note, we study necessary and sufficient conditions for a collection of splits of a given finite set X to give rise to a linearly independent collection of split metrics. In addition, we study collections of splits called affine split systems induced by a configurations of lines and points in the plane.
Abstract Ion channels are characterized by inherently stochastic behavior which can be represented by continuous-time Markov models (CTMM). Although methods for collecting data from single ion channels are available, translating a time... more
Abstract Ion channels are characterized by inherently stochastic behavior which can be represented by continuous-time Markov models (CTMM). Although methods for collecting data from single ion channels are available, translating a time series of open and closed channels to a CTMM remains a challenge. Bayesian statistics combined with Markov chain Monte Carlo (MCMC) sampling provide means for estimating the rate constants of a CTMM directly from single channel data.
Where plant species radiations are characterized by hybridization, introgression and polyploidy, complex patterns of phylogenetic relationships are expected, and bifurcating tree methods are often inadequate. In this situation, network... more
Where plant species radiations are characterized by hybridization, introgression and polyploidy, complex patterns of phylogenetic relationships are expected, and bifurcating tree methods are often inadequate. In this situation, network methods may have some potential for displaying patterns of phylogenetic incongruence, and in so doing facilitate interpretation of the data. One such method is Neighbour Net (Bryant and Moulton, 2004) implemented in SplitsTree4. 0 (http://www-ab. informatik. uni-tuebingen. de/software/jsplits/welcome.
Distance-based clustering algorithms such as UPGMA and neighbor joining have been very popular (eg, see Saitou and Nei 1987; Swofford et al. 1996). However, it is generally more desirable to optimize the fit of data to an assumed model... more
Distance-based clustering algorithms such as UPGMA and neighbor joining have been very popular (eg, see Saitou and Nei 1987; Swofford et al. 1996). However, it is generally more desirable to optimize the fit of data to an assumed model than to simply apply an algorithm (see Swofford et al. 1996). Examples of fit criteria applied to trees include ordinary, or unweighted, least squares (OLS); weighted least squares (WLS); and generalized least squares (GLS).
Standard likelihood-based frameworks in phylogenetics consider the process of evolution of a sequence site by site. Assuming that sites evolve independently greatly simplifies the required calculations. However, this simplification is... more
Standard likelihood-based frameworks in phylogenetics consider the process of evolution of a sequence site by site. Assuming that sites evolve independently greatly simplifies the required calculations. However, this simplification is known to be incorrect in many cases. Here, a computational method that allows for general dependence between sites of a sequence is investigated. Using this method, measures acting as sequence fitness proxies can be considered over a phylogenetic tree.
Abstract Although most often used to represent phylogenetic uncertainty, network methods are also potentially useful for describing the phylogenetic complexity expected to characterize recent species radiations. One network method with... more
Abstract Although most often used to represent phylogenetic uncertainty, network methods are also potentially useful for describing the phylogenetic complexity expected to characterize recent species radiations. One network method with particular advantages in this context is split decomposition. However, in its standard implementation this approach is limited by a conservative criterion for branch length estimation.
Abstract We present fast new algorithms for phylogenetic reconstruction from distance data or weighted quartets. The methods are conservative-they will only return edges that are well supported by the input data. This approach is not only... more
Abstract We present fast new algorithms for phylogenetic reconstruction from distance data or weighted quartets. The methods are conservative-they will only return edges that are well supported by the input data. This approach is not only philosophically attractive; the conservative tree estimate can be used as a basis for further tree refinement or divide and conquer algorithms. The capability to process quartet data allows these algorithms to be used in tandem with ordinal or qualitative phylogenetic analysis methods.
Normalizing the number of breakpoints between two genomes, previously reduced by deleting the genes specific to one or the other, gives a rapidly calculated index of gene order evolution which is not based on any assumptions about the... more
Normalizing the number of breakpoints between two genomes, previously reduced by deleting the genes specific to one or the other, gives a rapidly calculated index of gene order evolution which is not based on any assumptions about the relative importance of various possible rearrangement processes. This is used to compare chloroplast genomes with known gene orders, with a focus on recently sequenced members of the algal class Prasinophycae.
Matrix representation with parsimony (MRP) is a method that takes as input a collection of source trees, recodes them as binary matrices, and returns a tree that is closest to the source trees using a parsimony criterion (Baum, 1992;... more
Matrix representation with parsimony (MRP) is a method that takes as input a collection of source trees, recodes them as binary matrices, and returns a tree that is closest to the source trees using a parsimony criterion (Baum, 1992; Ragan, 1992).