A new method called the neighbor-joining method is proposed for reconstructing phylogenetic trees from evolutionary distance data. The principle of this method is to find pairs of operational taxonomic units (OTUs [= neighbors]) that minimize the total branch length at each stage of clustering of OTUs starting with a starlike tree. The branch lengths as well as the topology of a parsimonious tree can quickly be obtained by using this method. Using computer simulation, we studied the efficiency of this method in obtaining the correct unrooted tree in comparison with that of five other tree-making methods: the unweighted pair group method of analysis, Farris's method, Sattath and Tversky's method, Li's method, and Tateno et al.'s modified Farris method. The new, neighbor-joining method and Sattath and Tversky's method are shown to be generally better than the other methods.

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The neighbor-joining method: a new method for reconstructing phylogenetic trees.

The recently-developed statistical method known as the "bootstrap" can be used to place confidence intervals on phylogenies. It involves resampling points from one's own data, with replacement, to create a series of bootstrap samples of the same size as the original data. Each of these is analyzed, and the variation among the resulting estimates taken to indicate the size of the error involved in making estimates from the original data. In the case of phylogenies, it is argued that the proper method of resampling is to keep all of the original species while sampling characters with replacement, under the assumption that the characters have been independently drawn by the systematist and have evolved independently. Majority-rule consensus trees can be used to construct a phylogeny showing all of the inferred monophyletic groups that occurred in a majority of the bootstrap samples. If a group shows up 95% of the time or more, the evidence for it is taken to be statistically significant. Existing computer programs can be used to analyze different bootstrap samples by using weights on the characters, the weight of a character being how many times it was drawn in bootstrap sampling. When all characters are perfectly compatible, as envisioned by Hennig, bootstrap sampling becomes unnecessary; the bootstrap method would show significant evidence for a group if it is defined by three or more characters.

Confidence limits on phylogenies: an approach using the bootstrap.

The main purpose of this paper is to describe a process for partitioning an N-dimensional population into k sets on the basis of a sample. The process, which is called 'k-means,' appears to give partitions which are reasonably efficient in the sense of within-class variance. That is, if p is the probability mass function for the population, S = {S1, S2, * *, Sk} is a partition of EN, and ui, i = 1, 2, * , k, is the conditional mean of p over the set Si, then W2(S) = ff=ISi f z u42 dp(z) tends to be low for the partitions S generated by the method. We say 'tends to be low,' primarily because of intuitive considerations, corroborated to some extent by mathematical analysis and practical computational experience. Also, the k-means procedure is easily programmed and is computationally economical, so that it is feasible to process very large samples on a digital computer. Possible applications include methods for similarity grouping, nonlinear prediction, approximating multivariate distributions, and nonparametric tests for independence among several variables. In addition to suggesting practical classification methods, the study of k-means has proved to be theoretically interesting. The k-means concept represents a generalization of the ordinary sample mean, and one is naturally led to study the pertinent asymptotic behavior, the object being to establish some sort of law of large numbers for the k-means. This problem is sufficiently interesting, in fact, for us to devote a good portion of this paper to it. The k-means are defined in section 2.1, and the main results which have been obtained on the asymptotic behavior are given there. The rest of section 2 is devoted to the proofs of these results. Section 3 describes several specific possible applications, and reports some preliminary results from computer experiments conducted to explore the possibilities inherent in the k-means idea. The extension to general metric spaces is indicated briefly in section 4. The original point of departure for the work described here was a series of problems in optimal classification (MacQueen [9]) which represented special

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Some methods for classification and analysis of multivariate observations

genalex is a user-friendly cross-platform package that runs within Microsoft Excel, enabling population genetic analyses of codominant, haploid and binary data. Allele frequency-based analyses include heterozygosity, F statistics, Nei's genetic distance, population assignment, probabilities of identity and pairwise relatedness. Distance-based calculations include amova, principal coordinates analysis (PCA), Mantel tests, multivariate and 2D spatial autocorrelation and twogener. More than 20 different graphs summarize data and aid exploration. Sequence and genotype data can be imported from automated sequencers, and exported to other software. Initially designed as tool for teaching, genalex 6 now offers features for researchers as well. Documentation and the program are available at http://www.anu.edu.au/BoZo/GenAlEx/

genalex 6: genetic analysis in Excel. Population genetic software for teaching and research

Arlequin ver 3.0 is a software package integrating several basic and advanced methods for population genetics data analysis, like the computation of standard genetic diversity indices, the estimation of allele and haplotype frequencies, tests of departure from linkage equilibrium, departure from selective neutrality and demographic equilibrium, estimation or parameters from past population expansions, and thorough analyses of population subdivision under the AMOVA framework. Arlequin 3 introduces a completely new graphical interface written in C++, a more robust semantic analysis of input files, and two new methods: a Bayesian estimation of gametic phase from multi-locus genotypes, and an estimation of the parameters of an instantaneous spatial expansion from DNA sequence polymorphism. Arlequin can handle several data types like DNA sequences, microsatellite data, or standard multi-locus genotypes. A Windows version of the software is freely available on http://cmpg.unibe.ch/software/arlequin3.

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Arlequin (version 3.0): An integrated software package for population genetics data analysis

the origin of records. Except for the addition of other symbols the maps are ready for the printers when they come off the machine. The original maps are 14 inches x 12 inches and when reduced to a size of 5 inches x 4,5 inches the black dots made by a heavily inked ribbon are quite satisfactory. The maps have been printed by offset lithography and if, in proof, there are any minor flaws, these can be adjusted on the negative. One last point which is not strictly data processing but data analysing we have included in the Atlas 12 transparent overlays, as instructed by the 1950 conference. In our tight little islands, geology and topography change so rapidly that we found it impossible to produce conventional maps on the same scale. Here again we used the 10-kilometre square as a unit and showed by dots and other symbols the distribution of squares having outcrops of limestone, with which the distribution of species can be correlated either in a positive or negative way, and on squares having land over certain altitudes, which gives a reasonable understanding of the distribution of some of our mountain plants. Since the publication of the Atlas it is perhaps not suprising that British field botanists have given up square-bashing and have been taking a well earned rest playing noughts and crosses.

The principles and practice of numerical taxonomy

Taxonomic Congruence in the Leptopodomorpha Re-examined

Introducción a la bioestadística

Rohlf, F. J. 1 (IBM Thomas J. Watson Research Center, Yorktown Heights, New York 10598) and R. R. Sokal (Department of Ecology and Evolution, State University of New York, Stony Brook, New York 11794) 1981. Comparing numerical taxonomic studies. Syst. Zool., 30:459-490.-Recent proposals to measure the degree to which given taxometric methods meet goals defined by the three current schools of classification have led to quantitative comparisons of the methods. To aid in understanding such comparisons, a flow chart of taxonomic procedures is presented. Optimality tests are reviewed for each type of procedure. Possibly desirable properties of classifications include: the fit of a summary representation to a similarity matrix, stability, general utility, fit to a known cladistic relationship, and optimality criteria of numerical phylogenetic methods. We examine how they relate to the professed goals of the taxonomic schools and whether they can be used for comparative evaluations between these schools. Previous attempts at comparing numerical classifications are reexamined. Such comparisons have largely been made improperly. Published comparative tests of taxonomic congruence are based on inappropriate comparisons or were improperly executed and cannot furnish evidence on relative stability of phenetic, evolutionary, and phylogenetic classifications. Reports which claim to show that numerical phylogenetic classifications result in better fits to original similarity matrices than phenetic methods and therefore retain distance information better than phenetic classifications are shown to be misleading. In the first such study, the comparison was not relevant to the question asked. In all of these studies the results were biased in favor of phylogenetic methods by retaining redundant information during the computation of matrix correlations for the phylogenetic methods. In two later studies based on ten taxonomic data sets, the comparisons for the phylogenetic methods were in terms of unrooted trees rather than hierarchic classifications. By limiting the reference OTU to OTU 1 in each data set, results were obtained in these studies, that tended to favor the phylogenetic methods considerably more than if some other reference OTUs had been employed. Only in a few cases is there a significant increase in fit with the phylogenetic methods. Interpreted as classifications, UPGMA clustering of the original dissimilarity matrix gives the best fit in the majority of cases when compared with rooted trees (minimum length and least squares fitted). For these data, there is no evidence that classifications by any "phylogenetic" technique yield better summaries of phenetic information than UPGMA. A recent study of predictivity, while correctly designed, yielded complex results with no clear preference for any one school of taxonomy. Thus there is no current acceptable evidence that numerical phylogenetic methods yield classifications which contain more information than either phenetic or evolutionary ones. [Numerical taxonomy; classification; phenetics; phylogenetics; cladistics]. In this paper, we examine the methods proposed for measuring the degree to which various numerical methods meet the differing goals proposed by the various classificatory schools. Are given numerical methods consonant with the stated goals of a given school of taxonomy and can one develop criteria which measure how well these methods meet such goals? We also discuss the validity of usI Present address: Department of Ecology and Evolution, State University of New York, Stony Brook, New York 11794. ing the same criteria to compare phenetic and cladistic approaches to taxonomy. We first describe the normal flow of procedures in a numerical taxonomic study. Next we enumerate the types of criteria that have been used to evaluate the optimality of such procedures and discuss appropriate ways by which comparisons can be made between alternative taxonomic procedures. We suggest methods for improving the evaluation of numerical techniques and outline some principles for studies comparing numerical phenetic and phylogenetic techniques. Then we examine several pub-

Comparing numerical taxonomic studies

T HE, LAST FEW YEARS have seen the development of a number of methods for quantifying the classificatory process in systematics (Michener and Sokal, 1957; Sokal and Michener, 1958; Sokal, 1958; Sneath, 1957a; Sneath, 1957b, Cain and Harrison, 1958; Rogers and Tanimoto, 1960). These sudden developments, largely independently arrived at, appear to stem from, a growing dissatisfaction with the arbitrariness and subjectivity of the customary taxonomic procedure and would also appear to. be connected with the increasing availability of rapidmethods of data processing and computation. In spite of certain differences among them, these methods show substantial philosophical and procedural agreements. They call first of all for the computation of a measure of resemblance or similarity between taxa. Resemblances are computed between every pair of taxa in a given study and these resemblances are arranged in the form of a so-called Q-type matrix, which is a matrix of similarities among taxa. These matrices are subsequently analyzed by various types of clus-

Robert R. Sokal

Papers

The principles and practice of numerical taxonomy

Taxonomic Congruence in the Leptopodomorpha Re-examined

Introducción a la bioestadística

Comparing numerical taxonomic studies

Distance as a Measure of Taxonomic Similarity