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

Numerical Taxonomy: The Principles and Practice of Numerical Classification

Twenty-one allele frequencies of the human HLA loci from 58 localities in Europe and the Near East were subjected to spatial autocorrelation analysis. The frequencies were significantly heterogeneous over the localities. Significant clinal structure is shown by most allele frequencies. Collective study of the 21 variable surfaces and of their correlograms supports a hypothesis of migration leading to the observed patterns with three alternative explanatory hypotheses being eliminated. Cluster analysis of allele frequency surfaces and of correlograms shows that there are at least three distinct classes of patterns. By connecting localities along the established paths of the spread of agriculture into Europe, it can be shown that one of these surface clusters and their corresponding correlograms closely relate to the spread of farming. The results are compatible with a hypothesis of demic diffusion of early farmers into the hunter-gatherer population of Neolithic Europe first advanced by Ammerman and Cavall...

Spatial Autocorrelations of HLA Frequencies in Europe Support Demic Diffusion of Early Farmers

A simulation study was carried out to investigate the relative importance of tree topology (both balance and stemminess), evolutionary rates (constant, varying among characters, and varying among lineages), and evolutionary models in determining the accuracy with which phylogenetic trees can be estimated. The three evolutionary context models were phyletic (characters can change at each simulated time step), speciational (changes are possible only at the time of speciation into two daughter lineages), and punctuational (changes occur at the time of speciation but only in one of the daughter lineages). UPGMA clustering and maximum parsimony ("Wagner trees") methods for estimating phylogenies were compared. All trees were based on eight recent OTUs. The three evolutionary context models were found to have the largest influence on accuracy of estimates by both methods. The next most important effect was that of the stemminess × context interaction. Maximum parsimony and UPGMA performed worst under the punctuational models. Under the phyletic model, trees with high stemminess values could be estimated more accurately and balanced trees were slightly easier to estimate than unbalanced ones. Overall, maximum parsimony yielded more accurate trees than UPGMA-but that was expected for these simulations since many more characters than OTUs were used. Our results suggest that the great majority of estimated phylogenetic trees are likely to be quite inaccurate; they underscore the inappropriateness of characterizing current phylogenetic methods as being for reconstruction rather than for estimation.

Accuracy of estimated phylogenies: effects of tree topology and evolutionary model.

We review the recently developed local spatial autocorrelation statistics Zi, Ci, Gi, and G,?. We discuss two alternative randomization assumptions, total and conditional, and then newly derive expectations and variances under conditional randomization for Zi and ci, as well as under total randomization for ci. The four statistics are tested by a biological simulation model from population genetics in which a population lives on a 21 x 21 lattice of stepping stones (sixtyyour individuals per stone) and reproduces and disperses over a number of generations. Some designs model global spatial autocorrelation, others spatially random sugaces. We find that spatially random designs give reliable test results by permutational methods of testing signif cance. Globally autocorrelated designs do not fit expectations by any of the three tests we employed. Asymptotic methods of testing signif came failed consistently, regardless of design. Because most biological data sets are autocorrelated, significance testing for local spatial autocorrelation is problematic. However, the statistics are informative when employed in an exploratory manner. We found that hotspots (positive local autocorrelation) and coldspots (negative local autocorrelation) are successfully distinguished in spatially autocorrelated, biologically plausible data sets. Work on spatial autocorrelation (SA) has been frequently featured in the pages of this journal. Pioneered in the 1950s, this topic was comprehensively treated by Cliff and Ord (1973, 1981). It was introduced to biology by Jumars, Thistle, and Jones (1977) and by Sokal and Oden (1978a, b). It has been extensively applied by ecologists and population biologists to a variety of organisms including humans, not only to test for departures from spatial randomness, but also to make inferences about the processes underlying the observed patterns. Representative studies are Sokal and Wartenberg (1981), Sokal and Jacquez (1991), Epperson (1993), Barbujani (1987), Sokal, Oden, and Barker (1987), and Sokal and Thomson (1998). Contribution no. 1016 in Ecology and Evolution from SUNY-Stony Brook. This research was supported by grant DEB9220538 from the National Science Foundation to Robert R. Sokal. The extensive computations were made possibIe by a grant of supercomputer time from the Cornell Theory Center.

Local Spatial Autocorrelation in a Biological Model

Spatial autocorrelation (SA) methods have recently been extended to include the detection of local spatial autocorrelation at individual sampling stations. We review the formulas for these statistics and report on the results of an extensive population-genetic simulation study we have published elsewhere to test the applicability of these methods in spatially distributed biological data. We find that most biological variables exhibit global SA, and that in such cases the methods proposed for testing the significance of local SA coefficients reject the null hypothesis excessively. When global SA is absent, permutational methods for testing significance yield reliable results. Although standard errors have been published for the local SA coefficients, their employment using an asymptotically normal approach leads to unreliable results; permutational methods are preferred. In addition to significance tests of suspected non-stationary localities, we can use these methods in an exploratory manner to find and identify hotspots (places with positive local SA) and coldspots (negative local SA) in a dataset. We illustrate the application of these methods in three biological examples from plant population biology, ecology and population genetics. The examples range from the study of single variables to the joint analysis of several variables and can lead to successful demographic and evolutionary inferences about the populations studied.

Robert R. Sokal

Papers

Numerical Taxonomy: The Principles and Practice of Numerical Classification

Spatial Autocorrelations of HLA Frequencies in Europe Support Demic Diffusion of Early Farmers

Accuracy of estimated phylogenies: effects of tree topology and evolutionary model.

Local Spatial Autocorrelation in a Biological Model

Local spatial autocorrelation in biological variables