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

By means of three different methods we investigated whether 59 allele frequencies and ten cranial variables show increased change at 29 language-family boundaries in Europe. The quadrat-variance method compares variances of map quadrats crossed by language-family boundaries to variances of quadrats that are not crossed. The rate-of-change method examines the directional derivative of surfaces of the variables perpendicular to a language-family boundary and compares these derivatives to the same quantities obtained by randomly placing the language boundaries on the map of Europe. The difference method tests whether these variables differ more across language-family boundaries than across randomly placed boundaries. These special data-analytic techniques had to be developed to avoid the problem of spatial autocorrelation of both language and biological data. All three methods indicate increased genetic change at language-family boundaries. Clearer and more pronounced results are obtained by the first two methods than by the difference method. Thirteen language-family boundaries show significant gene frequency change by at least one of the methods. Changes are more marked in gene frequencies than in cranial variables. Different allele frequencies mark the increased change at different language boundaries. A model, based on the known history of each language-family boundary, was constructed to predict whether given boundaries should exhibit increased genetic change. The model is in good agreement with the observed results.

Genetic changes across language boundaries in Europe.

The rapid advances in molecular genetics during the final decade of the past century have brought about a veritable explosion in the number of publications on human population genetics. As ever more information on the fine genetic structure of nuclear DNA and mtDNA of different ethnic groups from all over the world has accumulated, population geneticists have used it to infer prehistoric demographic events and to corroborate accounts from historical sources. In doing so, they have had to reconcile their findings with those of past purveyors of prehistoric information—archeologists, linguists, and paleoanthropologists. Some of the workers in these fields have gladly welcomed the contributions of geneticists, whereas others have shown the expected resistance to the new approaches and paradigms. Perhaps the most enthusiastic champion of genetics in archeology is the first of the two editors of this volume, the distinguished archeologist Colin Renfrew. He considers the field sufficiently advanced to have given it a new name, “archaeogenetics,” which he defines as the study of the past by use of the techniques of molecular genetics.A field so rapidly growing outruns any attempt at a summary, but the present volume furnishes an excellent snapshot of the state of the new discipline in 1999, when a conference entitled “Human Diversity in Europe and Beyond: Retrospect and Prospect” was convened in Cambridge, England. It is appropriate that Europe should be studied, since it is the continent whose human genetic population structure has been most intensively sampled and researched. The book consists of 41 separate contributions organized into six themes. It is obviously impractical even to list, let alone discuss, each contribution. Instead, I shall describe the general tenor of each theme, singling out the occasional contribution for praise or criticism. Part I is introductory. In it, the goals and approaches of the field are outlined, and there is a concise tutorial in molecular genetics and in the analysis of its data (intended for archaeological newcomers to the field—not for regular readers of the Journal), as well as a historical survey of the field.In part II, six contributions treat the current archaeological and climatic findings and paradigms for Europe, based on other than genetic methods. I found this to be the most intellectually challenging—but also the most stimulating—section of the volume. All of the contributions in part II are linked by a common theme: the biological, cultural, and environmental processes involved in the peopling of Europe are far more complex than is indicated by the simple models investigated by the geneticists. Thus, in his contribution (chapter 7), Marek Zvelebil points out that the process of neolithization is unlikely to have been brought about by 100% population replacement (the migrationist position) or, alternatively, to have been generated fully in situ (the indigenist position). It is more likely, he states, that heterogeneity of the demographic processes will engender some of each (the integrationist position). Although some such response from the archaeological community can be expected as a Luddite reaction to newcomers poaching in their preserves, I cannot believe that this is the predominant reason. Rather, it is a manifestation of a common tension, found in many fields of science, between researchers who simplify models so that they can carry out tests of sufficient power to demonstrate the validity of their model while ignoring the contributions of subsidiary factors, and others, who perceive the complexity of the processes under study but who are unable to demonstrate their model convincingly because adequate tests for their complex hypotheses may not exist or their data are inadequate to the task of testing them. The correct approach will vary with the problem being investigated and will depend on the size distribution of the importance of the various factors affecting the process. In an L-shaped distribution, such as a decaying exponential function, the (over)simplification approach will probably provide a good explanation of the process, but this is not so in an approximately uniform or gradually declining distribution of factor importances.The six contributions in part III illustrate the types of data that human population geneticists analyze and the different analytical approaches that have been pursued, applied to data sets ranging from global to continentwide but always with an emphasis on Europe. We encounter mtDNA and Y chromosomes as well as autosomal nuclear variation of diverse types to which are applied (1) mismatch distributions (Excoffier and Schneider), (2) ordination (principal-components analysis and nonmetric multidimensional scaling), (3) spatial autocorrelation analysis (of gene and haplotype frequencies as well as of DNA data, following the AIDA methods of Bertorelle and Barbujani), and (4) phylogenetic analysis, including phylogeography. Parts IV and V are collections of regional studies of prehistory, based on molecular genetics for western and eastern Europe, respectively. Each part contains eight contributions.I am troubled by the lack of statistical-significance tests in some of the contributions (e.g., chapters 8 and 9) and by incorrect applications in some others. Geographically sampled data such as the ones presented in this volume are almost invariably spatially autocorrelated (Sokal and Oden 1978a,xSpatial autocorrelation in biology. I. Methodology. Sokal, RR and Oden, NL. Biol J Linn Soc Lond. 1978a; 10: 199–228CrossrefSee all References1978a,1978b;xSpatial autocorrelation in biology. II. Some biological implications and four applications of evolutionary and ecological interest. Sokal, RR and Oden, NL. Biol J Linn Soc Lond. 1978b; 10: 229–249CrossrefSee all References1978b; Upton and Fingleton 1985xSpatial data analysis by example. Upton, GJG and Fingleton, B. See all References1985). Typically, such data respond liberally when subjected to conventional significance tests; that is, they will indicate statistical significance much more frequently, even when the null hypothesis is true. Tables 6.1 and 6.2 in chapter 6 are examples: here, the radiocarbon dates are undoubtedly spatially autocorrelated, yet their correlations with longitude and latitude are tested at conventional significance levels instead of by the Clifford-Richardson-Hemon test (Clifford et al. 1989xAssessing the significance of the correlation between two spatial processes. Clifford, P, Richardson, S, and Hemon, D. Biometrics. 1989; 45: 123–134Crossref | PubMedSee all References1989). For the same reason, the significance values of the χ2 tests comparing frequencies of nonmetric cranial traits between Basque populations and other European populations (table 21.1 in chapter 21), as well as the significance values of the δα tests of the genetic impact of linguistic boundaries (table 40.1 in chapter 40), are questionable. Contributors in several parts of this volume mention synthetic maps for the representation of summaries of the variation of multiple genetic information (prominently featured in the book by Cavalli-Sforza et al. [1994xCavalli-Sforza, LL, Menozzi, P, and Piazza, A. See all References1994]), with the implication that this is a reliable method to be emulated. Yet Sokal et al. (1999axA problem with synthetic maps. Sokal, RR, Oden, NL, and Thomson, BA. Hum Biol. 1999a; 71: 1–13PubMedSee all References1999a, 1999bxProblems with synthetic maps remain: reply to Rendine et al. Sokal, RR, Oden, NL, and Thomson, BA. Hum Biol. 1999b; 71: 447–453PubMedSee all References1999b) have demonstrated clearly that the interpolation step in the preparation of synthetic maps introduces an added, frequently large component of spurious spatial autocorrelation, which falsely enhances or distorts true trends in such data. Furthermore, they showed that the spurious contribution is often so large that even random data suggest the presence of apparent but entirely artifactual geographic trends. These properties make trends exhibited by synthetic maps quite suspect. (For a contrary view, see the report by Rendine et al. [1999xA problem with synthetic maps: reply to Sokal et al. Rendine, S, Piazza, A, Menozzi, P, and Cavalli-Sforza, LL. Hum Biol. 1999; 71: 15–25See all References1999].)Finally, part VI is a catchall section of contributions, most of which are relevant to European archaeogenetics. They range from four purely methodological papers to another four discussing the insights gained into prehistoric human population structure from studies of the genetic origins of European domesticated animals and plants. The section concludes with two contributions on the relations between genetic and linguistic variation, and the volume ends with concluding remarks by Cavalli-Sforza, who discusses the prospects of the Human Genome Diversity Project.The editors are to be congratulated for assembling an excellent collection of contributions that accurately reflect the state of this relatively new field at the turn of the century. The editors and publishers have turned out a handsome, profusely illustrated volume, remarkably free of printing errors. For a number of years to come, this book will be a benchmark that will indicate what workers in other regions of the world need to accomplish. However, it will not remain a standard for too many years. The advances in the field are now so numerous and rapid that both techniques and knowledge in the study of European prehistory will surely have drastically changed by the end of this decade. In welcoming and advocating the employment of molecular genetic methods in archeology for quite a few years already, Colin Renfrew has shown considerable prescience and remarkably good judgement.

Archaeogenetics: DNA and the Population Prehistory of Europe

Cluster-Formation und Analyse.

The Two Taxonomies: Areas of Agreement and Conflict

We studied the factors affecting the accuracy of the neighbor-joining (NJ) method for estimating phylogenies by simulating character change under different evolutionary models applied to twenty different 8-OTU tree topologies that varied widely with respect to tree imbalance and stemmineEs. The models incorporated three evolutionary rates-constant, varying among lineages, varying among characters-and three evolutionary contexts concerning patterns of character change relative to speciation events-phyletic, speciational, and punctuational. All combinations of the rate and context models were studied. In addition, three different absolute rates of change were investigated. To measure the accuracy, the strict consensus index was computed between the estimated tree and the tree topology along which the data had been generated. The results were analyzed by analysis of variance and compared to a previous study that evaluated UPGMA clustering and maximum parsimony (MP) as phylogenetic estimation techniques. We found evo- lutionary context and tree imbalance to be the most important factors affecting the accuracy of the NJ method. NJ was more accurate than UPGMA or MP in terms of the average strict consensus index over all treatments. However, no one method was more accurate than the other two for all combinations of treatments. Higher absolute rate of change generally resulted in higher accuracy for all three methods.

Robert R. Sokal

Papers

Genetic changes across language boundaries in Europe.

Archaeogenetics: DNA and the Population Prehistory of Europe

Cluster-Formation und Analyse.

The Two Taxonomies: Areas of Agreement and Conflict

The accuracy of phylogenetic estimation using the neighbor-joining method.