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

Classifications of European populations were produced based on 59 gene frequencies and 10 cranial measurements, but recorded for different population samples. A map-quadrat approach circumvented the problem of noncorrespondence of sampling localities. Clustering by standard numerical taxonomic procedures shows that these data are represented poorly as hierarchic classifications, but are associated with geographic regions. The agreement between classifications based on gene frequencies and those based on cranial variables is substantial (88%). Ordinations show genetic and morphometric continuity among these populations, although there is good regional separation on the whole. The relationships between phenetics, geography and language affiliation were examined by quadratic assignment methods. Both gene frequency and craniometric distances show significant correlations with geographic distances. The expected significant correlation between geographic distances and language affiliation is demonstrated. The gene frequency distances also show significant correlations with language distances. None of the partial correlations are significant. These analyses demonstrate a significant association of phenetics with language and geography, despite the lack of clear cut taxonomic structure in quadratted population data. For gene frequencies, these associations are more pronounced than for cranial measurements.

A Classification of European Populations Based on Gene Frequencies and Cranial Measurements: A Map-Quadrat Approach

Geographic variation in cancer rates is thought to be the result of two major factors: environmental agents varying spatially and the attributes, genetic or cultural, of the populations inhabiting the areas studied. These attributes in turn result from the history of the populations in question. We had previously constructed an ethnohistorical database for Europe since 2200 B.C., permitting estimates of the ethnic composition of modern European populations. We were able to show that these estimates correlate with genetic distances. In this study, we wanted to see whether they also correlate with cancer rates. We employed two data sets of cancer mortalities from 42 types of cancer for the European Economic Community and for Central Europe. We subjected spatial differences in cancer mortalities, genetic, ethnohistorical, and geographic distances to matrix permutation tests to determine the magnitude and significance of their association. Our findings are that distances in cancer mortalities are correlated more with ethnohistorical distances than with genetic distances. Possibly the cancer rates may be affected by loci other than the genetic systems available to us, and/or by cultural factors mediated by the ethnohistorical differences. We find it remarkable that patterns of frequently ancient ethnic admixture are still reflected in modern cancer mortalities. Partial correlations with geography suggest that local environmental factors affect the mortalities as well.

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Ethnohistory, genetics, and cancer mortality in Europeans

Comparisons of the stability of classifications based on phenograms or estimated cladograms have attracted considerable interest and controversy in recent years Rohlf and Sokal (1981) discussed the general topic while others have addressed specific aspects of stability: OTU stability (Schuh and Farris, 1981; Sokal et al, 1984); character stability tested by congruence of classifications based on different classes of characters (Mickevich, 1978; Rohlf and Sokal, 1980; Mickevich and Farris, 1981; Rohlf et al, 1983a, b); and character stability tested by congruence of classifications derived from random bipartitions of characters (Schuh and Polhemus, 1980; Colless, 1981; Schuh and Farris, 1981; Sokal and Rohlf, 1981a; Sokal, 1983a, c; Sokal et al, 1984) Cladist authors have consistently concluded that cladistic classifications based on estimated cladograms are more stable than those based on phenograms Pheneticists have contended that the computations carried out by the cladists to support these conclusions were either misleading or erroneous and that, when these same data sets are reanalyzed appropriately, the results frequently show approximately equal stability for phenograms and estimated cladograms or, in some cases, appreciably greater stability of phenograms In recent studies, Sokal (1983c) and Sokal et al (1984) reported that the relative stability of phenograms and estimated cladograms was related to the ratio between number of characters and number of OTUs in any given data set These views are based on findings in four data sets, two

Character Stability in 39 Data Sets

LogXact: Logistic Regression Software Featuring Exact Methods.LogXact-Turbo: Logistic Regression Software Featuring Exact Methods.

Selection for changes in genetic facilitation: negative results in Tribolium and Musca . 4

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Robert R. Sokal

Papers

A Classification of European Populations Based on Gene Frequencies and Cranial Measurements: A Map-Quadrat Approach

Ethnohistory, genetics, and cancer mortality in Europeans

Character Stability in 39 Data Sets

LogXact: Logistic Regression Software Featuring Exact Methods.LogXact-Turbo: Logistic Regression Software Featuring Exact Methods.

Selection for changes in genetic facilitation: negative results in Tribolium and Musca . 4