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

A summary ethnohistory database on population movements in Europe between 2000 B.C. and A.D. 1970 was related to genetic variances and distances based on 26 genetic systems. For the purposes of these analyses, Europe was divided into 85 terrestrial quadrats measuring 5° × 5°. Counts, stratified by time, were taken of the number of movements out of and into each quadrat (called source and target counts, respectively) and between each pair of quadrats. The source and target counts have distinct and different patterns in Europe and vary significantly over time. Central Europe and the Pontic area have the quadrats with the highest source counts, and the Balkans have the highest target counts. Modern genetic variances per quadrat are significantly correlated with source and target counts, somewhat more prominently with source counts. Genetic distances between pairs of quadrats are correlated strongly with geographic distances and moderately and negatively correlated with the total number of movements ...

Ancient Movement Patterns Determine Modern Genetic Variances in Europe

The analytical method for simple structure proposed by Thurstone is applied to four separate cases and found to yield satisfactory results. The simple structure obtained by Thurstone's method is found to match closely that obtained by other methods and corresponds to the true structure of the matrix in those cases where true structure is known. Difficulties about the choice of the correct trial vector led the writer to develop a modification of Thurstone's method, useful where high speed computational facilities are available. Instructions are given for this so-called mass modification, and the procedure is illustrated with a 5-factor, 14-variable example. While the results do not fully correspond to a previous graphical solution, it can be argued that the results obtained by the new method show an improved simple structure. The modified method is applied to three other correlation matrices, yielding in each case a satisfactory simple structure.

Thurstone's analytical method for simple structure and a mass modification thereof

Experiments on competition in house flies reported here extend two previous studies by Sullivan and Sokal (1963) and Sokal and Sullivan (1963). The wild type OL strain, the autosomal recessive bwb, and the reciprocal crosses bwb? X OLd' (called A for short) and OL? X bwb& (called B) were reared at seven densities ranging from 40 to 2,560 eggs per 36 g of CSMA larval medium, both in pure and mixed cultures. Three possible mixtures, OL: bwb, A: bwb, and B: bwb, were set up in three proportions, 10: 90, 50: 50, and 90: 10 parts of wild phenotype to mutants, respectively. The nine possible combinations were replicated minimally five times per density. The numbers, dry weights, and times of emergence of adults were recorded by genotype. The responses of the hybrids resembled those established previously for the wild type flies. The reciprocal heterozygotes were not markedly different from each other. In mixed culture the emergence of bzob flies is affected more severely by an increase in density than that of their competitors. Hence the relative fitness of the wild phenotype increases markedly with density. At the highest densities hybrids weigh more in competition than they do in pure culture. Crowding increases the mean and variance of duration of adult emergence. Mutants emerged fastest in pure culture, whereas the wild phenotypes are fastest in mixed culture. Competition reduces the variance of duration of emergence in the wild type, though increasing it in the mutant. When the wild phenotype is present in low proportions in dense mixed culture its survival, weight, and duration of emergence are better than when it is frequent. These findings are reviewed and discussed from the point of view of genetic factors in competition, genetic facilitation, and gene frequency dependent changes in components of fitness. A brief comparison is made with a related study of the ge strain in the house fly.

Further Experiments on Competition Between Strains of House Flies

Numerical Taxonomy@@@Principles of Numerical Taxonomy.

Bird, J., B. Riska, and R. R. Sokal. (Department of Ecology and Evolution, State University of New York at Stony Brook, Stony Brook, New York 11794) 1981. Geographic variation in variability of Pemphigus populicaulis. Syst. Zool., 30:58-70.-Geographic variation of variability profiles is studied based on stem mother, alate and gall characters of the aphid Pemphigus populicaulis. Significant differences among the coefficients of variation of the suite of characters in every locality were found by two methods-Bartlett's test for homogeneity of variances (using log-transformed data) and Friedman's nonparametric test for randomize'd blocks. Nine characters are highly variable and six are consistently low in variability. Coefficients of variation show significant heterogeneity among localities for every character by Bartlett's test, and for all but two characters using a modified Friedman's test. The variability profiles of the 66 localities were clustered into three groups based on both size and shape by the k-means algorithm. A mixture of two types of profiles occurs throughout the middle latitudes of the study area, while the third type is found in its northern and southern regions. This geographic pattern may in part be due to the year of collection. Attempts to relate the magnitude of the coefficients of variation to several ecological indices were unsuccessful. [Variability, variability profiles, geographic variation, coefficients of variation, Pemphigus.] This study investigates whether relative morphological variability varies geographically. A measure of variability is a fundamental parameter in evolutionary research because of the intimate relationship between natural selection and variability. Natural selection shapes variability and is in turn limited in its potential effects by the extent of the variability of a given character. Low variability in a

https://www.jstor.org/stable/pdfplus/2992302.pdf

Robert R. Sokal

Papers

Ancient Movement Patterns Determine Modern Genetic Variances in Europe

Thurstone's analytical method for simple structure and a mass modification thereof

Further Experiments on Competition Between Strains of House Flies

Numerical Taxonomy@@@Principles of Numerical Taxonomy.

Geographic Variation in Variability of Pemphigus Populicaulis