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

Wombling is a method for discovering boundaries in a collection of continuous variables obsmed at the same geographic localities. We extend this method to categorical data. A categorical wombling statistic C,, which identi$es areas of rapid change, is &$ned for every pair i = 1,. . . , n of adjacent localities, and is equal to the average number of category mismatches at i. We use both simulation and theory to consider the or&r statistics of Ci under null hypotheses of randomness, and of spatial autocorrelation for each variable, but independence between variables. Graph-theoretical statistics derived from C, investigate whether areas of rapid change resemble bmnduries. Computer simulation is used to study the distributions of these under the two null hypotheses. The methods are applied to linguistic data in three European areas. Other potentid applications exist in biology, linguistics, anthropology, and other social sciences. A variable observed at a set of geographic localities may often be profitably viewed as being measured at discrete points on an underlying continuous surface. Wombling, a method first developed by Womble (1951) for gene frequencies and morphological measurements, and later refined by Barbujani, Oden, and Sokal (1989), is a technique for detecting zones of rapid spatial change in a collection of such surfaces. The method rests upon the notion of a “systemic function” defined over the geographic space. At any locality, the systemic function is equal to the average of the absolute values of the gradients of the separate continuous surfaces defined at that locality. Mapping the systemic function over geographic space reveals zones of rapid change. Related ideas have been developed by Monmonier (1973) and Adams (1970). Neal L Oden is a senior scientist at Applied Biomathnnotics, lnc., Setauket, New York. Robert R Sokal is a distinguished professor of ecology and evolution at the State University of New York at Stony Brook. Marie-Jmt?e Fdn is a postdoctoral research associate at the Centre dktudes Nordiqws, Universitk Luval, Quebec. Hans Goebl is a professor of romance linguistics at the University o Salzburg Austria.

Categorical Wombling: Detecting Regions of Significant Change in Spatially Located Categorical Variables

Genetic relations between various Jewish (J) and non-Jewish (NJ) populations were assessed using two sets of data. The first set contained 12 pairs of matched J and NJ populations from Europe, the Middle East, and North Africa, for which 10 common polymorphic genetic systems (13 loci) were available. The second set included 22 polymorphic genetic systems (26 loci) with various numbers of populations (ranging from 21 to 51) for each system. Therefore, each system was studied separately. Nei's standard genetic distance (D) matrices obtained for these two sets of data were tested against design matrices specifying hypotheses concerning the affiliations of the tested populations. The tests against single designs were carried out by means of Mantel tests. Our results consistently show lower distances among J populations than with their NJ neighbors, most simply explained by the common origin of the former. Yet, there is evidence also of genetic similarity between J and corresponding NJ populations, suggesting reciprocal gene flow between these populations or convergent selection in a common environment. The results of our study also indicate that stochastic factors are likely to have played a role in masking the descent relationships of the J populations.

Genetic affinities of Jewish populations.

To explore the extent to which microevolutionary inference can be made using spatial autocorrelation analysis of gene frequency surfaces, we simulated sets of surfaces for nine evolutionary scenarios, and subjected spatially-based summary statistics of these to linear discriminant analysis. Scenarios varied the amounts of dispersion, selection, migration, and deme sizes, and included: panmixia, drift, intrusion, and stepping-stone models with 0-2 migrations, 0-2 selection gradients, and migration plus selection. To discover how weak evolutionary forces could be and still allow discrimination, each scenario had both a strong and a weak configuration. Discriminant rules were calculated using one collection of data (the training set) consisting of 250 sets of 15 surfaces for each of the nine scenarios. Misclassification rates were verified against a second, entirely new set of data (the test set) equal in size. Test set misclassification rates for the 20 best discriminating variables ranged from 39·3% (weak) to 3·6% (strong), far lower than the expected rate of 88·9% absent any discriminating ability. Misclassification was highest when discriminating the number of migrational events or the presence or number of selection events. Discrimination of drift and panmixia from the other scenarios was perfect. A subsequent subjective analysis of a subset of the data by one of us yielded comparable, although somewhat higher, misclassification rates. Judging by these results, spatial autocorrelation variables describing sets of gene frequency surfaces permit some microevolutionary inferences.

A simulation study of microevolutionary inferences by spatial autocorrelation analysis

1. Mixtures of three genotypes (+/+, +/s, s/s) for the autosomal mutant sooty were reared at five initial gene frequencies and four densities. Replication of the experiments resulted in a total of 59,280 beetles being employed in the experiment. The heterozygote is distinguishable in adults. The frequency and dry weight of emerging adults was recorded by genotypes. A rough measure of total developmental time was also obtained. The wild type strain was found to be contaminated with sooty at a gene frequency of 0.02 for most replicates. 2. Adult survivorship is measured as the percentage of egg input for a given genotype. Figure 1 illustrates the results. The lower three densities did not have any pronounced effects; at density 100/g overall survivorship was markedly reduced. The homozygous wild type has the highest survivorship in the study; the heterozygote is intermediate through the lower densities but lowest in survivorship at the highest density. The relative survivorships of the three genotypes depend on the gene frequency of sooty: at 0.25qs relations may be summarized by +/+ > s/s > +/s, at 0.5qs by +/+ > +/s > s/s and at 0.75qs by +/s > +/+ > s/s. Relationships at 0.5qs are more consistent while those of the other two gene frequencies showed some heterogeneity among replicates. From the results it is clear that the performance of the heterozygote improves with an increase in the gene frequency of sooty. 3. Dry weights of adults were highest at 20/g. The three genotypes weighed as follows when in mixed culture: s/s >> +/+ > +/s. Gene frequency in the cultures has a marked effect on weights of +/+ and +/s individuals. These responses are illustrated in figure 2. Approximation to straight line functions are obtained when weight of +/+ and +/s individuals is graphed as a function of the proportion of +/s plus s/s individuals in the population. Thus, weight is not simply a function of the gene frequency of sooty in a culture, but of the frequencies of the two genotypes carrying the s allele. 4. Heterozygotes are intolerant to crowding, especially with their own genotype. Weight relations among genotypes depend on whether the beetles were reared in pure or mixed culture. Thus, the performance of genotypes when interacting with other genotypes cannot be predicted from their performance in pure culture. 5. At the higher gene frequencies heterozygotes predominate among the early emerging adults, while s/s individuals are largely late emerging ones. 6. The facilitation and interaction among genotypes is discussed from the general point of view of considering quality as well as frequencies of genotypes as comprising part of the milieu of any individual. Such studies will ultimately lead to adding a genetic dimension to our understanding of ecological phenomena.

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Robert R. Sokal

Papers

Categorical Wombling: Detecting Regions of Significant Change in Spatially Located Categorical Variables

Genetic affinities of Jewish populations.

A simulation study of microevolutionary inferences by spatial autocorrelation analysis

Competition among Genotypes in Tribolium Castaneum at Varying Densities and Gene Frequencies (the Black Locus)

The Species Problem Reconsidered