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

The classical method for analysis of variance of data divided in geographic regions is impaired if the data are spatially autocorrelated within regions, because the condition of independence of the observations is not met. Positive autocorrelation reduces within-group variability, thus artificially increasing the relative amount of among-group variance. Negative autocorrelation may produce the opposite effect. This difficulty can be viewed as a loss of an unknown number of degrees of freedom. Such problems can be found in population genetics, in ecology and in other branches of biology, as well as in economics, epidemiology, geography, geology, marketing, political science, and sociology. A computer-intensive method has been developed to overcome this problem in certain cases. It is based on the computation of pooled within-group sums of squares for sampled permutations of internally connected areas on a map. The paper presents the theory, the algorithms, and results obtained using this method. A computer program, written in PASCAL, is available.

Approximate analysis of variance of spatially autocorrelated regional data

Allele frequency distributions were generated by computer simulation of five models of microevolution in European populations. Genetic distances calculated from these distributions were compared with observed genetic distances among Indo-European speakers. The simulated models differ in complexity, but all incorporate random genetic drift and short-range gene flow (isolation by distance). The best correlations between observed and simulated data were obtained for two models where dispersal of Neolithic farmers from the Near East depends only on population growth. More complex models, where the timing of the farmers' expansion is constrained by archaeological time data, fail to account for a larger fraction of the observed genetic variation; this is also the case for a model including late Neolithic migrations from the Pontic steppes. The genetic structure of current populations speaking Indo-European languages seems therefore to largely reflect a Neolithic expansion. This is consistent with the hypothesis of a parallel spread of farming technologies and a proto-Indo-European language in the Neolithic. Allele-frequency gradients among Indo-European speakers may be due either to incomplete admixture between dispersing farmers, who presumably spoke proto-Indo-European, and pre-existing hunters and gatherers (as in the traditional demic diffusion hypothesis), or to founder effects during the farmers' dispersal. By contrast, successive migrational waves from the East, if any, do not seem to have had genetic consequences detectable by the present comparison of observed and simulated allele frequencies.

Indo‐European origins: A computer‐simulation test of five hypotheses

Fifteen allele frequencies have previously been determined for 50 villages of the Yanomama, an Amerindian tribe from southern Venezuela and northern Brazil. These frequencies were subjected to spatial autocorrelation analysis to investigate their population structure. There are significant spatial patterns for most allele frequencies. Clinal patterns, investigated by one-dimensional and directional spatial correlograms, were relatively few in number and were moderate in strength. Overall, however, there is a marked decline in genetic similarity with geographic distance. The results are compatible with a hierarchic population structure superimposed on the geography, and generated by a stochastic fission-fusion model of village propagation, followed by localized gene flow. Strong temporal autocorrelations of allele frequencies based on linguistic-historical distances representing time since divergence were also found. There appears to be a stronger relation between geography and linguistic-historical hierarchic subdivisions than between either feature and genetic distances. These findings confirm by different approaches the results of earlier analyses concerning the important roles of both stochastic and social factors in determining village allele frequencies and the occurrence within this tribe of some allele frequency clines most likely due to the operation of chance historical processes.

https://www.genetics.org/content/genetics/114/1/259.full.pdf

The genetic structure of a tribal population, the Yanomama Indians. XV. Patterns inferred by autocorrelation analysis.

Summary

From the biological viewpoint the tasks of systematics may be subdivided into analyses of infraspecific variation (both intra- and interpopulation studies), the separation of genetic from environmental effects on the phenotype, the definition of species (and possibly subspecies), the definition of supraspecific taxa, the measurement of similarity among taxa, life-history stages or organs, the measurement of evolutionary rates, the evaluation of biogeographical relationships and information-handling problems.



In all types of statistical analysis in systematics the correct choice of characters to be measured is of great importance. The sources of error and bias in measurement are listed here and ways are discussed for overcoming their effects. Ratios, frequently employed in systematics, have certain numerical disadvantages. Frequency distributions of characters provide insight into biological processes affecting the characters and they test assumptions about the distributions implied in the various statistical analyses. Simple description of single samples is carried out by statistics of location and dispersion, such as the mean and the variance.



Interpopulation variation usually involves two-dimensional comparison of geographically differing populations, but other comparisons are discussed as well. The analysis of variance is generally applicable. Care must be taken in choosing an appropriate sampling distribution for testing significance of differences among means. The frequently employed e-tests and the so-called ‘Dice-grams’ are not suitable. Graphical methods for representing geographical variation are still in need of considerable improvement. The definition of subspecies and the so-called percentage rules are critically reviewed.



Covariation between characters is studied by means of correlation and regression techniques. In correlation, individuals are randomly chosen with respect to two variables, while regression deals with the dependence of one (randomly chosen) variable upon the other, whose values are assumed to be fixed. Regression can be used in systematics descriptively (to show the relations of one variable upon the other), correctively (to permit samples differing in an important causal variable to be compared for other variables), and as an explanatory device (to relate character variation to climatic or other ecological factors).



Multivariate analyses permit simultaneous statistical treatment of several characters. They are laborious but the ever-growing speed and capacity of digital computers will increase their application. Resolution of covariation is carried out by analyses of covariance, partial correlations and factor analysis. It aims at understanding the interrelationships of characters among themselves. Partitioning of covariation into components representing environmental and genetic forces of various kinds helps to understand evolutionary factors in a given study.



The methods of numerical taxonomy for quantifying similarities among taxa and describing taxonomic structure are briefly reviewed. Similar methods may aid in biogeographic problems and in the measurement of rates of evolution. The discrimination of groups representing different taxa or sexes can be accomplished by means of discriminant functions.



Profound changes in the cataloguing and data-handling aspects of systematics are resulting from the development of electronic data processing. Many statistical computations in systematics can also be appreciably accelerated by processing them on a computer.



This article was prepared during my tenure of a Fulbright professorship at Tel Aviv University in Israel. I am greatly indebted to Professor H. Mendelssohn, Chairman of the Zoology Department of that institution, for his cordial hospitality and encouragement. The following persons have read various drafts of this manuscript and their comments and criticisms are very much appreciated: Anthony J. Boyce (Oxford University), Paul R. Ehrlich, Larry G. Mason (Stanford University), K. Reuven Gabriel (Hebrew University, Jerusalem), and F. James Rohlf (University of California, Santa Barbara).

Statistical methods in systematics.

We developed a simulation model of phylogenesis with which we generated a large number of phylogenies and associated data matrices We examined the characteristics of these and evaluated the success of three taxonomic methods (Wagner parsimony, character compatibility, and UPGMA clustering) as estimators of phylogeny, paying particular attention to the consequences of changes in certain evolutionary assumptions: relative rate of evolution in three different evolutionary contexts (phyletic, parent lineage, and daughter lineage); relative rate of evolution in different directions (novel forward, convergent forward, or reverse); variation of evolutionary rates; and topology of the phylogenetic tree Except for variation of evolutionary rates, all the evolutionary parameters that we controlled had significant effects on accuracy of phylogenetic reconstructions Unexpectedly, the topology of the phylogeny was the most important single factor affecting accuracy; some phylogenies are more readily estimated than others for simply historical reasons We conclude that none of the three estimation methods is very accurate, that the differences in accuracy among them are rather small, and that historical effects (the branching pattern of a phylogeny) may outweigh biological effects in determining the accuracy with which a phylogeny can be reconstructed

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Robert R. Sokal

Papers

Approximate analysis of variance of spatially autocorrelated regional data

Indo‐European origins: A computer‐simulation test of five hypotheses

The genetic structure of a tribal population, the Yanomama Indians. XV. Patterns inferred by autocorrelation analysis.

Statistical methods in systematics.

Factors determining the accuracy of cladogram estimation: evaluation using computer simulation.