Numerical Taxonomic Methods Research Articles

On a method for character weighting a similarity coefficient, employing the concept of information

A similarity coefficient is defined in which characters are weighted in proportion to the information they convey, and in inverse proportion to their overall association with other characters. The characters may be discrete or continuously variable, or a mixture of both. With discrete characters, and under ideal conditions, it reduces to the ordinary Sokal-Mitchener coefficient. Under nonideal conditions, it offers a significant gain in the objectivity of numerical taxonomic methods by reducing considerably the need for personal skill and judgment in the selection and scoring of characters for use in an analysis of a group of OTU’s.

PHENETIC SIMILARITY AND PHYLOGENETIC RELATIONSHIPS AMONG STRAINS OF ORYZA PERENNIS, ESTIMATED BY METHODS OF NUMERICAL TAXONOMY.

The relationship between taxa can be estimated from different viewpoints: (a) comparison of characters ranging from protein structure to outward appearance (phenetics, if overall similarity is considered), (b) crossability, meiotic chromosome behavior, fertility and other features of hybrids, (c) ecological and distributional features, and so on. These represent different aspects of relationship between existing taxa, but do not necessarily indicate phylogeny. The advances in numerical taxonomy, however, have inevitably tempted workers to consider the possibility of deduction of phylogeny by numerical evaluation of information obtained from existing organisms (Doolittle and Blomback, 1964; Camin and Sokal, 1965; Wilson, 1965; Throckmorton, 1965; Fitch and Margoliash, 1967; Cavalli-Sforza and Edwards, 1967; Horne, 1967). Oryza perennis Moench is a wild species distributed in swampy habitats throughout the humid tropics, and is a complex of different forms. Usually its strains are classified into Asian, African and American forms or groups (I. R. R. I. 1964, p. 251252). The taxonomy and nomenclature of this species have been a matter of controversy among taxonomists; Tateoka (1963) considered the African form as a distinct species, 0. barthii A. Chev., and called other forms 0. rufipogon Griff., while Henderson (1964) considered all three forms as subspecies of 0. perennis. The present writer takes the latter view. The Asian annual form has become known under various names, for instance, 0. sativa f. spontanea Roschev. or 0. sativa var. fatua Prain or 0. rufipogon subsp. rufipogon. It is considered here as a form of 0. perennis, since the strains of the Asian group show a continuous array of intergrades between perennial and annual types (Morishima et al., 1961). Further, the present work suggests that certain strains from New Guinea and Australia may be considered as a new, Oceanian, form. The various strains all have the same number of chromosomes (n = 12), and can be hybridized with one another. The F1 hybrids show no disturbance in meiotic chromosome pairing, but show sterilities of varying degrees and some other deteriorative phenomena (Chu et al., 1969). The strains are adapted to different kinds of ecological niches and differ in their breeding system (Oka and Morishima, 1967). We initiated studies of this species because its Asian perennial form was considered to be the progenitor of cultivated rice, Oryza sativa L. (Oka and Chang, 1962; Oka, 1964). For a systematic investigation of variations within 0. perennis, data for various characters of the strains and their F1 sterility relationships were analyzed by methods of numerical taxonomy. This paper deals with the methods and results, distinguishing between the phenetic and phylogenetic standpoints. An attempt was made to introduce a relative time scale into the diagram showing the hypothesized phylogenetic relationships of the strains.

Phenetic Similarity and Phylogenetic Relationships Among Strains of Oryza perennis, Estimated by Methods of Numerical Taxonomy

Phenetic Similarity and Phylogenetic Relationships Among Strains of Oryza perennis, Estimated by Methods of Numerical Taxonomy

Measurement and Classification of Genetic Variability in Horseradish1

Abstract The genetic variability of 20 cultivars of horseradish, Armoracia rusticana Gaertn., Mey., & Scherb., was measured and classified. These cultivars were chosen from a gene pool containing over 400 cultivars, and collectively they appeared to represent the extreme and intermediate forms of variability found in horseradish. Two methods of classification were compared. One classification was based on 2 highly diagnostic characters that showed the extreme and intermediate limits of the germplasm in the form of a scatter diagram. The other classification was based on 40 characters. For this classification methods of numerical taxonomy were used to show the germplasm complex by scatter diagrams and phenograms. The two classifications appeared to be equal in defining the extreme limits of the genetic variability. The main area of disagreement was found among the relative positions of the intermediate forms or genotypes. The use of scatter diagrams as an aid to the selection and conservation of genetic variability for future use is discussed.

Robustness of Numerical Taxonomic Methods and Errors in Homology

The effect of random errors in homology on the results of a numerical taxonomic study was investigated. The correlation coefficient was found to be much more sensitive to the effects of these errors than the distance coefficient. These analyses suggest that in a study composed of around 74 characters one could tolerate confusions about homologies in as many as 6 characters, but not very many more. We investigated the effect of errors in determining the homology of characters on the results of a numerical taxonomic study. The study gives an indication of how phenograms, resulting from cluster analysis of correlation and distance coefficients by an unweighted pair group method (UPGMA, see Sokal and Sneath, 1963) change when operational homology is determined at random within a set of characters where the correct homology is less certain.

Robustness of Numerical Taxonomic Methods and Errors in Homology

Robustness of Numerical Taxonomic Methods and Errors in Homology

Immunologic Comparisons of Selected Coleoptera With Analyses of Relationships Using Numerical Taxonomic Methods

The status of the cicindelids with respect to the carabids (Coleoptera) is an issue among taxonomists. Data from immunoelectrophoresis and immunodiffusion were processed using detailed computerized, numerical taxonomic methods which included cluster and principal components analyses. Results indicated that the cicindelids are preferably regarded as a subfamily of the family Carabidae. The genera in the family Carabidae exhibited large amounts of molecular variation. In detailed comparisons, using the computer, unstandardized logarithms of the per cent cross-reaction values gave the highest correlations of the immunological data with morphological classifications of the Coleoptera. In the Coleoptera the status of the cicindelids (tiger beetles) with respect to the carabids (ground beetles) and to the suborder Adephaga is still an issue among taxonomists. A number of taxonomists, including LeConte and Horn (1883), Blatchley (1910:25-242, 247-270), Leng (1920: 39-86, 157, 235, 255), Portevin (1929), Bradley (1930:307-325), Jeannel (1949: 1032-1069), Borror and DeLong (1954:296426), and Ball (1963:55-182, personal communication in 1966 and 1968), consider the cicindelids as a separate family; others, such as Hatch (1938:225-240), Crowson (1955), Moore (1958), Linssen (1959:51157 [series 1], 70-122 [series 2] ), and Bell (1967), place the tiger beetles in a subfamily, Cicindelinae, of the family Carabidae. For the purpose of discussion in this paper, we shall refer to the carabids and cicindelids as separate families. Taxonomic investigations in the class Insecta, using immunological techniques, are few in number and have been concerned mostly with orders in the subclass Pterygota. Although beetles have been used incidentally in several immunotaxonomic studies, the work of Butler and Leone (1967b) was the first study dealing exclusively with a wide variety of coleopterans. They observed that, with certain exceptions, the immunological classification of beetles confirmed morphological classifications. Butler (1965) encountered inconsistencies and ambiguities when performing immunological comparisons of carabids and cicindelids. Such findings prompted this investigation, and the work here reported re-examines the carabid-cicindelid relationship. Data were obtained from an extensive series of immunological comparisons of saline extracts of adults from 11 species in the families Carabidae and Cicindelidae. Species from six other families, including two dytiscids, three hydrophilids, and one each from the families Tenebrionidae, Gyrinidae, Scarabaeidae and Meloidae were chosen to provide taxonomic references for comparisons with the carabidcicindelid relationship. Numerical taxonomic methods, including cluster and principal components analyses, were used. METHODS AND MATERIALS The specimens used in this study were collected in the vicinity of Lawrence, Kansas, except Tenebrio, which was cultured in the laboratory. The beetles were kept alive and unfed 24 to 48 hours prior to processing in the laboratory to permit the digestion of any food in the gut, then were quick-frozen and stored at -150C in airtight containers until needed for homogenization.

Immunologic Comparisons of Selected Coleoptera with Analyses of Relationships Using Numerical Taxonomic Methods

Immunologic Comparisons of Selected Coleoptera with Analyses of Relationships Using Numerical Taxonomic Methods

The Science of Diversity

This is the first of the newly instituted presidential addresses of the Systematics Association and explores the future of systematics. Simpson's definition of “systematics” as “the study of differentiation” has been followed by developments in the fields of molecular biology, epigenetics, biophysics, prebiology, and exobiology. A “new taxonomy” will arise when the methods of numerical taxonomy are employed for phylogenetic research. Perhaps in the future systematics will invade the province of non-biological evolution.

The Relationships of Bacteria Within the Family Bacteroidaceae as shown by Numerical Taxonomy

SUMMARY: A comparison, by numerical taxonomy methods, was made of 72 named or freshly isolated strains of Gram-negative anaerobes which were considered to belong within the family Bacteroidaceae. In the first analysis 57 strains were compared. Representative strains were then selected and compared with additional named strains in a second analysis. Four phena were identified: (1) strains of Sphaerophorus, Fusobacterium and Bacteraides melaninogenicus, (2) Bacteroides, (3) unnamed poultry isolates, (4) a second group of unnamed poultry isolates. The most useful differential tests were found to be: (a) cell morphology, (b) the terminal pH value in glucose broth and the production of formic, acetic, propionic or butyric acids, (c) the production of propionic acid from threonine, (d) growth stimulation by bile, (e) the effect of various inhibitors.

A Study of Faunal Resemblance Using Numerical Taxonomy and Factor Analysis

This paper is an analysis of patterns of animal distribution by means of ( 1 ) calculation and clustering of a distance matrix, (2) factor analysis and trend surface maps of scores of five centroid factors, and (3) a stereogram of the counties projected on the principal axes. The data, which are the incidences of amphibians, reptiles, and mammals in the 105 counties of Kansas, were used principally for illustrative purposes, and comprise 185 OTU's consisting of 137 species (37 of which were subdivided into 85 subspecies). Five factors were extracted from a matrix of correlations among OTU's and mapped by trend surface analysis. These were shown to be of interest even though they yielded overlapping faunal zones. The predictive powers of the method, by the inclusion of environmental variables, is discussed. The present study is an application of certain multivariate analytical techniques in the description and analysis of faunal distribution patterns. Quantitative estimates of faunal resemblances have been largely limited to coefficients of resemblance, which authors often derive anew for a particular use. Simpson (1960) and Long (1963) have reviewed the various coefficients in the literature. Hagmeier and Stults (1964) and Hagmeier (1966) used a coefficient which measured the relative number of species distributions ending in areas of 50-miles-square. They grouped areas with low values into faunal zones, using areas of high values as borders. Coefficients were calculated between faunal zones and the resulting matrix was clustered by numerical taxonomic methods. R-type factor analyses of species distributions have been used extensively by some ecologists to describe vegetation (see Goodall, 1954). The uses of factor analysis in systematics have been reviewed by Sokal (1965). The major purpose of this analysis is to test the applicability of the methods of numerical taxonomy and trend surface analysis to biogeographic distribution patterns. The analysis is best viewed primarily as an illustrative example and not as a definitive study of the distribution of vertebrates in Kansas. THE DATA The data were taken from distribution maps for Kansas by Hall (1955), for mammals, and Smith (1956), for amphibians and reptiles. Because the data were used only as an example, the maps were assumed to depict accurately the distributions of these animals without further corroboration. The study included 61 species of mammals (17 of which were divided into 2 subspecies each, 6 into 3 subspecies, 1 into 4 subspecies, and 1 into 5 subspecies), 52 species of reptiles (7 of which were divided into 2 subspecies each), and 24 species of amphibians (5 of which were divided into 2 subspecies each), yielding a total of 185 OTU's. The raw data can be obtained by writing to the author. They comprise a data matrix consisting of ones and zeroes, representing presence and absence, respectively, of each species or subspecies within each of the 105 counties. The computations were carried out at the Computation Center of The University of Kansas using the NT-SYS system of multivariate routines developed by F. J. Rohlf, R. L. Bartcher and J. R. L. Kishpaugh for the IBM 7040 and the GE 625 computers. RESULTS USING A PHENOGRAM

A classification of marine microorganisms by numerical taxonomy

A method of numerical taxonomy is presented, namely a clustering technique by which bacteria are classified into clusters according to their overall similarity. In this way it is possible to establish a taxonomic system and hence to construct dendrograms. It is furthermore possible to evaluate the fundamental characteristics of the clusters by the determination of typical sequences.

A numerical taxonomy of Orthopteroid insects

Two numerical taxonomic methods, including one that incorporates phylogenetic ideas and one which has a strictly phenetic approach, were applied to the evaluation of the affinities of the orthopteroid orders of insects. These methods were adapted to the special problems which arise when higher taxa are being compared. A total of 92 characters covering most of the internal and external anatomy served as the basis for the calculations, which indicated that similar diagrams of affinities were obtained, whether or not phylogenetic ideas were incorporated into the analysis. The stability of the pattern of affinities was such that repeating the analysis with a random sample of 30 characters instead of the full set of 92 entrained only trivial differences. Although the characters used in this study were qualitative, the extent to which existing multi- variate theory can be used in evaluating the results is stressed. Australian orthopteroids were mainly used for this experiment. A close relationship between the Australian Morabinae and the South American Proscopiidae was found. This group seems to have split off at an early stage from the stem of the Caelifera, which is distinct from the stem bearing the Ensifera. Another fairly close relationship revealed was that between the Phasmatodea and the Dermaptera. Attempts to reveal inconsistencies in the currently accepted taxonomic groupings suggested that the distinction between blattids and mantids within the Dictyoptera is of less than subordinal rank. The essential homogeneity of the orthopteroid orders is shown by the fact that even the most disparate groups share almost half the 92 characters.

Bacteriological Studies on the White Perch, Roccus americanus

A total of 169 bacterial cultures were isolated from the internal organs of healthy white perch (Roccus americanus), and were characterized by the method of numerical taxonomy. These cultures sorted into 7 major groups and were identified as representingBacillus, achromobacter, Pseudomonas, Aeromonas, Enterobacter, andMicrococcus.

Taxonomic Structure from Randomly and Systematically Scanned Biological Images

Random masks made from twenty-five IBM cards, each perforated with twenty-five randomly chosen holes, were placed over black and white drawings of twenty-nine of Caminalcules and pupae of thirty-two species of Culicine mosquitoes. Black lines appearing through a hole were scored 1, and empty holes were scored O. Similarity matrices were constructed on the basis of matching scores for corresponding masks and holes. The resulting phenograms agreed well with previous numerical taxonomic studies obtained by deliberately looking for and scoring characters. Complete scanning of the entire image also gave satisfactory results, but classifications were not necessarily better than by the random scanning method. Increasing the size of the apertures in the mask degraded the classification somewhat when compared with the complete scans, but it is not obvious that the overall classifications so obtained are worse than those from the complete scan. Some of the problems of scanning organisms for taxonomic analysis and the implications of such work for taxonomy are discussed. One of the major bottlenecks in taxonomic procedure at the present time is the inability of biologists to measure and record the diversity of organized nature at speeds and in quantities that present computer technology is prepared to handle (Sokal and Sneath, 1966). Once taxonomic data are available, rapid methods of computing similarities among taxa and defining taxonomic structure exist through the methods of numerical taxonomy (Sokal and Sneath, 1963). Among automatic data recording devices, optical scanners are likely to have a greater impact on the field of taxonomy than most others. Such scanners 'Contribution No. 1286 from the Department of Entomology, The University of Kansas and paper No. 8 in a series entitled Experiments in Numerical Taxonomy, of which Sokal (1961), Rohlf and Sokal (1962), Sokal and Rohlf (1962), Rohlf and Sokal (1965), Rohlf (1963), Michener and Sokal (1966), and Sokal and Michener (1967) are the first seven papers. This investigation was supported by grant GM11935 and also in part by a Public Health Service research career program award (No. 3-K3-GM-22, 021-OlSI), both from the National Institute of General Medical Sciences to Robert R. Sokal. A preliminary report on portions of this work has been published (Sokal and Rohlf, 1966). 2 C. D. Michener and P. H. A. Sneath gave us the benefit of their comments on an earlier draft of this paper. We are indebted to Ronald Bartcher, Yu-Jen Chen, and William G. Hanis for technical assistance. convert objects or drawings, and images from photographs, film, microscopes, or other sources, into digitized input for the computer by measuring the optical density in many small areas of the image and converting this measurement into a numerical code. In using optical scanners for taxonomic descriptions, two distinct approaches should be separated. A logically simple approach would be the measurement of predefined characters. From the scanned image of an organism the length, breadth, circumference, surface area, and so forth, could be computed as long as homologous landmarks for these measurements are defined for the computer. An example in point is scanning to recognize and classify chromosome configurations (Ledley, 1964). The trend surface approach by Sneath (1967) also falls into this category. A second, more challenging approach is to program the computer to recognize likenesses among scanned structures and on the basis of these establish operational homologies and define characters that subsequently are measured. This would require extremely sophisticated programming. A simpler and more simple-minded alternative to this approach is to record agreement in visible structures over selected minute areas of the images of two orga-

A Numerical Taxonomic Analysis of the Peripsocidae of the Oriental Region and the Pacific Basin

The relationships of 83 species of psocids of the family Peripsocidae (Insecta: Psocoptera) were analysed numerico-taxonomically, using alternative methods of processing. The results of using different sets of adult morphological characters and different combinations of them were compared. The effect of admitting a large number of species with incomplete data (known from one sex only) into the system was investigated. Certain modifications of the accepted classification of the family were suggested. Numerical taxonomy was developed to provide an objective and repeatable method of evaluating the phenetic affinity between taxonomic units (see Sokal and Sneath, 1963). The method rests on the hypothesis that there are no special groups of genes the effects of which are confined to single mQrphological regions, and that a random sample of the genotype is best obtained by sampling many and various characters. A large number of characters is used and each character is considered to be of equal weight, and the larger the number of characters used, the more stable is the value of the overall similarity coefficient, up to an asymptote which will vary for each analysis. Rohlf (1963) used numerical taxonomic methods to compare the classification of Aedes using only adult characters with that using only larval characters and found a definite though low correlation between the resulting classifications. In 1963 Sokal and Michener (see Rohlf, 1963) compared the results of classifications based on female and male, and on head and non-head characters, and found similar values of correlation. In the study reported here species with incomplete data (known from one sex only) are admitted to the analysis by degrees, and the effect of these admissions on the classification based on individuals with information on both sexes is noted. Also, different sets of characters are omitted in different analyses and the results compared. Alternate methods in the processing of data are used, in order to find the combination best suited for the classification of Peripsocidae. MATERIAL AND METHODS General.-Eighty-three species of the family Peripsocidae representing three of the five genera were examined, using numerical taxonomic methods. Previously described species of which examples were unobtainable were not included in the study, due to reason which will be obvious later. A preliminary survey was run to find some 60 characters that vary among species (Sokal and Sneath, 1963). These characters were then carefully studied and their characteristic expression or dimensions recorded, males and females separately. Whenever possible, five of each sex (selected at random) were used. This figure represented over 30% of the sample in hand in 75% of the species studied. In the present study 146 characters were used, comprising 52 asexual characters, 52 female charters and 42 male characters. The distribution of these characters over the animal was as follows: 14 head characters, 45 thoracic characters and 87 abdominal characters. Of these, 90 are descriptive, 16 metric, 20 ratios, and 20 meristic. A histogram of these characters and the number thereof applicable to Ectopsocus and Peripsocus is provided in Fig. 1; the species, their code numbers, and the number of individuals used in this study are listed in Table 1. A description of characters in some detail can be found in the manuscript of a thesis by the junior author submitted for the degree of Ph.D. at the University of Hong Kong. Analyses of the distribution of the number of states for the various types of

PHENETICS OF NATURAL POPULATIONS I. PHENETIC RELATIONSHIPS OF INSULAR POPULATIONS OF THE SIDE-BLOTCHED LIZARD.

This report discusses an attempt to apply the methods of numerical taxonomy in assessing the phenetic relationships of closely related populations of a lizard, the side-blotched lizard (Uta stanburiana, sensu lato) on 18 islands in the Gulf of California and from two mainland populations, Tonopah, Nevada, and Bahia de los Angeles in Baja California, Mexico (Fig. 1). Certain methodological questions are raised and discussed. These include the problem of growth in comparative studies, the effect of using a small number of correlated characters in such a numerical analysis, and the appropriateness of a two-dimensional hierarchy to represent what may be a non-hierarchical pattern. The biogeography of the Gulf of California region, and the evolutionary trends of the sideblotched lizards on the Gulf islands are discussed elsewhere (Soule and Sloan, 1966; Soule, 1966).

Correlated Characters in Numerical Taxonomy

The effect of using only intercorrelated characters in a nuimerical taxonomic study was investigated using 74 external morphological characters of pupae in 45 species of North American mosquitoes. Correlation and distance coefficients were computed based upon standardized data. Cluster analyses and factor analyses were performed and compared. In addition, analyses were made of the correlation among the characters using centroid components analysis and multiple factor analysis with rotation to simple structure. The only effect of using correlated characters appears to be that it causes the generic clusters to appear very elongated in the n dimensional character space. Standard methods of cluster analysis have a tendency to make the OTU's at the ends of these clusters appear much more isolated than they should be. Methods for correcting for this bias were discussed. This study is concerned with an investigation of the effects of using numerical taxonomic methods when the characters were intentionally selected so that the entire set of characters would be expected to be intercorrelated. This is of special interest since numerical taxonomic methods have been criticized (e.g., Mayr, 1965) for not taking into consideration the correlation among the characters. In addition, methods for investigating the patterns of correlation among the characters were also explored to see if more information could be extracted from the data than has usually been done in numerical taxonomic studies. It was also of interest to investigate the effects of using a set of characters (pupal chaetotaxy) which were generally considered poor compared to the more conspicuous and more numerous group and specific characters of the larvae and adults upon which the conventional classifications are largely based. The purposes of this study are therefore largely experimental and not necessarily to form the most natural classification of the organisms studied (although it appears that a useful phenetic classification was obtained).

On Apharyngostrigea (Apharyngostrigea) simplex (Johnston, 1904) new comb, and A. (Apharyngostrigea) serpentia n. sp. (Strigeidae: Trematoda) with an Evaluation of the Taxonomy of the genus Apharyngostrigea Ciurea, 1927 by the method of Numerical Taxonomy

1. The anatomy of Apharyngostrigea (Apharyngostrigea) simplex (Johnston, 1904) new comb, from young cattle egrets is described in detail, involving the reconstruction of its internal organisation from serial sections.2. The relationships of the species within the genus Apharyngostrigea Ciurea, 1927 is discussed using the method of Numerical Taxonomy by Sneath and Sokal (1902). It is found that the original genus can be split into two genera. The genus Apharyngostrigea comprises two subgenera; Apharyngostrigea (Apharyngostrigea) n. subgen. and A. (Brasiliana) n. subgen. made up of seven species groups. The generic diagnosis of Apharyngostrigea Ciurea, 1927 and Chaseostrigea n. gen. are given as well as a key for separating the species of the genus Apharyngostrigea.

CLASSIFICATION OF SOILS BY NUMERICAL METHODS

SummaryTwenty‐three profile descriptions of soils in Glamorganshire and the laboratory measurements on soil samples of the ninety‐one horizons into which they were divided by the surveyor were examined by the methods of numerical taxonomy. The similarities between the horizons calculated by these methods were reduced to a table of similarities between profiles by averaging the similarities of those horizons that matched best, judged by their similarity and order in the profile. The soil‐similarity matrix was sorted to give a dendrogramme. Calculation of the latent roots and vectors of the matrix gave a two dimensional representation of the relationships between the soils. The Great Soil Groups to which the surveyor assigned his profiles can be picked out in this diagram.