MULTIVARIATE ANALYSIS IN ECOLOGY AND SYSTEMATICS: PANACEA OR PANDORA'S BOX?

Multivariate analysis provides statistical methods for study of the joint rela­ tionships of variables in data that contain intercorrelations. Because several variables can be considered simultaneously, interpretations can be made that are not possible with univariate statistics. Applications are now common in medicine (117), agriculture (218), geology (50), the social sciences (7, 178, 193), and other disciplines. The opportunity for succinct summaries of large data sets, especially in the exploratory stages of an investigation, has contrib­ uted to an increasing interest in multivariate methods. The first applications of multivariate analysis in ecology and systematics were in plant ecology (54, 222) and numerical taxonomy (187) more than 30 years ago. In our survey of the literature, we found 20 major summaries of recent applications. Between 1978 and 1988, books, proceedings of sym­ posia, and reviews treated applications in ecology (73, 126, 155, 156), ordination and classification (13, 53, 67, 78,81,83,90,113,121,122,159), wildlife biology (33, 213), systematics (148), and morphometries (45, 164,

[1]  J. Felley,et al.  Multivariate Assessment of Environmental Preferences of Cyprinid Fishes of the Illinois River, Oklahoma , 1983 .

[2]  S. Peterson,et al.  Seasonal micro-habitat relationships of ruffed grouse in southeastern Idaho , 1985 .

[3]  F. Rohlf.  PERSPECTIVES ON THE APPLICATION OF MULTIVARIATE STATISTICS TO TAXONOMY , 1971 .

[4]  Lawrence D. Harder,et al.  Morphology as a Predictor of Flower Choice by Bumble Bees , 1985 .

[5]  A. Dempster.  Elements of Continuous Multivariate Analysis , 1969 .

[6]  J. Rising,et al.  The measurement of overall body size in birds , 1989 .

[7]  P. Digby,et al.  Multivariate Analysis of Ecological Communities , 1987, Population and Community Biology.

[8]  M. Austin,et al.  New approaches to direct gradient analysis using environmental scalars and statistical curve-fitting procedures , 1984 .

[9]  H. Charles Romesburg,et al.  WILDLIFE SCIENCE: GAINING RELIABLE KNOWLEDGE , 1981 .

[10]  László Orlóci,et al.  Applying Metric and Nonmetric Multidimensional Scaling to Ecological Studies: Some New Results , 1986 .

[11]  T. Cook,et al.  Quasi-experimentation: Design & analysis issues for field settings , 1979 .

[12]  R. Corruccini.  Shape in morphometrics: Comparative analyses , 1987 .

[13]  R. M. Thorndike,et al.  Correlational Procedures for Research , 1979 .

[14]  Peter A. Lachenbruch,et al.  Classification: Methods for the Exploratory Analythi of Multivariate Data , 1982 .

[15]  R. R. Hocking.  Developments in linear regression methodology: 1959-1982 , 1983 .

[16]  J. Mosimann,et al.  NEW STATISTICAL METHODS FOR ALLOMETRY WITH APPLICATION TO FLORIDA RED‐WINGED BLACKBIRDS , 1979, Evolution; international journal of organic evolution.

[17]  B. Efron.  Bootstrap Methods: Another Look at the Jackknife , 1979 .

[18]  Joan T. Richtsmeier,et al.  Finite-Element Scaling Applied to Sexual Dimorphism in Rhesus Macaque (Macaca Mulatta) Facial Growth , 1986 .

[19]  B. Efron,et al.  A Leisurely Look at the Bootstrap, the Jackknife, and , 1983 .

[20]  M. Turelli.  PHENOTYPIC EVOLUTION, CONSTANT COVARIANCES, AND THE MAINTENANCE OF ADDITIVE VARIANCE , 1988, Evolution; international journal of organic evolution.

[21]  S. Ferson,et al.  Measuring shape variation of two-dimensional outlines , 1985 .

[22]  Stephen E. Fienberg,et al.  The analysis of cross-classified categorical data , 1980 .

[23]  M. Nei.  Molecular Evolutionary Genetics , 1987 .

[24]  László Orlóci,et al.  Multivariate Analysis in Vegetation Research , 1975 .

[25]  Donald F. Charles,et al.  Relationships between surface sediment diatom assemblages and lakewater characteristics in Adirondack lakes , 1985 .

[26]  F. Bookstein,et al.  A PATH‐ANALYTIC MODEL FOR THE MEASUREMENT OF SELECTION ON MORPHOLOGY , 1989, Evolution; international journal of organic evolution.

[27]  S. Gould,et al.  THE CONSEQUENCES OF BEING DIFFERENT: SINISTRAL COILING IN CERION , 1985, Evolution; international journal of organic evolution.

[28]  Stephen E. Fienberg,et al.  The Analysis of Multidimensional Contingency Tables , 1970 .

[29]  Newton E. Morton,et al.  The Neolithic Transition and the Genetics of Populations in Europe. , 2022 .

[30]  C. McCulloch,et al.  Data Analysis and the Design of Experiments in Ornithology , 1985 .

[31]  Alan C. Kamil,et al.  Experimental Design in Ornithology , 1988 .

[32]  A. Flew,et al.  Patterns of Discovery. , 1961 .

[33]  R. Cranley,et al.  Multivariate Analysis—Methods and Applications , 1985 .

[34]  E. Nagel.  The structure of science : problems in the logic of scientific explanation , 1961 .

[35]  D. Goodall,et al.  Objective methods for the classification of vegetation. III. An essay in the use of factor analysis , 1954 .

[36]  R. Green,et al.  A Multivariate Statistical Approach to the Hutchinsonian Niche: Bivalve Molluscs of Central Canada. , 1971, Ecology.

[37]  Geometric and Probabilistic Aspects of Statistical Distance Functions , 1982 .

[38]  M. Hill.  Correspondence Analysis: A Neglected Multivariate Method , 1974 .

[39]  E. C. Pielou.  The Interpretation of Ecological Data: A Primer on Classification and Ordination , 1984 .

[40]  F. Bookstein,et al.  Morphometrics in Evolutionary Biology: The Geometry of Size and Shape Change, With Examples from Fishes , 1985 .

[41]  M. Zelditch.  Evaluating Models of Developmental Integration in the Laboratory Rat Using Confirmatory Factor Analysis , 1987 .

[42]  W. T. Williams,et al.  Multivariate Methods in Plant Ecology: I. Association-Analysis in Plant Communities , 1959 .

[43]  A. J. Collins,et al.  Introduction to Multivariate Analysis , 1982 .

[44]  H. Gauch,et al.  Multivariate analysis of plant communities and environmental factors in Ngari, Tibet , 1986 .

[45]  J. Travis.  VARIATION IN DEVELOPMENT PATTERNS OF LARVAL ANURANS IN TEMPORARY PONDS. I. PERSISTENT VARIATION WITHIN A HYLA GRATIOSA POPULATION , 1983, Evolution; international journal of organic evolution.

[46]  Mike P. Austin,et al.  Continuum Concept, Ordination Methods, and Niche Theory , 1985 .

[47]  R. H. Benson.  Biomechanical stability and sudden change in the evolution of the deep-sea ostracode Poseidonamicus , 1983, Paleobiology.

[48]  R. Ricklefs,et al.  The Correlation Between Ecology and Morphology in Deciduous Forest Passerine Birds , 1984 .

[49]  J. Travis,et al.  A QUANTITATIVE‐GENETIC ANALYSIS OF LARVAL LIFE‐HISTORY TRAITS IN HYLA CRUCIFER , 1987, Evolution; international journal of organic evolution.

[50]  Alvin C. Rencher,et al.  On the use of correlations to interpret canonical functions , 1988 .

[51]  Robert R. Sokal,et al.  A statistical method for evaluating systematic relationships , 1958 .

[52]  Roger S. Thorpe,et al.  A Review of the Numerical Methods for Recognising and Analysing Racial Differentiation , 1983 .

[53]  Leslie F. Marcus,et al.  Morphometrics: Multivariate Analysis of Biological Data. , 1978 .

[54]  J. Hartigan,et al.  Statistical Analysis of Hominoid Molecular Evolution , 1987 .

[55]  R. Sokal,et al.  OTU stability and factors determining taxonomic stability: examples from the caminalcules and the leptopodomorpha , 1984 .

[56]  Peter R. Stopher,et al.  Survey sampling and multivariate analysis for social scientists and engineers , 1979 .

[57]  John W. Tukey,et al.  Data Analysis and Regression: A Second Course in Statistics , 1977 .

[58]  Michael L. Morrison,et al.  Development and testing of linear regression models predicting bird-habitat relationships , 1987 .

[59]  Byron K. Williams,et al.  Assessment of sampling stability in ecological applications of discriminant analysis , 1988 .

[60]  E. C. Pielou,et al.  The Interpretation of Ecological Data: A Primer on Classification and Ordination. , 1986 .

[61]  J. Armstrong,et al.  Derivation of Theory by Means of Factor Analysis or Tom Swift and His Electric Factor Analysis Machine , 2015 .

[62]  John L. Harper,et al.  The Growth, Distribution and Neighbour Relationships of Trifolium Repens in a Permanent Pasture: I. Ordination, Pattern and Contact , 1979 .

[63]  R. Reyment,et al.  Statistics and Data Analysis in Geology. , 1988 .

[64]  N. Moran.  MORPHOLOGICAL ADAPTATION TO HOST PLANTS IN UROLEUCON (HOMOPTERA: APHIDIDAE) , 1986, Evolution; international journal of organic evolution.

[65]  F. Bookstein.  FOUNDATIONS OF MORPHOMETRIeS , 1982 .

[66]  F. A. Bazzaz,et al.  The Response of Natural Ecosystems to the Rising Global CO2 Levels , 1990 .

[67]  John W. Tukey,et al.  We Need Both Exploratory and Confirmatory , 1980 .

[68]  Bruce A. Carnes,et al.  Some Comments on Niche Analysis in Canonical Space , 1982 .

[69]  Richard Levins,et al.  Dialectics and reductionism in ecology , 1980 .

[70]  R. W. Cannon,et al.  Guild structure of a riparian avifauna relative to seasonal cattle grazing , 1988 .

[71]  Fred L. Bookstein,et al.  Foundations of Morphometrics , 1982 .

[72]  S. O'Brien,et al.  A MOLECULAR PHYLOGENY OF THE FELIDAE: IMMUNOLOGICAL DISTANCE , 1985, Evolution; international journal of organic evolution.

[73]  A. Baker,et al.  Morphometric Variation in Introduced Populations of the Common Myna (Acridotheres tristis): An Application of the Jackknife to Principal Component Analysis , 1984 .

[74]  M. Rosenzweig,et al.  Detecting interspecific competition in the field: testing the regression method , 1986 .

[75]  Thomas H. Wonnacott,et al.  Regression: A Second Course in Statistics , 1981 .

[76]  F. Bazzaz,et al.  Differentiation Among Nine Populations of Phlox: Response to Environmental Gradients , 1987 .

[77]  A. D. Gordon,et al.  Classification : Methods for the Exploratory Analysis of Multivariate Data , 1981 .

[78]  Joseph S. Meyer,et al.  Estimating Uncertainty in Population Growth Rates: Jackknife vs. Bootstrap Techniques , 1986 .

[79]  R. R. Hocking.  Developments in Linear Regression Methodology: 1959–l982 , 1983 .

[80]  Richard J. Harris.  A primer of multivariate statistics , 1975 .

[81]  D. Faith,et al.  Compositional dissimilarity as a robust measure of ecological distance , 1987, Vegetatio.

[82]  M. Zelditch.  ONTOGENETIC VARIATION IN PATTERNS OF PHENOTYPIC INTEGRATION IN THE LABORATORY RAT , 1988, Evolution; international journal of organic evolution.

[83]  M. Aitkin,et al.  Interactive Regression Modelling , 1982 .

[84]  S. Ferson,et al.  Putting Things in Order: A Critique of Detrended Correspondence Analysis , 1987, The American Naturalist.

[85]  R. Gittins,et al.  Canonical Analysis: A Review with Applications in Ecology , 1985 .

[86]  R. Clarke,et al.  Theory and Applications of Correspondence Analysis , 1985 .

[87]  F. Gehlbach,et al.  Nest-site preferences of Flammulated Owls in western New Mexico , 1988 .

[88]  Pierre Jolicoeur,et al.  The multivariate generalization of the allometry equation , 1963 .

[89]  J. Jaenike.  Host Specialization in Phytophagous Insects , 1990 .

[90]  R. W. Mannan,et al.  Bird populations and vegetation characteristics in managed and old-growth forests, northeastern Oregon. , 1984 .

[91]  J. Neter,et al.  Applied Linear Regression Models , 1983 .

[92]  W. Mcgillivray.  Size, sexual size dimorphism, and their measurement in Great Horned Owls in Alberta , 1985 .

[93]  J. Mosimann.  Statistical Problems of Size and Shape. I. Biological Applications and Basic Theorems , 1975 .

[94]  William G. Eberhard,et al.  Function and Phylogeny of Spider Webs , 1990 .

[95]  D'arcy W. Thompson,et al.  On Growth and Form , 1917, Nature.

[96]  P. Sprent,et al.  The mathematics of size and shape. , 1972, Biometrics.

[97]  C. Findlay,et al.  LIFE HISTORY STUDIES OF THE LESSER SNOW GOOSE (ANSER CAERULESCENS CAERULESCENS). VI. PLUMAGE POLYMORPHISM, ASSORTATIVE MATING AND FITNESS , 1985, Evolution; international journal of organic evolution.

[98]  Fred L. Bookstein,et al.  MULTIVARIATE DISCRIMINATION BY SHAPE IN RELATION TO SIZE , 1981 .

[99]  Jon E. Ahlquist,et al.  Phylogeny and classification of birds based on the data of DNA-DNA hybridization , 1983 .

[100]  Byron K. Williams,et al.  Chance-corrected classification for use in discriminant analysis: Ecological applications , 1984 .

[101]  J. Scheibe.  Climate, Competition, and the Structure of Temperate Zone Lizard Communities , 1987 .

[102]  C. C. Taylor,et al.  Multivariate Analysis of Variance and Repeated Measures: A practical approach for behavioural scientists , 1988 .

[103]  L. Moses,et al.  Think and Explain with Statistics , 1988 .

[104]  R. Good,et al.  The seedling habitat of Pinus echinata and Melampyrum lineare in oak-pine forest of the New Jersey Pinelands , 1987 .

[105]  William R. Atchley,et al.  Multivariate statistical methods, within-groups covariation , 1976 .

[106]  D. Holt,et al.  Planning and Analysis of Observational Studies. , 1983 .

[107]  W. Wilson.  Competition and Predation in Marine Soft-Sediment Communities , 1990 .

[108]  K. Kershaw,et al.  Quantitative and Dynamic Plant Ecology , 1973 .

[109]  J. Doolan,et al.  An empirical approach to guild structure: habitat relationships in nine species of eastern-Australian cicadas , 1986 .

[110]  S. J. Arnold,et al.  THE MEASUREMENT OF SELECTION ON CORRELATED CHARACTERS , 1983, Evolution; international journal of organic evolution.

[111]  B. Carnes,et al.  The Use of Regression for Detecting Competition with Multicollinear Data , 1988 .

[112]  Fred L. Bookstein,et al.  [Size and Shape Spaces for Landmark Data in Two Dimensions]: Rejoinder , 1986 .

[113]  P A Lachenbruch,et al.  Discriminant Analysis and its Applications in Epidemiology , 1980, Methods of Information in Medicine.

[114]  Fred L. Bookstein,et al.  A Comment on Shearing as a Method for “Size Correction” , 1987 .

[115]  J. J. C. Smart,et al.  The Structure of Science. Problems in the Logic of Scientific Explanation , 1962 .

[116]  G. Niemi.  Patterns of Morphological Evolution in Bird Genera of New World and Old World Peatlands , 1985 .

[117]  H. J. Gold.  Pattern analysis in agricultural science. , 1978 .

[118]  Andrew F. Siegel,et al.  On The Measurement of Morphology and its Change , 1982, Paleobiology.

[119]  R. Redak,et al.  SPATIAL AND TEMPORAL PATTERNS IN THE SEED BANK AND VEGETATION OF A DESERT GRASSLAND COMMUNITY , 1988 .

[120]  J. Mosimann.  Size Allometry: Size and Shape Variables with Characterizations of the Lognormal and Generalized Gamma Distributions , 1970 .

[121]  R. Szaro.  Guild management: an evaluation of avian guilds as a predictive tool , 1986 .

[122]  F. Bookstein,et al.  The Measurement of Biological Shape and Shape Change. , 1979 .

[123]  C. Braak,et al.  Principal Components Biplots and Alpha and Beta Diversity , 1983 .

[124]  R. D. Ohmart,et al.  Habitat Selection Attributes of an Avian Community: A Discriminant Analysis Investigation , 1983 .

[125]  P. Greig-Smith,et al.  An application of principal components analysis to vegetation change in permanent plots , 1980 .

[126]  J. Schuerman.  Multivariate analysis in the human services , 1983 .

[127]  Peter H. A. Sneath,et al.  Numerical Taxonomy: The Principles and Practice of Numerical Classification , 1973 .

[128]  Michael Greenacre,et al.  Graphical Display and Interpretation of Antelope Census Data in African Wildlife Areas, Using Correspondence Analysis , 1984 .

[129]  R. Kirk Steinhorst,et al.  A COMPARISON OF PRINCIPAL COMPONENTS FROM REAL AND RANDOM DATA , 1985 .

[130]  David E. Capen.  The use of multivariate statistics in studies of wildlife habitat , 1981 .

[131]  F. Rohlf,et al.  EVALUATION OF THE RESTRICTED MAXIMUM‐LIKELIHOOD METHOD FOR ESTIMATING PHYLOGENETIC TREES USING SIMULATED ALLELE‐FREQUENCY DATA , 1988, Evolution; international journal of organic evolution.

[132]  F. Rohlf,et al.  A COMPARISON OF FOURIER METHODS FOR THE DESCRIPTION OF WING SHAPE IN MOSQUITOES (DIPTERA: CULICIDAE) , 1984 .

[133]  R. D. Ohmart,et al.  Nonlinear Relationships between Birds and Vegetation , 1983 .

[134]  B. Manly.  Multivariate Statistical Methods : A Primer , 1986 .

[135]  R. D. Ohmart,et al.  Comparison of the importance of different habitat attributes to avian community organization , 1984 .

[136]  R. Green.  Multivariate Niche Analysis with Temporally Varying Environmental Factors , 1974 .

[137]  D. Erwin.  The End-Permian Mass Extinction , 1990 .

[138]  Brian A. Maurer,et al.  Predicting habitat quality for grassland birds using density- habitat correlations. , 1986 .

[139]  W. Atchley,et al.  Statistical Properties of Ratios. I. Empirical Results , 1976 .

[140]  H. Wilbur,et al.  Regulation of Structure in Complex Systems: Experimental Temporary Pond Communities , 1987 .

[141]  A. Siegel,et al.  A robust comparison of biological shapes. , 1982, Biometrics.

[142]  Joseph Felsenstein,et al.  DISTANCE METHODS FOR INFERRING PHYLOGENIES: A JUSTIFICATION , 1984, Evolution; international journal of organic evolution.

[143]  M. Austin,et al.  The Problem of Non-Linearity in Ordination: Experiments with Two-Gradient Models , 1971 .

[144]  Hugh G. Gauch,et al.  Multivariate analysis in community ecology , 1984 .

[145]  R. Hansell,et al.  The impact of observer bias on multivariate analyses of vegetation structure , 1985 .

[146]  Kamaljit S. Bawa,et al.  Plant-Pollinator Interactions in Tropical Rain Forests , 1990 .

[147]  P. Greig-Smith,et al.  QUANTITATIVE PLANT ECOLOGY , 1959 .

[148]  R. Lande.  QUANTITATIVE GENETIC ANALYSIS OF MULTIVARIATE EVOLUTION, APPLIED TO BRAIN:BODY SIZE ALLOMETRY , 1979, Evolution; international journal of organic evolution.

[149]  F. Bookstein.  “Size and Shape”: A Comment on Semantics , 1989 .

[150]  H. V. Henderson,et al.  Building Multiple Regression Models Interactively , 1981 .

[151]  T. Rich.  Habitat and Nest-Site Selection by Burrowing Owls in the Sagebrush Steppe of Idaho , 1986 .

[152]  D'arcy W. Thompson.  On growth and form i , 1943 .

[153]  J. Darroch,et al.  Canonical and principal components of shape , 1985 .

[154]  T. Mitchell-Olds,et al.  REGRESSION ANALYSIS OF NATURAL SELECTION: STATISTICAL INFERENCE AND BIOLOGICAL INTERPRETATION , 1987, Evolution; international journal of organic evolution.

[155]  W. Atchley,et al.  Ratios and the Statistical Analysis of Biological Data , 1978 .

[156]  W. Atchley.  Some Genetic Aspects of Morphometric Variation , 1983 .

[157]  M. Hill,et al.  Reciprocal Averaging : an eigenvector method of ordination , 1973 .

[158]  C. Oxnard.  The architecture of the shoulder in some mammals , 1968, Journal of morphology.

[159]  K. Gabriel,et al.  The biplot graphic display of matrices with application to principal component analysis , 1971 .

[160]  W. Atchley,et al.  QUANTITATIVE GENETICS OF DEVELOPMENT: GENETIC CORRELATIONS AMONG AGE‐SPECIFIC TRAIT VALUES AND THE EVOLUTION OF ONTOGENY , 1983, Evolution; international journal of organic evolution.

[161]  David R. Anderson,et al.  Questionable multivariate statistical inference in wildlife habitat and community studies (a reply) , 1988 .

[162]  Peter R. Grant,et al.  ECOLOGICAL CORRELATES OF MORPHOLOGICAL EVOLUTION IN A DARWIN'S FINCH, GEOSPIZA DIFFICILIS , 1984, Evolution; international journal of organic evolution.

[163]  D. Campbell,et al.  EXPERIMENTAL AND QUASI-EXPERIMENT Al DESIGNS FOR RESEARCH , 2012 .

[164]  M. Samways,et al.  Developments in Numerical Ecology , 1989 .

[165]  A. Baker,et al.  RAPID GENETIC DIFFERENTIATION AND FOUNDER EFFECT IN COLONIZING POPULATIONS OF COMMON MYNAS (ACRIDOTHERES TRISTIS) , 1987, Evolution; international journal of organic evolution.

[166]  E. Pianka,et al.  Biogeography of nocturnal insectivores : historical events and ecological filters , 1990 .

[167]  Mark J. Schervish,et al.  A Review of Multivariate Analysis , 1987 .

[168]  K. Somers.  MULTIVARIATE ALLOMETRY AND REMOVAL OF SIZE WITH PRINCIPAL COMPONENTS ANALYSIS , 1986 .

[169]  Charles Ernest Oxnard.  The Analysis of Form: Without Measurement and Without Computers , 1980 .

[170]  Richard A. Johnson,et al.  Applied Multivariate Statistical Analysis , 1983 .

[171]  S. Collins,et al.  The seedling regeneration niche: habitat structure of tree seedlings in an oak-pine forest , 1987 .

[172]  L. F. Marcus,et al.  A survey of multivariate methods for systematics , 1980 .

[173]  T. Hassard,et al.  Applied Linear Regression , 2005 .

[174]  Dennis M. Heisey,et al.  Analyzing Selection Experiments with Log-Linear Models , 1985 .

[175]  Byron K. Williams,et al.  Some Observations of the Use of Discriminant Analysis in Ecology , 1983 .

[176]  F. Bookstein.  Size and Shape Spaces for Landmark Data in Two Dimensions , 1986 .

[177]  B. Efron.  The Efficiency of Logistic Regression Compared to Normal Discriminant Analysis , 1975 .

[178]  Peter R. Minchin,et al.  An evaluation of the relative robustness of techniques for ecological ordination , 1987 .

[179]  G. H. Albrecht.  Some Comments on the Use of Ratios , 1978 .

[180]  Gerald J. Niemi,et al.  The Grinnellian Niche of the Wood Thrush , 1984, The American Naturalist.

[181]  J. H. Looney,et al.  Quantitative and Dynamic Plant Ecology. , 1986 .

[182]  P. S. Humphrey,et al.  FLIGHTLESSNESS IN STEAMER‐DUCKS (ANATIDAE: TACHYERES): ITS MORPHOLOGICAL BASES AND PROBABLE EVOLUTION , 1986, Evolution; international journal of organic evolution.

[183]  P. G. N. Digby,et al.  Multivariate Analysis of Ecological Communities , 1987 .

[184]  B. V. Horne,et al.  Niche Breadth Calculation Based on Discriminant Analysis , 1982 .