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Multivariate Statistics for Wildlife and Ecology Research pp 19–80Cite as

Ordination: Principal Components Analysis

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Bibliography

Procedures

  • Anderson, A.J.B. 1971. Ordination methods in ecology. Journal of Ecology 59:713–726.

    Article  Google Scholar 

  • Anscombe, F.J. 1960. Rejection of outliers. Technometrics 2:123–146.

    Article  Google Scholar 

  • Austin, M.P. 1976. On non-linear species response models in ordination. Vegetatio 33:33–41.

    Article  Google Scholar 

  • Austin, M.P., and Greig-Smith, P. 1968. The application of quantitative methods to vegetation survey. II. Some methodological problems of data from rain forest. Journal of Ecology 56:827–844.

    Article  Google Scholar 

  • Austin, M.P., and Noy-Meir, I. 1971. The problem of nonlinearity in ordination: experiments with two-gradient models. Journal of Ecology 59:763–773.

    Article  Google Scholar 

  • Austin, M.P., and Orloci, L. 1966. Geometric models in ecology. II: An evaluation of some ordination techniques. Journal of Ecology 54:217–227.

    Article  Google Scholar 

  • Beals, E.W. 1973. Ordination: mathematical elegance and ecological naivete. Journal of Ecology 61:23–35.

    Article  Google Scholar 

  • Bhattacharyya, H. 1981. Theory and methods of factor analysis and principal components. In The Use of Multivariate Statistics in Studies on Wildlife Habitat, ed. D.E. D.E. Capen, pp 72–79. U.S. For. Serv. Gen. Tech. Report RM-87.

    Google Scholar 

  • Blalock, H.M., Jr. 1979. Social Statistics. New York: McGraw-Hill.

    Google Scholar 

  • Bliss, C.I., Cochran, W.G., and Tukey, J.W. 1956. A rejection criterion based upon the range. Biometrika 43:418–422.

    Google Scholar 

  • Bray, J.R., and Curtis, J.T. 1957. An ordination of the upland forest communities of southern Wisconsin. Ecological Monographs 27:325–349.

    Article  Google Scholar 

  • Cattell, R.B. 1966. The scree test for the number of factors. Multivariate Behavioral Research 1:245–276.

    Article  Google Scholar 

  • Cliff, N. 1988. The eigenvalues-greater-than-one rule and the reliability of components. Psychological Bulletin 103:276–279.

    Article  Google Scholar 

  • Dale, M.B. 1975. On objectives of methods of ordination. Vegetatio 30:15–32.

    Article  Google Scholar 

  • Edgington, E.S. 1995. Randomization Tests, 3rd ed. New York: Marcel Dekker.

    Google Scholar 

  • Efron, B. 1979. Computers and the theory of statistics: thinking the unthinkable. Society for Industrial and Applied Mathematics (SIAM) Review 21:460–480.

    Google Scholar 

  • Efron, B. 1982. The jackknife, the bootstrap and other resampling plans. Society for Industrial and Applied Mathematics (SIAM), Monograph #38, CBMS-N8F.

    Google Scholar 

  • Efron, B, and Gong, G. 1983. A leisurely look at the bootstrap, the jackknife, and cross-validation. American Statistician 37:36–48.

    Google Scholar 

  • Fasham, M.J.R. 1977. A comparison of nonmetric multidimensional scaling, principal components and reciprocal averaging for the ordination of simulated coenoclines and coeno-planes. Ecology 58:551–561.

    Article  Google Scholar 

  • Frontier, S. 1976. Etude de la decroissance des valeurs propres dans une analyze en composantes principales: comparison avec le modele de baton brise. Journal of Experimental Marine Biology and Ecology 25:67–75.

    Article  Google Scholar 

  • Gauch, H.G. 1973. A quantitative evaluation of the Bray-Curtis ordination technique. Ecology 54:829–836.

    Article  Google Scholar 

  • Gauch, H.G. 1973. The relationship between sample similarity and ecological distance. Ecology 54:618–622.

    Article  Google Scholar 

  • Gauch, H.G. 1982. Multivariate Analysis in Community Ecology. Cambridge: Cambridge University Press.

    Book  Google Scholar 

  • Gauch, H.G. 1982. Noise reduction by eigenvector ordinations. Ecology 63:1643–1649.

    Article  Google Scholar 

  • Gauch, H.G., and Whittaker, R.H. 1972. Comparison of ordination techniques. Ecology 53:868–875.

    Article  Google Scholar 

  • Gauch, H.G., Whittaker, R.H., and Wentworth, T.R. 1977. A comparative study of reciprocal averaging and other ordination techniques. Journal of Ecology 65:157–174.

    Article  Google Scholar 

  • Grubbs, F.E. 1950. Sample criteria for testing outlying observations. Annals of Mathematical Statistics 21:27–28.

    Article  Google Scholar 

  • Guttman, L. 1954. Some necessary conditions for common factor analysis. Psychometrika 19:149–161.

    Article  Google Scholar 

  • Hair, J.F., Jr., Anderson, R.E., and Tatham, R.L. 1987. Multivariate Data Analysis, 2nd ed. New York: Macmillan.

    Google Scholar 

  • Harman, H.H. 1968. Modern Factor Analysis, 2nd ed. Chicago: University of Chicago Press.

    Google Scholar 

  • Harris, R.J. 1975. A Primer of Multivariate Statistics. New York: Academic Press.

    Google Scholar 

  • Hill, M.O. 1973. Reciprocal averaging: an eigenvector methodof ordination. Journal of Ecology 61:231–249.

    Google Scholar 

  • Hill, M.O. 1974. Correspondence analysis: a neglected multivariate method. Journal of the Royal Statistical Society, Ser. C 23:340–354.

    Google Scholar 

  • Hill, M.O., and Gauch, H.G. 1980. Detrended correspondence analysis, an improved ordination technique. Vegetatio 42:47–58.

    Article  Google Scholar 

  • Horn, J.L. 1965. A rationale and test for the number of factors in factor analysis. Psychometrika 30:179–185.

    Article  PubMed  CAS  Google Scholar 

  • Jackson, D.A. 1993. Stopping rules in PCA: a comparison of heuristical and statistical approaches. Ecology 74(8):2205–2214.

    Article  Google Scholar 

  • Johnson, D.H. 1981. The use and misuse of statistics in wildlife habitat studies. In The Use of Multivariate Statistics in Studies on Wildlife Habitat, ed. D.E. Capen, pp 11–19. U.S. Forest Service Gen. Tech. Report RM-87.

    Google Scholar 

  • Johnson, D.H. 1981. How to measure—a statistical perspective. In The Use of Multivariate Statistics in Studies on Wildlife Habitat, ed. ed. D.E. Capen, pp 53–58. U.S. Forest Service Gen. Tech. Report RM-87.

    Google Scholar 

  • Karr, J.R., and Martin, T.E. 1981. Random numbers and principal components: further searches for the unicorn? In The Use of Multivariate Statistics in Studies on Wildlife Habitat, ed. ed. D.E. Capen, pp 20–25. U.S. Forest Service Gen. Tech. Report RM-87.

    Google Scholar 

  • Kesseil, S.R., and Whittaker, R.H. 1976. Comparison of three ordination techniques. Vegetatio 32:21–29.

    Article  Google Scholar 

  • Kruskal, W.H. 1960. Some remarks on wild observations. Technometrics 2:1–3.

    Article  Google Scholar 

  • Ludwig, J.A., and Reynolds, J.F. 1988. Statistical Ecology: A Primer on Methods and Computing. New York: Wiley and Sons.

    Google Scholar 

  • Marcus, M., and Minc, H. 1968. Elementary Linear Algebra. New York: Macmillan.

    Google Scholar 

  • Manly, B.F.I. 1997. Randomization, Bootstrap and Monte Carlo Methods in Biology, 2nd ed. London: Chapman and Hall.

    Google Scholar 

  • McCune, B. 1997. Influence of noisy environmental data on canonical correspondence analysis. Ecology 78(8):2617–2623.

    Article  Google Scholar 

  • Meot, A., Legendre, P., and Borcard, D. 1998. Partialling out the spatial component of variation: questions and propositions in the linear modelling framework. Environmental and Ecological Statistics 5(1):1–27.

    Article  Google Scholar 

  • Miles, D.B. 1990. A comparison of three multivariate statistical techniques for the analysis of avian foraging data. In Studies in Avian Biol. No. 13—Avian Foraging: Theory, Methodology, and Applications, ed. M.L. Morrison, C.J. Ralph, J. Verner, and J.R. Jehl, Jr., pp 309–317.

    Google Scholar 

  • Morrison, D.F. 1967. Multivariate Statistical Methods, 2nd ed. New York: McGraw-Hill.

    Google Scholar 

  • Mosteller, F., and Tukey, W. 1977. Data Analysis and Regression: A Second Course in Statistics. Reading: Addision-Wesley.

    Google Scholar 

  • Nichols, S. 1977. On the interpretation of principal components analysis in ecological contexts. Vegetatio 34:191–197.

    Article  Google Scholar 

  • Noy-Meir, I. 1973. Data transformations in ecological ordination. I. Some advantages of non-centering. Journal of Ecology 61:329–341.

    Article  Google Scholar 

  • Noy-Meir, I., and Austin, M.P. 1970. Principal component ordination and simulated vegetational data. Ecology 61:551–552.

    Article  Google Scholar 

  • Noy-Meir, I., Walker, D., and Williams, W.T. 1975. Data transformations in ecological ordination. II. On the meaning of data standardization. Journal of Ecology 63:779–800.

    Article  Google Scholar 

  • Okland, R.H. 1996. Are ordination and constrained ordination alternative or complementary strategies in general ecological studies? Journal of Vegetation Science 7(2):289–292.

    Article  Google Scholar 

  • Oksanen, J., and Minchin, P.R. 1997. Instability of ordination results under changes in input data order—explanations and remedies. Journal of Vegetation Science 8(3):447–454.

    Article  Google Scholar 

  • Orloci, L. 1966. Geometric models in ecology. I. The theory and application of some ordination methods. Journal of Ecology 54:193–216.

    Article  Google Scholar 

  • Palmer, M.J. 1993. Putting things in even better order: the advantages of canonical correspondence analysis. Ecology 74(8):2215–2230.

    Article  Google Scholar 

  • Philippi, T.E., Dixon, P.M., and Taylor, B.E. 1998. Detecting trends in species composition. Ecological Applications 8(2):300–308.

    Article  Google Scholar 

  • Robertson, P.A. 1978. Comparison of techniques for ordinating and classifying old-growth floodplain forests in southern Illinois. Vegetatio 37:43–51.

    Google Scholar 

  • Stauffer, D.F., Garton, E.O., and Steinhorst, R.K. 1985. A comparison of principal components from real and random data. Ecology 66:1693–1698.

    Article  Google Scholar 

  • Stewart, D.W. 1981. The application and misapplication of factor analysis in marketing research. Journal of Marketing Research 18:51–62.

    Article  Google Scholar 

  • Swan, J.M.A. 1970. An examination of some ordination problems by use of simulated vege-tational data. Ecology 51:89–102.

    Article  Google Scholar 

  • Tabachnick, B.G., and Fidell, L.S. 1989. Using Multivariate Statistics. New York: Harper and Row.

    Google Scholar 

  • Tatsuoka, M.M. 1971. Multivariate Analysis: Techniques for Educational and Psychological Research. New York: Wiley and Sons.

    Google Scholar 

  • TerBraak, C.J.F. 1986. Canonical correspondence analysis: a new eigenvector technique for multivariate direct gradient analysis. Ecology 67(5):1167–1178.

    Article  Google Scholar 

  • TerBraak, C.J.F. 1987. The analysis of vegetation-environment relationships by canonical correspondence analysis. Vegetatio 69:69–77.

    Article  Google Scholar 

  • TerBraak, C.J.F., and Prentice, C.I. 1988. A theory of gradient analysis. Advances in Ecological Research 18:272–313.

    Article  Google Scholar 

  • Wartenberg, D., Ferson, S., and Rohlf, F.J. 1987. Putting things in order: a critique of detrended correspondence analysis. American Naturalist 129:434–448.

    Article  Google Scholar 

  • Whittaker, R.H., and Gauch, H.G. 1978. Evaluation of ordination techniques. In Ordination of Plant Communities, ed. R.H. Whittaker, pp 277–336. The Hague: W. Junk.

    Chapter  Google Scholar 

  • Wilson, M.W. 1981. A statistical test of the accuracy and consistency of ordinations. Ecology 62:8–12.

    Article  Google Scholar 

Applications

  • Birch, J.M. 1997. Comparing wing shape of bats: the merits of principal-components analysis and relative-warp analysis. Journal of Mammalogy. 78(4):1187–1198.

    Article  Google Scholar 

  • Blair, R.B., and Launer, A.E. 1997. Butterfly diversity and human land use: species assemblages along an urban gradient. Biological Conservation 80(1):113–125.

    Article  Google Scholar 

  • Boiger, D.T., Scott, T.A., and Rotenberry, J.T. 1997. Breeding bird abundance in an urbanizing landscape in coastal southern California. Conservation Biology 11(2):406–421.

    Article  Google Scholar 

  • Bray, J.R., and Curtis, J.T. 1957. An ordination of the upland forest communities of southern Wisconsin. Ecological Monographs 27:325–349.

    Article  Google Scholar 

  • Burke, A. 1997. The impact of large herbivores on floral composition and vegetation structure in the Naukluft mountains, Namibia. Biodiversity & Conservation. 6(9):1203–1217.

    Article  Google Scholar 

  • Carey, A.B. 1981. Multivariate analysis of niche, habitat and ecotope. In The Use of Multivariate Statistics in Studies on Wildlife Habitat, ed. ed. D.E. Capen, pp 104–114. U.S. Forest Service Gen. Tech. Report RM-87.

    Google Scholar 

  • Clark, T.E., and Samways, M.J. 1996. Dragonflies (Odonata) as indicators of biotope quality in the Kruger National Park, South Africa. Journal of Applied Ecology. 33(5):1001–1012.

    Article  Google Scholar 

  • Conner, R.N., and Adkisson, C.S. 1977. Principal components analysis of woodpecker nesting habitat. Forest Science 22:122–127.

    Google Scholar 

  • Gibson, A.R., Baker, A.J., and Moeed, A. 1984. Morphometric variation in introduced populations of the common myna (Acridotheres tristis): an application of the jackknife to principal components analysis. Systematic Zoology 33:408–421.

    Article  Google Scholar 

  • Ellis, B.A., Mills, J.N., Childs, J.E., Muzzini, M.C., Mckee, K.T., Enria, D.A., and Glass, G.E. 1997. Structure and floristics of habitats associated with five rodent species in an agroecosystem in central Argentina. Journal of Zoology 243(3):437–460.

    Article  Google Scholar 

  • Fuller, R.J., Trevelyan, R.J., and Hudson, R.W. 1997. Landscape composition models for breeding bird populations in lowland English farmland over a 20-year period. Ecography 20(3):295–307.

    Article  Google Scholar 

  • Grigal, D.F., and Goldstein, R.A. 1971. An integrated ordination-classification analysis of an intensively sampled oak-hickory forest. Journal of Ecology 59:481–492.

    Article  Google Scholar 

  • Hamer, K.C., Hill, J.K., Lace, L.A., and Langan, A.M. 1997. Ecological and biogeographical effects of forest disturbance on tropical butterflies of Sumba, Indonesia. Journal of Biogeography 24(1):67–75.

    Article  Google Scholar 

  • Hanowski, J.M., Niemi, G.J., and Christian, D.C. 1997. Influence of within-plantation heterogeneity and surrounding landscape composition on avian communities in hybrid poplar plantations. Conservation Biology 11(4):936–944.

    Article  Google Scholar 

  • Hamer, E.J., and Whitmore, R.C. 1981. Robust principal component and discriminant analysis of two grassland bird species’ habitat. In The Use of Multivariate Statistics in Studies on Wildlife Habitat, ed. ed. D.E. Capen, pp 209–221. U.S. Forest Service Gen. Tech. Report RM-87.

    Google Scholar 

  • Harshbarger, T.J., and Bhattacharyya, H. 1981. An application of factor analysis in an aquatic habitat study. In The Use of Multivariate Statistics in Studies on Wildlife Habitat, ed. D.E. Capen, pp 180–185. U.S. Forest Service Gen. Tech. Report RM-87.

    Google Scholar 

  • Hawrot, R.Y., and Niemi, G.J. 1996. Effects of edge type and patch shape on avian communities in a mixed conifer-hardwood forest. Auk 113(3):586–598.

    Article  Google Scholar 

  • James, F.C. 1971. Ordinations of habitat relationships among breeding birds. Wilson Bulletin 83:215–236.

    Google Scholar 

  • Kirk, D.A., Diamond, A.W., Hobson, K.A., and Smith, A.R. 1996. Breeding bird communities of the western and northern Canadian boreal forest: relationship to forest type. Canadian Journal of Zoology 74(9):1749–1770.

    Article  Google Scholar 

  • Lima, A.P., and Magnusson, W.E. 1998. Partitioning seasonal time: interactions among size, foraging activity and diet in leaf-litter frogs. Oecologia 116(1–2):259–266.

    Article  Google Scholar 

  • Madhsudan, M.D., and Johnsingh, A.J.T. 1998. Analysis of habitat-use using ordination: the Nilgiri Thar in southern India. Current Science 74(11):1000–1003.

    Google Scholar 

  • Martinsmith, K.M. 1998. Relationships between fishes and habitat in rainforest streams in Sabah, Malaysia. Journal of Fish Biology 52(3):458–482.

    Google Scholar 

  • Maurer, B.A., McArthur, L.B., and Whitmore, R.C. 1981. Habitat associations of birds breeding in clearcut deciduous forests in West Virginia. In The Use of Multivariate Statistics in Studies on Wildlife Habitat, ed. D.E. Capen, pp 167–172. U.S. Forest Service Gen. Tech. Report RM-87.

    Google Scholar 

  • Moser, E.B., Barrow, W.C. Jr., and Hamilton, R.B. 1990. An exploratory use of correspondence analysis to study relationships between avian foraging behavior and habitat. In The Use of Multivariate Statistics in Studies on Wildlife Habitat, ed. D.E. Capen, pp 309–317. U.S. Forest Service Gen. Tech. Report RM-87.

    Google Scholar 

  • Niemi, G.J., and Hanowski, J.M. 1984. Relationships of breeding birds to habitat characteristics in logged areas. Journal of Wildlife Management 48:438–443.

    Article  Google Scholar 

  • Murkin, H.R., Murkin, E.J., and Ball, J.P. 1997. Avian habitat selection and prairie wetland dynamics: a ten year experiment. Ecological Applications 7(4):1144–1159.

    Article  Google Scholar 

  • Pappas, J.L., and Stoermer, E.F. 1997. Multivariate measure of niche overlap using canonical correspondence analysis. Ecoscience 4(2):240–245.

    Google Scholar 

  • Pearman, P.B. 1997. Correlates of amphibian diversity in an altered landscape of Amazonian Ecuador. Conservation Biology 11(5):1211–1225.

    Article  Google Scholar 

  • Rotenberry, J., and Wiens, J.A. 1981. A synthetic approach to principal components analysis of bird/habitat relationships. In The Use of Multivariate Statistics in Studies on Wildlife Habitat, ed. by D.E. Capen, pp 197–208. U.S. Forest Service Gen. Tech. Report RM-87.

    Google Scholar 

  • Schaeffer, J.A., Stevens, S.D., and Messier, F. 1996. Comparative winter habitat use and associations among herbivores in the high Arctic. Arctic 49(4):387–391.

    Google Scholar 

  • Sczerzenie, P.J. 1981. Principal components analysis of deer harvest-land use relationships in Massachusetts. In The Use of Multivariate Statistics in Studies on Wildlife Habitat, ed. by D.E. Capen, pp 173–179. U.S. Forest Service Gen. Tech. Report RM-87.

    Google Scholar 

  • Shank, C.C. 1982. Age-sex differences in the diets of wintering Rocky Mountain bighorn sheep. Ecology 63:627–633.

    Article  Google Scholar 

  • Smith, K.G. 1977. Distribution of summer birds along a forest moisture gradient in an Ozark watershed. Ecology 58:810–819.

    Article  Google Scholar 

  • Velazquez, A., and Heil, G.W. 1996. Habitat suitability for the conservation of the volcano rabbit (Romerolagus diazi). Journal of Applied Ecology 33(3):543–554.

    Article  Google Scholar 

  • Whitmore, R.C. 1975. Habitat ordination of passerine birds of the Virgin River Valley, southwestern Utah. Wilson Bulletin 87:65–74.

    Google Scholar 

  • Whitmore, R.C. 1977. Habitat partitioning in a community of passerine birds. Wilson Bulletin 89:253–265.

    Google Scholar 

  • Yu, C.C., Quinn, J.T., Dufournaud, C.M., Harrington, J.J., Rogers, P.P., and Lohani, B.N. 1998. Effective dimensionality of environmental indicators: a principal components analysis with bootstrap confidence intervals. Journal of Environmental Management 53(1):101–119.

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Natural Resources Conservation, University of Massachusetts, Amherst, MA, 01003-5810, USA

    Kevin McGarigal

  2. Department of Forest Sciences, Colorado State University, Fort Collins, CO, 80523-1470, USA

    Susan Stafford

  3. Organismic and Evolutionary Biology, University of Massachusetts, Amherst, MA, 01003-5810, USA

    Sam Cushman

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  1. Kevin McGarigal
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  3. Sam Cushman
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McGarigal, K., Stafford, S., Cushman, S. (2000). Ordination: Principal Components Analysis. In: Multivariate Statistics for Wildlife and Ecology Research. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1288-1_2

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