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Discriminating Groups of Organisms

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Morphometrics for Nonmorphometricians

Part of the book series: Lecture Notes in Earth Sciences ((LNEARTH,volume 124))

Abstract

A common problem in morphometric studies is to determine whether, and in what ways, two or more previously established groups of organisms differ. Discrimination of predefined groups is a very different problem than trying to characterize the patterns of morphological variation among individuals, and so the kinds of morphometric tools used for these two kinds of questions differ. In this paper I review the basic procedures used for discriminating groups of organisms based on morphological characteristics – measures of size and shape. A critical reading of morphometric discrimination studies of various kinds of organisms in recent years suggests that a review of procedures is warranted, particularly with regard to the kinds of assumptions being made. I will discuss the main concepts and methods used in problems of discrimination, first using conventional morphometric characters (measured distances between putatively homologous landmarks), and then using landmarks directly with geometric morphometric approaches.

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References

  • Adams DC (1999) Methods for shape analysis of landmark data from articulated structures. Evolutionary Ecology Research 1: 959–970

    Google Scholar 

  • Airoldi JP, Flury BK (1988) An application of common principal component analysis to cranial morphometry of Microtus californicus and Microtus ochrogaster (Mammalia, Rodentia). Journal of Zoology (London) 216: 21–36

    Article  Google Scholar 

  • Albrecht GH (1980) Multivariate analysis and the study of form, with special reference to canonical variate analysis. American Zoologist 20: 679–693

    Google Scholar 

  • Albrecht GH (1992) Assessing the affinities of fossils using canonical variates and generalized distances. Human Evolution 7: 49–69

    Article  Google Scholar 

  • Albrecht GH, Gelvin BR, Hartman SE (1993) Ratios as a size adjustment in morphometrics. American Journal of Physical Anthropology 91: 441–468

    Article  Google Scholar 

  • Anderson MJ (2001) A new method for non-parametric multivariate analysis of variance. Austral Ecology 26: 32–46

    Google Scholar 

  • Anderson MJ, Robinson J (2003) Generalized discriminant analysis based on distances. Australian and New Zealand Journal of Statistics 45: 301–318

    Article  Google Scholar 

  • Bartoletti S, Flury BD, Nel DG (1999) Allometric extension. Biometrics 55: 1210–1214

    Article  Google Scholar 

  • Baudat G, Anouar F (2000) Generalized discriminant analysis using a kernel approach. Neural Computation 12: 2385–2404

    Article  Google Scholar 

  • Baylac M, Villemant C, Simbolotti G (2003) Combining geometric morphometrics with pattern recognition for the investigation of species complexes. Biological Journal of the Linean Society 80: 89–98

    Article  Google Scholar 

  • Bookstein FL (1978) The Measurement of biological shape and shape change. Lecture Notes in Biomathematics 24. Springer-Verlag, New York

    Book  Google Scholar 

  • Bookstein FL (1989a) “Size and shape”: a comment on semantics. Systematic Zoology 38: 173–180

    Article  Google Scholar 

  • Bookstein FL (1989b) Principal warps: thin-plate splines and the decomposition of deformations. IEEE Transactions on Pattern Analysis and Machine Intelligence 11: 567–585

    Article  Google Scholar 

  • Bookstein FL (1991) Morphometric tools for landmark data: geometry and biology, Cambridge University Press, Cambridge

    Google Scholar 

  • Bookstein FL (1996) Combining the tools of geometric morphometrics. In Marcus LF, Corti M, Loy A, Naylor GJP, Slice DE (Eds.) Advances in morphometrics, Plenum Press, New York, 131–151 pp

    Google Scholar 

  • Bookstein FL, Chernoff B, Elder RL, Humphries JM, Smith GR, Strauss RE (1985) Morphometrics in evolutionary biology: the geometry of size and shape change. Academy of Natural Sciences, Philadelphia

    Google Scholar 

  • Bryant EH (1986) On use of logarithms to accommodate scale. Systematic Zoology 35: 552–559

    Article  Google Scholar 

  • Burnaby TP (1966) Growth-invariant discriminant functions and generalized distances. Biometrics 22: 96–110

    Article  Google Scholar 

  • Campbell NA, Atchley WR (1981) The geometry of canonical variates analysis. Systematic Zoology 30: 268–280

    Article  Google Scholar 

  • Dalgleish LI (1994) Discriminant analysis: statistical inference using the jackknife and bootstrap procedures. Psychological Bulletin 116: 498–508

    Article  Google Scholar 

  • Davison AC, Hinkley DV (1996) Bootstrap methods and their application, Cambridge University Press, Cambridge

    Google Scholar 

  • Depecker M, Berge C, Penin X, Renous S (2006) Geometric morphometrics of the shoulder girdle in extant turtles (Chelonii). Journal of Anatomy 208: 35–45

    Article  Google Scholar 

  • Dobigny G, Baylac M, Denys C (2002) Geometric morphometrics, neural networks and diagnosis of sibling Taterillus species (Rodentia, Gerbillinae). Biological Journal of the Linnean Society 77: 319–327

    Article  Google Scholar 

  • dos Reis SF, Pessoa LM, Strauss RE (1990) Application of size-free canonical discriminant analysis to studies of geographic differentiation. Revista Brasileira de Genética 13: 509–520

    Google Scholar 

  • Dryden IL, Mardia KV (1998) Statistical shape analysis. John Wiley, New York

    Google Scholar 

  • Edgington ES (1995) Randomization tests. Marcel Dekker, New York

    Google Scholar 

  • Everitt BS, Dunn G (2001) Applied multivariate data analysis, Second Edition. Wiley & Sons, New York

    Google Scholar 

  • Fisher RA (1936) The use of multiple measurements in taxonomic problems. Annals of Eugenics 7: 179–188

    Article  Google Scholar 

  • Flury B, Schmid MJ, Narayanan A (1994) Error rates in quadratic discrimination with constraints on the covariance matrices. Journal of Classification 11: 101–120

    Article  Google Scholar 

  • Flury BK (1988) Common principal components and related multivariate models, Wiley, New York

    Google Scholar 

  • Fu WJ, Carroll RJ, Wang S (2005) Estimating misclassification error with small samples via bootstrap cross-validation. Bioinformatics 21: 1979–1986

    Article  Google Scholar 

  • Goodall CR (1995) Procrustes methods in the statistical analysis of shape revisited. In Mardia KV, Gill CA (Eds.) Current issues in statistical shape analysis, University of Leeds Press, Leeds, 18–33 pp

    Google Scholar 

  • Gower JC (1975) Generalized procrustes analysis. Psychometrika 40: 33–51

    Article  Google Scholar 

  • Gower JC (1976) Growth-free canonical variates and generalized inverses. Bulletin of the Geological Institutions of the University of Uppsala 7: 1–10

    Google Scholar 

  • Gower JC, Krzanowski WJ (1999) Analysis of distance for structured multivariate data and extensions to multivariate analysis of variance. Royal Statistical Society: Series C (Applied Statistics) 48: 505–519

    Article  Google Scholar 

  • Hand DJ (1981) Discrimination and classification. John Wiley, New York

    Google Scholar 

  • Higgins CL, Strauss RE (2004) Discrimination and classification of foraging paths produced by search-tactic models. Behavioral Ecology 15: 248–254

    Article  Google Scholar 

  • Hochberg Y, Tamhane AC (1987) Multiple comparison procedures, Wiley & Sons, New York

    Book  Google Scholar 

  • Hosmer DW, Lemeshow S (2000) Applied logistic regression analysis, Second Edition, John Wiley & Sons, New York

    Book  Google Scholar 

  • Howland P, Park H (2004) Generalizing discriminant analysis using the generalized singular value decomposition. IEEE Transactions on Pattern Analysis and Machine Intelligence 26: 995–1006

    Article  Google Scholar 

  • Humphries JM, Bookstein FL, Chernoff B, Smith GR, Elder RL, Poss S (1981) Multivariate discrimination by shape in relation to size. Systematic Zoology 30: 291–308

    Article  Google Scholar 

  • Jolicoeur P, Mosimann JE (1960) Size and shape variation in the painted turtle: a principal component analysis. Growth 24: 399–354

    Google Scholar 

  • Jolicoeur P, Pirlot P, Baron G, Stephan H (1984) Brain structure and correlation patterns in Insectivora, Chiroptera, and primates. Systematic Zoology 33: 14–29

    Article  Google Scholar 

  • Jungers WL, Falsetti AB, Wall CE (1995) Shape, relative size, and size-adjustments in morphometrics. Yearbook of Physical Anthropology 38: 137–161

    Article  Google Scholar 

  • Keene ON (1995) The log transformation is special. Statistics in Medicine 14: 811–819

    Article  Google Scholar 

  • Kiang MY (2003) A comparative assessment of classification methods. Decision Support Systems 35: 441–454

    Article  Google Scholar 

  • Klingenberg CP, Froese R (1991) A multivariate comparison of allometric growth patterns. Systematic Zoology 40: 410–419

    Article  Google Scholar 

  • Klingenberg CP, Neuenschwander BE, Flury BD (1996) Ontogeny and individual variation: analysis of patterned covariance matrices with common principal components. Systematic Biology 45: 135–150

    Article  Google Scholar 

  • Manly BFJ (1997) Randomization, bootstrap and Monte Carlo methods in biology. Chapman & Hall, London

    Google Scholar 

  • Marks S, Dunn OJ (1974) Discriminant functions when covariance matrices are unequal. Journal of the American Statistical Association 69: 555–559

    Article  Google Scholar 

  • Meshbane A, Morris JD (1995) A method for selecting between linear and quadratic classification models in discriminant analysis. Journal of Experimental Education 63: 263–273

    Article  Google Scholar 

  • Owen JG, Chmielewski MA (1985) On canonical variates analysis and the construction of confidence ellipses in systematic studies. Systematic Zoology 34: 366–374

    Article  Google Scholar 

  • Penin X, Baylac M (1995) Analysis of skull shape changes in apes, using 3D Procrustes superimposition. In Mardia KV, Gill CA (Eds.) Current issues in statistical shape analysis, Leeds University Press, Leeds, England, 208–210 pp

    Google Scholar 

  • Pimentel RA (1979) Morphometrics: the multivariate analysis of biological data. Kendall-Hunt, Dubuque

    Google Scholar 

  • Press SJ, Wilson S (1978) Choosing between logistic regression and discriminant analysis. Journal of the American Statistical Association 73: 699–705

    Article  Google Scholar 

  • Raudys S (2001) Statistical and neural classifiers: an integrated approach. Springer, New York

    Book  Google Scholar 

  • Reiser B (2001) Confidence intervals for the Mahalanobis distance. Communications in Statistics – Simulation and. Computation 30: 37–45

    Google Scholar 

  • Ringrose TJ (1996) Alternative confidence regions for canonical variate analysis. Biometrika 83: 575–587

    Article  Google Scholar 

  • Ripley BD (1994) Neural networks and related methods for classification. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 56: 409–456

    Google Scholar 

  • Rohlf FJ (1993) Relative warp analysis and an example of its application to mosquito wings. In Marcus LF, Bello E, Garcia-Valdecasas A (Eds.) Contributions to morphometrics, Museo Nacional de Ciencias Naturales, Madrid, Spain, 131–159 pp

    Google Scholar 

  • Rohlf FJ, Bookstein FL (1987) A comment on shearing as a method for “size correction”. Systematic Zoology 36: 356–367

    Article  Google Scholar 

  • Rohlf FJ, Slice D (1990) Extensions of the Procrustes method for the optimal superposition of landmarks. Systematic Zoology 39: 40–59

    Article  Google Scholar 

  • Schulte-Hostedde AI, Zinner B, Millar JS, Hickling GJ (2005) Restitution of mass-size residuals: validating body condition indices. Ecology 86: 155–163

    Article  Google Scholar 

  • Small CG (1996) The statistical theory of shape. Springer, New York

    Book  Google Scholar 

  • Smith GR (1973) Analysis of several hybrid cyprinid fishes from western North America. Copeia 1973: 395–410

    Article  Google Scholar 

  • Stone M (1974) Cross-validatory choice and assessment of statistical predictions. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 36: 111–147

    Google Scholar 

  • Strauss RE (1993) The study of allometry since Huxley. In Huxley JS (Ed.) Problems of relative growth, Johns Hopkins University Press, Baltimore, 47–75 pp

    Google Scholar 

  • Strauss RE, Bookstein FL (1982) The truss: body form reconstruction in morphometrics. Systematic Zoology 31: 113–135

    Article  Google Scholar 

  • Thorpe RS (1983) A review of the numerical methods for recognising and analysing racial differentiation. In Felsenstein J (Ed.) Numerical taxonomy, Springer-Verlag, Berlin, 404–423 pp

    Chapter  Google Scholar 

  • Thorpe RS (1988) Multiple group principal components analysis and population differentiation. Journal of Zoology (London) 216: 37–40

    Article  Google Scholar 

  • Thorpe RS, Leamy L (1983) Morphometric studies in inbred and hybrid housemice (Mus sp.): multivariate analysis of size and shape. Journal of Zoology (London) 199: 421–432

    Article  Google Scholar 

  • Von Zuben FJ, Duarte LC, Stangenhaus G, Pessoa LM, dos Reis SF (1998) Bootstrap confidence regions for canonical variates: application to studies of evolutionary differentiation. Biometrical Journal 40: 327–339

    Article  Google Scholar 

  • Weihs C (1995) Canonical discriminant analysis: comparison of resampling methods and convex-hull approximation. In Krzanowski WJ (Ed.) Recent advances in descriptive multivariate analysis, Clarendon Press, Oxford, UK, 34–50 pp

    Google Scholar 

  • White JW, Ruttenberg BI (2007) Discriminant function analysis in marine ecology: some oversights and their solutions. Marine Ecology Progress Series 329: 301–305

    Article  Google Scholar 

  • Wilcox RR (2005) Introduction to robust estimation and hypothesis testing, Academic Press, New York

    Google Scholar 

  • Williams BK (1982) A simple demonstration of the relationship between classification and canonical variates analysis. American Statistician 36: 363–365

    Google Scholar 

  • Willig MR, Owen RD (1987) Univariate analyses of morphometric variation do not emulate the results of multivariate analyses. Systematic Zoology 36: 398–400

    Article  Google Scholar 

  • Ye J, Janardan R, Park CH, Park H (2004) An optimization criterion for generalized discriminant analysis on undersampled problems. IEEE Transactions on Pattern Analysis and Machine Intelligence 26: 982–994

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Biological Sciences, Texas Tech University, Lubbock, TX, 79409-3131, USA

    Richard E. Strauss

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  1. Richard E. Strauss
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Correspondence to Richard E. Strauss .

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Editors and Affiliations

  1. Fac. Science, Dept. Geology, Minia University, Minia, 61519, Egypt

    Ashraf M.T. Elewa

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Strauss, R.E. (2010). Discriminating Groups of Organisms. In: Elewa, A. (eds) Morphometrics for Nonmorphometricians. Lecture Notes in Earth Sciences, vol 124. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-95853-6_4

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