Abstract
Indirect gradient analysis, or ordination, is primarily a method of exploratory data analysis. However, to support biological interpretations of resulting axes as vegetation gradients, or later confirmatory analyses and statistical tests, these axes need to be stable or at least robust into minor sampling effects. We develop a computer-intensive bootstrap (resampling) approach to estimate sampling effects on solutions from nonlinear ordination.
We apply this approach to simulated data and to three forest data sets from North Carolina, USA and examine the resulting patterns of local and global instability in detrended correspondence analysis (DCA) solutions. We propose a bootstrap coefficient, scaled rank variance (SRV), to estimate remaining instability in species ranks after rotating axes to a common global orientation. In analysis of simulated data, bootstrap SRV was generally consistent with an equivalent estimate from repeated sampling. In an example using field data SRV, bootstrapped DCA showed good recovery of the order of common species along the first two axes, but poor recovery of later axes. We also suggest some criteria to use with the SRV to decide how many axes to retain and attempt to interpret.
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Abbreviations
- DCA=:
-
detrended correspondence analysis
- SRV=:
-
scaled rank variance
References
Austin, M.P. 1968. An ordination study of a chalk grassland community. J. Ecol. 56: 739–757.
Austin, M.P. 1985. Continuum concept, ordination methods, and niche theory. Ann. Rev. Ecol. Syst. 16: 39–61.
Austin, M.P. 1987. Models for the analysis of species' response to environmental gradients. Vegetatio 69: 35–45.
Baggaley, A.R. 1982. Deciding on the ratio of number of subjects to number of variables in factor analysis. Multivar. Exp. Clin. Res. 6: 81–85.
Baggaley, A.R. 1986. Heterogeneous correlations and estimates of required sample size in factor analysis. Multivar. Exp. Clin. Res. 8: 161–163.
deLeeuw, J. & Meulman, J. 1986. A special jackknife for multidimensional scaling. J. Classification 3: 97–112.
Diaconis, P. & Efron, B. 1983. Computer-intensive methods in statistics. Sci. Am. 248(5): 116–130.
Efron, B. 1979. Bootstrap methods: another look at the jackknife. Ann. Statist. 7: 1–26.
Efron, B. 1982. The jackknife, the bootstrap, and other resampling plans. SIAM Monograph 38.
Efron, B. 1987. Better bootstrap confidence intervals. J. Amer. Statist. Assoc. 82: 171–185.
Efron, B. & Tibshirani, R. 1986. Bootstrap methods for standard errors, confidence intervals, and other measures of statistical accuracy. Statist. Sci. 1: 54–77.
Fasham, M.R.J. 1977. A comparison of nonmetric multidimensional scaling, principal components and reciprocal averaging for the ordination of simulated coenoclines, and coenoplanes. Ecology 58: 551–561.
GauchJr, H.G., 1982a. Noise reduction by eigenvector ordinations. Ecology 63: 1643–1649.
GauchJr, H.G., 1982b. Multivariate analysis in community ecology. Cambridge University Press, Cambridge.
GauchJr, H.G. & Whittaker, R.H. 1972. Coenocline simulation. Ecology 53: 446–451.
GauchJr, H.G. & Whittaker, R.H. 1976. Simulation of community patterns. Vegetatio 33: 13–16.
GauchJr, H.G. & Whittaker, R.H. & Singer, S.B. 1981. A comparative study of nonmetric ordinations. J. Ecol. 69: 135–152.
GauchJr, H.G. & Whittaker, R.H. & Wentworth, T.R. 1977. A comparative study of reciprocal averaging and other ordination techniques. J. Ecol. 65: 157–174.
Greenacre, M.J. 1984. Theory and applications of correspondence analysis. Academic Press, London.
Hartigan, J.A. 1986. Comment (on: Bootstrap methods for standard errors, confidence intervals, and other measures of statistical accuracy) Statist. Sci. 1: 75–77.
Hill, M.O. 1974. Correspondence analysis: a neglected multivariate method. Applied Statistics 23: 340–354.
Hill, M.O. 1979. DECORANA-a FORTRAN program for detrended correspondence analysis and reciprocal averaging. Cornell University, Ithaca, New York.
Hill, M.O. & GauchJr, H.G., 1980. Detrended correspondence analysis: an improved ordination technique. Vegetatio 42: 47–58.
Kenkel, N.C. & Orlóci, L. 1986. Applying metric and nonmetric multidimensional scaling to ecological studies: some new results. Ecology 67: 919–928.
Knox, R.G. 1987. Hypothesis testing in plant community ecology: analysis of long-term experiments and regional vegetation data. Ph. D. Diss. University of North Carolina, Chapel Hill, North Carolina.
Legendre, L. & Legendre, P. 1983. Numerical ecology. Elsevier, Amsterdam.
McLeod, D.E. 1988. Vegetation patterns, floristics, and environmental relationships in the Black and Craggy Mountains of North Carolina. Ph. D. Diss., University of North Carolina, Chapel Hill, North Carolina.
Minchin, P. 1987a. Simulation of multidimensional community patterns: towards a comprehensive model. Vegetatio 71: 145–156.
Minchin, P. 1987b. An evaluation of the relative robustness of techniques for ecological ordination. Vegetatio 69: 89–107.
Mueller-Dombois, D. & Ellenberg, H. 1974. Aims and methods of vegetation ecology, John Wiley and Sons, New York.
Noy-Meir, I. & van derMaarel, E. 1987. Relations between community theory and community analysis in vegetation science: some historical perspectives. Vegetatio 69: 5–15.
Oksanen, J. 1988. A note on the occasional instability of detrending in correspondence analysis. Vegetatio 74: 29–32.
Palmer, M.W. 1988. Fractal geometry: a tool for describing spatial patterns of plant communities. Vegetatio 75: 91–102.
Peet, R.K. & Christensen, N.L. 1980. Hardwood forests of the North Carolina piedmont. Veröff. Geobot. Inst. Rübel 69: 14–39.
Peet, R.K., Knox, R.G., Case, J.S. & Allen, R.B. 1988. Putting things in order: the advantages of detrended correspondence analysis. Amer. Nat. 131: 924–934.
Schöneman, P.H. & Carroll, R.M. 1970. Fitting one matrix to another under choice of a central dilation and a rigid motion. Psychometrika 35: 245–255.
Weinberg, S.L., Carroll, J.D. & Cohen, H.S. 1984. Confidence regions for INDSCAL using the jackknife and bootstrap techniques. Psychometrika 49: 475–491.
Weiner, J. 1985. Size hierarchies in experimental populations of annual plants. Ecology 66: 743–752.
Whittaker, R.H. 1967. Gradient analysis of vegetation. Biol. Rev. 42: 207–264.
Whittaker, R.H. (ed.) 1978. Ordination of plant communities. Handbook of Vegetation Science 5. 2nd ed. Junk, The Hague.
Williams, B.K. 1983. Some observations on the use of discriminant analysis in ecology. Ecology 64: 1283–1291.
Wilson, J.B. 1987. Methods for detercting non-randomness in species co-occurrences: a contribution. Oecologia 73: 579–582.
Wilson, J.B., Gitay, H., Agnew, A.D.Q. 1987. Does niche limitation exist? Funct. Ecology 1: 391–397.
Wilson, M.V. 1981. A statistical test of the accuracy and consistency of ordinations. Ecology 62: 8–12.
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Knox, R.G., Peet, R.K. Bootstrapped ordination: a method for estimating sampling effects in indirect gradient analysis. Vegetatio 80, 153–165 (1989). https://doi.org/10.1007/BF00048039
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DOI: https://doi.org/10.1007/BF00048039