Abstract
Detrending and non-linear axis rescaling potentially improve the accuracy of gradient recovery in correspondence analyses but also reduce the stability or consistency of solutions. Variation among bootstrapped ordination solutions was compared across methods in analyses of both field and simulated data. Solution accuracy, measured with mean squared errors from Procrustes analysis, was compared using simulated data with known structure.
Standard detrending-by-segments combined with non-linear rescaling entailed some cost in solution stability, but could improve the accuracy of solutions for long gradients. Without non-linear rescaling these solutions were usually less stable and less accurate. Although detrending-by-polynomials might be preferable on other grounds, it did not produce more accurate or stable solutions than detrending-by-segments.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Abbreviations
- CA:
-
correspondence analysis
- DCA:
-
detrended correspondence analysis
- MSE:
-
Procrustes mean squared error statistic
- SD:
-
standard deviation units of species turnover
- SRV:
-
scaled variance in species ranks
References
Bradfield, G. E. & Kenkel, N. C. 1987. Nonlinear ordination using flexible shortest path adjustment of ecological distances. Ecology 68: 750–753.
Faith, D. P., Minchin, P. R. & Beibin, L. 1987. Compositional dissimilarity as a robust measure of ecological distance. Vegetatio 69: 57–68.
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.
Gauch Jr., H. G. 1982. Multivariate analysis in community ecology. Cambridge Univ. Press, Cambridge.
Gauch Jr., H. G. & Whittaker, R. H. 1972. Coenocline simulation. Ecology 53: 446–451.
Gauch Jr., H. G. & Whittaker, R. H. 1976. Simulation of community patterns. Vegetatio 33: 13–16.
Greenacre, M. J. 1984. Theory and applications of correspondence analysis. Academic Press, London.
Hill, M. O. 1974. Correspondence analysis: a neglected multivariate method. Appl. Statist. 23: 340–354.
Hill, M. O. 1979. DECORANA — a FORTRAN program for detrended correspondence analysis and reciprocal averaging. Section of Ecology and Systematics, Cornell University, Ithaca, New York.
Hill, M. O. & Gauch Jr., H. G. 1980. Detrended correspondence analysis: an improved ordination technique. Vegetatio 42: 47–58.
Ihm, P. & van Groenewoud, H. 1984. Correspondence analysis and gaussian ordination. In: Chambers, J. M., Gordesch, J., Klas, A., Lebart, L. & Sint, P. P. (eds), Compstat Lectures 3, Lectures in computational statistics. Physica-Verlag, Vienna.
Jongman, R. H. G. ter Braak, C. J. F., & van Tongeren, O. F. R. 1987. Data analysis in community and landscape ecology. Pudoc, Wageningen.
Kenkel, N. C. & Orlôci, L. 1986. Applying metric and non-metric multidimensional scaling to ecological studies: some new results. Ecology 67: 919–928.
Knox, R. G. & Peet, R. K. 1989. Bootstrapped ordination: a method for estimating sampling effects in indirect gradient analysis. Vegetatio 80: 153–165.
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. R. 1987. An evaluation of the relative robustness of techniques for ecological ordination. Vegetatio 69: 89–107.
Oksanen, J. 1988. A note on the occasional instability of detrending in correspondence analysis. Vegetatio 74: 29–32.
Peet, R. K. & Christensen, N. L. 1980. Hardwood forests of the North Carolina piedmont. Veröff. Geobot. Inst. Rubel 69: 14–39.
Peet, R. K., Knox, R. G., Case, J. S & Allen, R. 1988. Putting things in order: the advantages of detrended correspondence analysis. Amer. Nat. 131: 924–934.
Pielou, E. C. 1984. The interpretation of ecological data. Wiley, New York.
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.
ter Braak, C. J. F. 1986. Canonical correspondence analysis: a new eigenvector technique for multivariate direct gradient analysis. Ecology 67: 1167–1179.
ter Braak, C. J. F. 1987. The analysis of vegetation-environment relationships by canonical correspondence analysis. Vegetatio 69: 69–77.
ter Braak, C. J. F. 1988a. CANOCO — a FORTRAN program for canonical community ordination by [partial] [de-trended] [canonical] correspondence analysis, principal components analysis and redundancy analysis (version 2.1). Report LWA-88–02. Agricultural Mathematics Group, Wageningen.
ter Braak, C. J. F. 1988b. CANOCO — and extension of DECORANA to analyze species-environment relationships. Vegetatio 75: 159–160.
ter Braak, C. J. F. & Prentice, I. C. 1988. A theory of gradient analysis. Adv. Ecol. Res. 18: 271–317.
Wartenberg, D., Ferson, S. & Rohlf, F. J. 1987. Putting things in order: A critique of detrended correspondence analysis. Amer. Nat. 129: 434–448.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1990 Kluwer Academic Publishers
About this chapter
Cite this chapter
Knox, R.G. (1990). Effects of detrending and rescaling on correspondence analysis: solution stability and accuracy. In: Grabherr, G., Mucina, L., Dale, M.B., Ter Braak, C.J.F. (eds) Progress in theoretical vegetation science. Advances in vegetation science, vol 11. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-1934-1_10
Download citation
DOI: https://doi.org/10.1007/978-94-009-1934-1_10
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-7363-9
Online ISBN: 978-94-009-1934-1
eBook Packages: Springer Book Archive