Multiple Parallel Ordinations: the Importance of Choice of Ordination Method and Weighting of Species Abundance Data

Open access


Most species-abundance matrices subjected to ordination are analysed by applying one ordination method to one single weighting (transformation) of the raw abundance values. We argue that such an approach is sub-optimal for identification of species-environment relationships. In order to capture the full range of qualitative and quantitative components of variation unique to each species-abundance matrix, data sets covering the full range of abundance weights from presence/absence to raw abundance data should be subjected to ordination. Furthermore, two or more ordination methods should be used in parallel to enhance detection of artifacts in the results. We describe and exemplify a multiple parallel ordination (MPO) procedure, which ensures that both qualitative and quantitative properties of the data set are revealed. This procedure implies that different ordination methods are applied in parallel, each with different weightings of elements in the species-abundance matrix. Two species-abundance matrices are used to exemplify the MPO procedure, one of individual counts from a marine benthic study of mollusc and echinoderm species and one of percent cover of vascular plants, bryophytes and lichens from a study of boreal forest understory vegetation. Striking differences between point configurations obtained by different ordination methods and strong dependence of ordination results on the weights given to abundance are demonstrated. Properties of species and data sets that may explain the observed variation in ordination results are analyzed and discussed. We show that the widely held belief that changes in ordination structure with changes of weighting function are brought about only by highly abundant and frequent species is an over-simplification. We conclude that the MPO procedure - applying more than one ordination method and more than one weighting function is likely to enhance the user’s insight into the multivariate structure of species-abundance matrices resulting from ordination analyses.

If the inline PDF is not rendering correctly, you can download the PDF file here.

  • Austin M.P. & Greig-Smith P. 1968. The application of quantitative methods to vegetation survey: II. Some methodological problems of data from rain forest. J. Ecol 56: 827-844.

  • Beals E.W. 1973. Ordination: Mathematical elegance and ecological naivete. J. Ecol. 61: 23-35.

  • Bratli H. Økland T. Økland R.H. Dramstad W.E. Elven R. Engan G. Fjellstad W. Heegaard E. Pedersen O. & Solstad H. 2006. Patterns of variation in vascular plant species richness and composition in SE Norwegian agricultural landscapes. Agric. Ecosyst. & Environ. 114: 270-286.

  • Brown J.H. 1984. On the relationship between abundance and distribution of species. Am. Nat. 124: 255-279.

  • Buckley H.L. & Freckleton R.P. 2010. Understanding the role of species dynamics in abundanceoccupancy relationships. J Ecol. 98: 645-658.

  • Cao Y. & Epifanio J. 2010. Quantifying the responses of macroinvertebrate assemblages to simulated stress: are more accurate similarity indices less useful? Meth. Ecol. Evol. 1: 380-388.

  • Clarke K. 1993. Non-parametric multivariate analyses of changes in community structure. Aus. J. Ecol. 18: 117-143.

  • Clymo R. 1980. Preliminary survey of the peat-bog Hummell Knowe Moss using various numerical methods. Vegetatio 42: 129-148.

  • Collins S. L. Glenn S.M. & Roberts D.W. 1993. The hierarchical continuum concept. J. Veg. Sci. 4: 149-156.

  • De’ath G. 1999. Extended dissimilarity: a method of robust estimation of ecological distances from high beta diversity data. Pl. Ecol. 144: 191-199.

  • Eilertsen O. Økland R.H. Økland T. & Pedersen O. 1990. Data manipulation and gradient length estimation in DCA ordination. J. Veg. Sci. 1: 261-270.

  • Ellingsen K.E. & Gray J.S. 2002. Spatial patterns of benthic diversity: is there a latitudinal gradient along the Norwegian continental shelf? J. Anim. Ecol. 71: 373-389.

  • Ellingsen K.E. Hewitt J.E. & Thrush S.F. 2007. Rare species habitat diversity and functional redundancy in marine benthos. J. Sea Res. 58: 291-301.

  • Faith D.P. Minchin P.R. & Belbin L. 1987. Compositional dissimilarity as a robust measure of ecological distance. Vegetatio 69: 57-68.

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

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

  • Gauch H.G. Jr. 1973b. The relationship between sample similarity and ecological distance. - Ecology 54: 618-622.

  • Goodall D.W. 1954. Vegetational classification and vegetational continua. Festschr. Aichinger 1: 168-182.

  • Gogina M. Glockzin M. & Zettler M.L. 2010. Distribution of benthic macrofaunal communities in the western Baltic Sea with regard to near-bottom environmental parameters. 1. Causal analysis. J. Mar. Syst. 79: 112-123.

  • Halvorsen R. 2012. A gradient analytic perspective on distribution modeling. Sommerfeltia 35: 1-165.

  • Hanski I. 1982. Dynamics of regional distribution: the core and satellite species hypothesis. Oikos 38: 210.

  • Heino J. Muotka T. Mykrä H. Paavola R. Hämäläinen H. & Koskenniemi E. 2003. Defining macroinvertebrate assemblage types of headwater streams: Implications for bioassessment and conservations. Ecol. App. 13: 842-852.

  • Hill M.O. 1973. Reciprocal averaging: An eigenvector method for ordination. J. Ecol. 61: 237-249.

  • Hill M. O. 1979. DECORANA - A FORTRAN program for detrended correspondence analysis and reciprocal averaging. Ithaca.

  • Hill M.O. Bell N. Bruggeman-Nannenga M.A. Brugués M. Cano M.J. Enroth J. Flatberg K.I. Frahm J.P. Gallego M.T. Garilleti R. Guerra J. Hedenäs L. Holyoak D.T. Hyvönen J. Ignatov M.S. Lara F. Mazimpaka V. Muñoz J. & Söderström L. 2006. An annotated checklist of the mosses of Europe and Macaronesia. J. Bryol. 28: 198-267.

  • Hill M.O. & Gauch H.G. Jr. 1980. Detrended correspondence analysis: an improved ordination technique. Vegetatio 42: 47-58.

  • Jackson D.A. 1993. Multivariate analysis of benthic invertebrate communities: the implication of choosing particular data standardizations measures of association and ordination methods. Hydrobiologia 268: 9-26.

  • Kenkel N.C. 2006. On selecting an appropriate multivariate analysis. Canadian Journal of Pl. Sci. 86: 663-676.

  • Krog H. Østhagen H. & Tønsberg T. 1994. Lavflora. Norske busk- og bladlav. Ny revidert utgave ved Hildur Krog og Tor Tønsberg ed. 2. Universitetsforlaget Oslo.

  • Legendre P. & Legendre L. 1998. Numerical ecology 2nd Edition. Elsevier Amsterdam.

  • Lengyel A. Csiky J. & Botta-Dukát Z. 2012. How do locally infrequent species influence numerical classification? A simulation study. Comm. Ecol. 13: 64-71.

  • Lid J. & Lid D.T. 2005. Norsk flora. 7 utgåve ved R. Elven. Det Norske Samlaget Oslo.

  • Liu H. Økland T. Halvorsen R. Gao J. Liu Q. Eilertsen O. & Bratli H. 2008. Gradient analyses of forests ground vegetation and its relationships to environmental variables in five subtropical forest areas S and SW China. Sommerfeltia 32: 1-196.

  • Lundblad E.R. Wright D.J. Miller J. Larkin E.M. Rinehart R. Naar D.F. Donahue D.T. Anderson S.M. & Battista T. 2006. A Benthic Terrain Classification Scheme for American Samoa.

  • Mar. Geod. 29: 89-111. van der Maarel E. 1979. Transformation of cover-abundance values in phytosociology and its effects on community similarity. Vegetatio 39: 97-114. van der Maarel E. 1982. On the manipulation and editing of phytosociological and ecological data. Vegetatio 50: 71-76.

  • Mahecha M.D. Martínez A. Lischeid G. & Beck E. 2007. Nonlinear dimensionality reduction: Alternative ordination approaches for extracting and visualizing biodiversity patterns in tropical montane forest vegetation data. Ecol. Inf. 2: 138-149.

  • Minchin P.R. 1987. An evaluation of the relative robustness of techniques for ecological ordination. Vegetatio 69:89-107.

  • Noy-Meir I. Walker D. & Williams W.T. 1975. Data Transformations in Ecological Ordination: II. On the Meaning of Data Standardization. J. Ecol. 63: 779-800.

  • Økland R.H. 1986a. Rescaling of ecological gradients. I. Calculation of ecological distance between vegetation stands by means of their floristic composition. Nord. J. Bot. 6: 651-660.

  • Økland R.H. 1986b. Reseating of ecological gradients. II. The effect of scale on symmetry of species response curves. Nord. J. Bot. 6: 661-670.

  • Økland R.H. 1990a. Vegetation ecology: theory methods and applications with reference to Fennoscandia. Sommerfeltia 1:1-233.

  • Økland R.H. 1990b. A phytoecological study of the mire Northern Kisselbergmosen SE Norway. II. Identification of gradients by detrended (canonical) correspondence analysis. Nord. J. Bot. 10:79-108.

  • Økland R.H. 1996. Are ordination and constrained ordination alternative or complementary strategies in general ecological studies? J. Veg. Sci. 7: 289-292.

  • Økland R.H. & Eilertsen O. 1993. Vegetation-environment relationships of boreal coniferous forests in the Solhomfjell area Gjerstad S Norway. Sommerfeltia 16:1-254.

  • Økland R.H. Eilertsen O. & Økland T. 1990. On the relationship between sample plot size and beta diversity in boreal coniferous forests. Vegetatio 87:187-192.

  • Økland R. H. Økland T. & Rydgren K. 2001. Vegetation-environment relationships of boreal spruce swamp forests in Østmarka Nature Reserve SE Norway. Sommerfeltia 29:1-190.

  • Økland T. 1996. Vegetation-Environment relationships of boreal spruce forests in ten monitoring reference areas in Norway. Sommerfeltia 22:1-349.

  • Økland T. Rydgren K. Økland R.H. Storaunet K.O. & Rolstad V. 2003. Variation in environmental conditions understorey species richness abundance and composition among natural and managed Picea abies forest stands. For. Ecol. Man 177: 17-37.

  • Oksanen J. 1988. A note on the occasional instability of detrending in correspondence analysis. Vegetatio 74: 29-32.

  • Oksanen J. Blanchet F.G. Kindt R. Legendre P. O’Hara R.B. Simpson G.L. Solymos P. Stevens M.H.H. & Wagner H. 2012. Community ecology package “vegan” version 2.0-4.

  • Olsgard F. 1993. Do toxic algal blooms affect subtidal soft-bottom communities? Mar. Ecol. Prog. Ser. 102: 269-286.

  • Olsgard F. & Gray J.S. 1995. A comprehensive analysis of the effects of offshore oil and gas exploration and production on the benthic communities of the Norwegian continental shelf. Marine Ecology Progress Series 122: 277-306.

  • Olsgard F. Somerfield P. & Carr M. 1997. Relationships between taxonomic resolution and data transformations in analyses of a macrobenthic community along an established pollution gradient. Mar. Ecol. Prog. Ser. 149: 173-181.

  • Orlóci L. 1978. Multivariate analysis in vegetation research. Second ed. Junk The Hague. Palmer M.W. 1993. Putting things in even better order: The advantages of canonical correspondence analysis. Ecology 74:2215-2230.

  • Peet R.K. Knox R.G. Case J.S. & Allen R.B. 1988. Putting things in order: The advantages of detrended correspondence analysis. Am Nat 131: 924-934.

  • Podani J. 1989. Comparison of ordinations and classifications of vegetation data. Vegetatio 83:11-128.

  • Raunkiær C. 1918. Recherches statistiques sur les formations végétales. Biologiske meddelelser udgivne af Det kongelige danske videnskabernes selskab 1:1-80. R Development Core Team. 2012. R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing Vienna Austria.

  • Rydgren K. 1993. Herb-rich spruce forests in W Nordland N Norway: an ecological and methodological study. Nord. J. Bot. 13: 667-690.

  • Smartt P.F.M. Meacock S.E. & Lambert J.M. 1974. Investigations into the properties of quantitative vegetational data: I. Pilot study. J.Ecol. 62: 735-759.

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

  • Thorne R.S.J. Williams W.P. & Cao Y. 1999. The influence of data transformations on biological monitoring studies using macroinvertebrates. Water Res. 33: 343-350.

  • Wartenberg D. Ferson S. & Rohlf F.J. 1987. Putting things in order: A critique of detrended correspondence analysis. Am Nat 129: 434-448.

  • Whittaker R.H. 1956. Vegetation of the Great Smokey Mountains. Ecol. Monogr. 26: 1-80.

  • Whittaker R.H. 1967. Gradient analysis of vegetation. Biol. Rev. 42: 207-264.

  • Wildi O. 1980. Management and multivariate analysis of large data sets in vegetation research. Vegetatio 42: 175-180.

  • Wilson J.B. 2012. Species presence/abundance sometimes represents a plant community as well as species abundances do or better. J. Veg. Sci. 23: 1013-1023.

  • Wright I.A N.A. Chessman B.C. Fairweather P.G. & Benson L.E.E.J. 1995. Measuring the impact of sewage effluent on the macroinvertebrate community of an upland stream: the effect of different levels of taxonomic resolution and quantification. Aus. J. Ecol. 20: 142-149.

Journal information
Cited By
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 348 178 5
PDF Downloads 221 119 1