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Topics in constrained and unconstrained ordination

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Abstract

In this paper, we reflect on a number of aspects of ordination methods: how should absences be treated in ordination and how do model-based methods, including Gaussian ordination and methods using generalized linear models, relate to the usual least-squares (eigenvector) methods based on (log−) transformed data. We defend detrended correspondence analysis by theoretical arguments and by reanalyzing data that previously gave bad results. We show by examples that constrained ordination can yield more informative views on effects of interest compared to unconstrained ordination (where such effects can be invisible) and show how constrained axes can be interpreted. Constrained ordination uses an ANOVA/regression approach to enable the user to focus on particular aspects of species community data, in particular the effects of qualitative and quantitative environmental variables. We close with an analysis examining the interaction effects between two factors, and we demonstrate how principal response curves can help in their visualisation. Example data and Canoco 5 projects are provided as Supplementary Material.

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Acknowledgments

This paper benefitted from comments by David Warton and Pierre Legendre. The contribution of PS was funded by the Center of Excellence PLADIAS, 14-36079G, Czech Science Foundation.

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Correspondence to Cajo J. F. ter Braak.

Additional information

Communicated by P. R. Minchin and J. Oksanen.

Electronic supplementary material

Below is the link to the electronic supplementary material.

11258_2014_356_MOESM1_ESM.zip

Supplementary material 1 Canoco 5 projects detailing how analyses are carried out; these details can be inspected by any reader by asking for an one-month trial copy of Canoco 5 at trial@microcomputerpower.com (ZIP 732 kb)

11258_2014_356_MOESM2_ESM.zip

Supplementary material 2 Data tables of the examples Tikus Island, Minchin87_2b and Sod in comma separated format (two tables per example, one for the community data and one for the explanatory data) (ZIP 8 kb)

Supplementary material 3 Readme file for the zip files with screenshots of the example Canoco 5 projects (PDF 410 kb)

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ter Braak, C.J.F., Šmilauer, P. Topics in constrained and unconstrained ordination. Plant Ecol 216, 683–696 (2015). https://doi.org/10.1007/s11258-014-0356-5

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