Michael Greenacre. 2013. Fuzzy coding in constrained ordinations. *Ecology* 94:280–286. http://dx.doi.org/10.1890/12-0981.1

Supplement

Artificial and real data sets, and R functions and scripts to perform canonical correspondence analysis using fuzzy-coded explanatory variables, with adjustment of the variance explained.
*Ecological Archives* E094-021-S1.

Authors

File list (downloads)

Description

Michael Greenacre

Department of Economics and Business

Universitat Pompeu Fabra

Ramon Trias Fargas 25--27

Barcelona

E-08005 Spain

Faculty of Biological Sciences, Fisheries and Economics

University of Tromsø

Tromsø

N-9037 Norway

E-mails: michael.greenacre@upf.edu, michael.greenacre@gmail.com

File list

artificial.csv (md5: 2dcf93451985a5205c88df0f24dcc709) - abundance data for 300 samples on 5 species (A, B, C, D and E) and environmental data on 2 variables (X and Y).

BarentsFish.csv (md5: e61ef26ef9a7fec70f831535587a5966) - fish abundance data set ‘BarentsFish’, on 89 samples from the Barents Sea, along with longitude and latitude positions, depth and temperature

fuzzy.tri.R (md5: 0bf5013ae24752cd27ed48e585a53870) - R function fuzzy.tri for fuzzy coding into any number of categories using triangular membership functions

CCA.R (md5: c6b9a3207e7e3405545a673b5a536daa) - R function CCA for basic computations of a CCA

fuzzyscript.R (md5: 4ce442235d7d6e107ff498fc62cc1789) - R script illustrating several analyses from this report (see description below)

Description

The two data files used in the report are given in csv format.
Two R functions are provided: (i) to fuzzy code continuous variables into a chosen number of fuzzy categories, or into categories based on user-defined hinge points:
(ii) to compute a basic canonical correspondence analysis, using the singular-value decomposition,
with output of the sample (row) principal coordinates and the variable (column) contribution coordinates,
as well as parts of constrained and unconstrained inertia. This function is useful for computing the adjusted percentage of variance explained (see R script next).
Finally an R script is provided illustrating the following analyses:
(a) the computation of the adjusted *R*^{2} values in CCA by the permutation procedure proposed by Peres-Neto et al. (2006),
(b) the conversion of continuous environmental variables (including spatial ones) into fuzzy-coded variables, and
(c) plotting the results of the ‘BarentsFish’ analysis.

Reference: Peres-Neto, P. R., P. Legendre, S. Dray, and D. Borcard. 2006. Partitioning of species data matrices: estimation and comparison of fractions. Ecology 87:2614–2625.

Reference: Peres-Neto, P. R., P. Legendre, S. Dray, and D. Borcard. 2006. Partitioning of species data matrices: estimation and comparison of fractions. Ecology 87:2614–2625.

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