Double constrained correspondence analysis (dc-CA) for analyzing
(multi-)trait (multi-)environment ecological data using library vegan
and native R code. It has a formula interface which allows to assess,
for example, the importance of trait interactions in shaping ecological
communities. The function dc_CA has an option to divide the abundance
data of a site by the site total, giving equal site weights. This division
has the advantage that the multivariate analysis corresponds with an
unweighted (multi-trait) community-level analysis, instead of being weighted.
Throughout the two step algorithm of ter Braak et al. (2018) is used. This algorithm combines and extends community- (sample-) and species-level analyses, i.e. (1) the usual community weighted means (CWM) regression analysis and (2) the species-level analysis of species-niche centroids (SNC) regression analysis. The SNC is the center of the realized niche of the species along an environmental variable or, in the case of dc-CA, an environmental gradient, i.e. the dc-CA ordination axis. Computationally, dc-CA can be carried out by a single singular value decomposition (ter Braak et al. 2018), but it is here computed in two steps.
The first step uses canonical correspondence analysis
(cca) to regress the (transposed) abundance data on to
the traits and the second step uses weighed redundancy analysis
(wrda or, with equal site weights, rda)
to regress the CWMs of the orthonormalized traits,
obtained from the first step, on to the environmental predictors.
The second step is thus a community-level analysis.
If divideBySiteTotals = FALSE, the second step uses
wrda and performs a weighted redundancy analysis of the CWMs
on to the environmental variables.
Division of the abundance data by the site totals has the advantage that the resulting analysis (without dimension reduction, i.e. retaining all dc-CA axes) corresponds with a series of unweighted community-level analyses, instead of the analyses being weighted.
Warning: The dcCA package was built from vegan version 2.6-4
and uses some of the internal structure of the vegan
cca.object in the not-exported functions
f_inertia and get_QR in the source code file
functions_using_cca_object_internals.r.
The main user-functions are dc_CA, plot.dcca,
scores.dcca, print.dcca and
anova.dcca.
Maintainer: Bart-Jan van Rossum bart-jan.vanrossum@wur.nl (ORCID)
Authors:
Cajo J.F ter Braak cajo.terbraak@wur.nl (ORCID)
ter Braak, CJF, Šmilauer P, and Dray S. 2018. Algorithms and biplots for double constrained correspondence analysis. Environmental and Ecological Statistics, 25(2), 171-197. tools:::Rd_expr_doi("10.1007/s10651-017-0395-x")
Oksanen, J., et al. (2022) vegan: Community Ecology Package. R package version 2.6-4. https://CRAN.R-project.org/package=vegan.
cca and rda