Task E
Work through these exercises after reading the Detrended Correspondence Analysis chapter. The most useful thing a DCA reports is the gradient length in \(\beta\)-diversity standard-deviation units, so the task is built around extracting and using that number. Four exercises are hands-on calculations and two are short conceptual questions. A worked answer is given under each exercise; try it yourself before opening it.
decorana() (remember to drop the empty site first); extract the axis lengths and report the length of the first DCA axis in SD units.
Call:
decorana(veg = spe)
Detrended correspondence analysis with 26 segments.
Rescaling of axes with 4 iterations.
Total inertia (scaled Chi-square): 1.1669
DCA1 DCA2 DCA3 DCA4
Eigenvalues 0.538 0.1964 0.08759 0.17777
Additive Eigenvalues 0.538 0.1264 0.07535 0.04787
Decorana values 0.601 0.1283 0.06111 0.03293
Axis lengths 3.855 1.4672 2.39227 1.79048[1] 3.855271The decorana printout gives an Axis lengths row; the first-axis length for the Doubs fish is 3.86 SD units. That is a long gradient: end to end, the community turns over several times, so few species are shared between the upper and lower river. The length is the single most useful number DCA gives, and the rest of the task uses it.
Two things change. Detrending removes the arch: in the CA the sites curve as a horseshoe, whereas in the DCA they fall along a much straighter first axis, because the quadratic distortion that CA forced into axis 2 has been taken out. Rescaling changes the spacing: DCA stretches and compresses axis 1 so that a unit of distance corresponds to a constant amount of species turnover (one SD), which is what makes the axis length interpretable as gradient length. The two corrections are the whole point of DCA over CA.
data(dune)) and the bird communities along the elevation gradient in Yushan Mountain, Taiwan — report each first-axis gradient length, and produce the DCA biplot for each.# --- dune meadows ---
data(dune)
dca_dune <- decorana(dune)
gl_dune <- diff(range(scores(dca_dune, display = "sites", choices = 1)))
# --- Yushan birds ---
ybirds_spe <- read.table(
here::here("data", "BCB743", "ybirds_spe.txt"),
header = TRUE, row.names = 1
)
ybirds_spe <- ybirds_spe[rowSums(ybirds_spe) > 0, ]
dca_yush <- decorana(ybirds_spe)
gl_yush <- diff(range(scores(dca_yush, display = "sites", choices = 1)))
c(dune = round(gl_dune, 2), yushan = round(gl_yush, 2)) # first-axis gradient lengths (SD) dune yushan
3.70 5.13 
Both datasets produce fairly long first-axis gradients — the dune meadows about 3.7 SD (turnover from wet, heavily managed meadows to dry, lightly managed ones) and the Yushan birds about 5.1 SD (the elevation gradient) — and the biplots show the sites spread along that first axis in each case. Reporting the number, rather than just plotting, is the habit to build: it tells you, before you choose an ordination, whether the community spans a long unimodal gradient (favouring CA/CCA) or a short, near-linear one (favouring PCA/RDA).
Icme Blbj Abbr Gyce Anan
-2.034728 -1.903686 -1.864374 -1.811335 -1.486738 Satr Thth Cogo Phph Teso
2.858182 2.635932 2.463739 1.730789 1.257536 The species at the two extremes of DCA1 are the indicators of the two ends of the river: cold-water upper-reach species (trout, minnow, bullhead and their associates) sit at one end, and warm-water lowland cyprinids (breams and their associates) at the other. The first DCA axis is therefore the source-to-mouth gradient written in the fish, exactly as the environmental correlations and the CA both implied; the species scores simply name which taxa mark each end.
With a first-axis length of 3.86 SD, the Doubs fish gradient sits at the long end of the scale, so the rule of thumb (set out in Using the Gradient Length to Choose a Method in the DCA chapter) recommends unimodal methods (CA, CCA, or distance-based approaches) rather than linear ones (PCA, RDA on raw data). That agrees with the Correspondence Analysis chapter: the species showed clear unimodal, hump-shaped responses along the river, and the CA produced the arch that signals one long gradient. A PCA of the same species data would have imposed a linear model on inherently unimodal responses and produced a horseshoe artefact, so the diagnostic and the observed species behaviour point the same way.
I would use DCA mainly as a diagnostic and ordinate with another method for display. The detrending-by-segments algorithm is sensitive to arbitrary choices (the number of segments, rescaling details), and it can introduce artefacts of its own, so the configuration of a DCA diagram is not always stable or reproducible. Its gradient length, however, is a robust and genuinely useful summary. The defensible workflow is therefore to run DCA to read the gradient length, use that to justify the family of methods (here unimodal/distance-based), and then present the ordination with a method whose geometry is well understood, such as CA, nMDS, or a distance-based ordination. DCA earns its place as a measuring tool, not as the final picture.
This Task is not formally assessed. It is built around four hands-on analyses (Exercises 1–4) and two short conceptual questions (Exercises 5–6); work through all six and bring your annotated Quarto document to class for discussion.
@online{smit2026,
author = {Smit, A. J.},
title = {9b: {Detrended} {Correspondence} {Analysis} {(DCA)}},
date = {2026-06-14},
url = {https://tangledbank.netlify.app/BCB743/tasks/Task_E.html},
langid = {en}
}