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I'm trying to understand the predicted patterns of a Canonical Correspondence Analysis (CCA). I understand one of this method's strengths in understanding ecological patterns lies in its assumption of a unimodal distribution pattern of a given species along an environmental gradient (i.e. optimum). I am trying to visualize the CCA's predicted response with this in mind, but am unable to see such a unimodal pattern in the predicted community patterns.

For example, I would have expected that the following script would produce a prediction of the species counts along the environmental gradient A1, which would be unimodal in shape (even if the gradient only captured one side of the the distribution):

# load library and data ---------------------------------------------------
library(vegan)
data(dune)
data(dune.env)


#  fit model --------------------------------------------------------------
mod <- cca(dune ~ A1, data=dune.env)
summary(mod)

# predict model -----------------------------------------------------------
pred <- as.data.frame(
  predict(mod, type = "response")
)

# visualize prediction
plot(dune.env$A1, pred$Achimill)

enter image description here

Since there is only one explanatory variable, I would have also expected the predicted values to clearly show the effect. Using rda produces the expected linear pattern.

mod <- rda(dune ~ A1, data=dune.env)

pred <- as.data.frame(
  predict(mod, type = "response")
)
plot(dune.env$A1, pred$Achimill)

enter image description here

I have actually never seen CCA results presented in this way, so perhaps I am incorrect in expecting this result. Any insights would be greatly appreciated!

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