Canonical Correspondence Analysis as an approximation to Gaussian ordination

Canonical Correspondence Analysis is an approximation to maximum likelihood estimation for Gaussian ordination under certain restrictions of the ordination model. Species tolerances must be equal, and species maxima must be equal or at least independent of the location of the optima. These assumptions are often violated in practice. This paper develops graphical displays to explore how well species abundances approximate Gaussian curves along the derived environmental axes. As well, a simulation study was performed to determine how well Canonical Correspondence Analysis recovered the true axes when the Gaussian model for species abundance is correct, but the assumptions about the tolerances, maxima and location of optima are violated. The methods were applied to an analysis of an observational study conducted on a fen in the Black Hills of South Dakota.