Detrended correspondence analysis (DCA) was developed to correct perceived inadequacies of correspondence analysis in the ordination of community data.  Nonlinear rescaling, incorporated into DCA to correct the compression of sampling unit scores towards the axis extremes, adjusts the scaling of species scores within axis segments in an effort to equalize the dispersions of species scores within sampling units.  It has been claimed that rescaling produces axes along which the mean Gaussian tolerances of species’ responses is 1.0, so that the length of the rescaled axis is a measure of beta diversity.  Though it has been shown to lack robustness as an ordination method, DCA and its constrained form, detrended canonical correspondence analysis (DCCA), are now routinely used to assess the beta diversity of community data.  The detailed algorithm for nonlinear rescaling has not been published so we examined the DECORANA source code and implemented the procedure in our own software.  We then used both simulated community data, in which species had specified Gaussian responses to gradients, and field data for which the major driving gradients are understood to investigate the behavior of nonlinear rescaling and its success in producing axis lengths that matched the beta diversity of the data.

Results/Conclusions

For a simple species packing model, in which species have Gaussian responses with equal heights and tolerances and both species’ optima and sampling units are evenly distributed along the gradient, nonlinear rescaling performs well, producing axis lengths that agree with simulated beta diversities.  With field data and more realistic models, in which heights, tolerances, the spacing of optima or the sampling intensity varied, rescaling no longer performs as suggested.  The adjustment tends to spread the optima of species more evenly across the rescaled gradient but this usually does not equalize tolerances.  In fact, variation among tolerances is often enhanced by rescaling.  We show that equalizing the dispersions of species scores within sampling units does not, in general, result in rescaled axes along which the mean tolerance approaches 1.0 within all regions of the axis.  Hence we conclude that axis lengths in DCA and DCCA do not provide meaningful estimates of beta diversity.