Rate of compositional turnover along gradients and total gradient length

A new measure of compositional turnover rate at any gradient point is proposed. The absolute values of the derivatives of estimated species response curves are used to estimate the instantaneous rate of change of the community. The total gradient length can be found by integrating the instantaneous turnover rates over the gradient span. Both the instantaneous rate and total gradient length have been known under the name of beta diversity. Our method is elaborated for the Gaussian response function. It is compared to Hill's SD measure, much used for estimating the gradient length in connection of Detrended Correspondence Analysis with non-linear rescaling for axes. The turnover rate along a canopy cover gradient in forest vegetation in Finland was used as an example. Forest site type and stand age were used as subsidiary gradients. The two ways to compute Hill's scaling gave very different results and were not comparable with the new method. The turnover rate was dependent on the gradient position. However, the turnover rate along the gradient of interest and its total length were dependent on the subsidiary gradients.