# The rate of compositional turnover along gradients and the
total gradient length

*Jari Oksanen and Tiina Tonteri*

*Journal of Vegetation Science* **6**, 815-824 (1995)

## Abstract

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 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 proposed ways to compute Hill's scaling gave very different
results and neither was comparable to 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.

*Keywords*: Beta diversity; Boreal forest vegetation; Compositional
turnover; Gaussian response function; Generalized linear models;*
*Gradient analysis; Hill's SD scaling; Succession.