Why the beta function cannot be used to estimate skewness of species responses

Journal of Vegetation Science 8, 147-152 (1997)

Jari Oksanen

Abstract

The beta-function (ß-function) has been suggested for testing the significance of skewness of speces responses along a gradient. However, the location of the optimum and skewness are correlated so that these parameters cannot be estimated independently. The only way for an independent estimation is to let the endpoints of the response curve vary. In that case they would no longer define the range of species occurrence. However, non-linear estimation of endpoints often leads to overwhelming problems in model fitting. Therefore, the beta-function is not suitable to test the shape of species response curves. Hierarchic models proposed by Huisman et al. (1993) seem to be superior to generalized additive models or third degree polynomials, and seem to be the best alternative to study the skewness of responses.

Keywords: Artefact, Gaussian function, Generalized linear models, Gradient analysis, Model fitting