Determining Alternative Models for Vegetation Response Analysis: A Non-Parametric Approach

Vegetation models based on multiple logistic regression are of growing interest in environmental studies and decision making. The relatively simple sigmoid Gaussian optimum curves are most common in current vegetation models, although several different other response shapes are known. However, improvements in the technical means for handling statistical data now facilitate fast and interactive calculation of alternative complex, more data-related, non-parametric models. The aim in this study was to determine whether, and if so how often, a complex response shape could be more adequate than a linear or quadratic one. Using the framework of Generalized Additive Models, both parametric (linear and quadratic) and non-parametric (smoothed) stepwise multiple logistic regression techniques were applied to a large data set on wetlands and water plants and to six environmental variables: pH, chloride, orthophosphate, inorganic nitrogen, thickness of the sapropelium layer and depth of the water-body. All models were tested for their goodness-of-fit and significance. Of all 156 generalized additive models calculated, 77 % were found to contain at least one smoothed predictor variable, i.e. an environmental variable with a response better fitted by a complex, non-parametric, than by a linear or quadratic parametric curve. Chloride was the variable with the highest incidence of smoothed responses (48 %). Generally, a smoothed curve was preferable in 23 % of all species-variable correlations calculated, compared to 25 % and 18 % for sigmoid and Gaussian shaped curves, respectively. Regression models of two plant species are presented in detail to illustrate the potential of smoothers to produce good fitting and biologically sound response models in comparison to linear and polynomial regression models. We found Generalized Additive Modelling a useful and practical technique for improving current regression-based vegetation models by allowing for alternative, complex response shapes.