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How to model species responses along ecological gradients – Huisman–Olff–Fresco models revisited




In species response modelling, can a hierarchical logistic regression framework compete against GAM in terms of statistical inference? Are bimodal shapes useful to model species responses along ecological gradients?




In hierarchical logistic regression modelling [also known as Huisman, Olff, Fresco (HOF) models], the best model is chosen from a set of predetermined models using statistical information criteria, i.e. a balance between model fit to the data and simplicity of the model. We extended the classical five model types with two bimodal shapes. We improved the model optimization process to inhibit unrealistically steep slopes and abrupt changes. The stability of model choices is safeguarded through bootstrapping. The framework was tested on a data set of 547 vegetation plots of arable land with measured soil pHKCL. The ability to reproduce known shapes was tested with artificial data sets. Shape parameters, e.g. niche width and range, slope (turnover) and species optima, can be calculated from the models and used for further analyses. The model framework together with advanced plot functions is included in the package eHOF for the statistical software environment R.


Based on the AIC, 66 out of 131 species are modelled with a better compromise between model fit and model complexity by one of the logistic regression models as compared to GAM with automatic smoother selection. Within the model framework, 17 species (13%) are best modelled with one of the new bimodal types. The test with artificial data of known shape reveals good reliability of eHOF models for unimodal responses in areas with homogeneous information, but increasing uncertainty if the sampling is uneven or if only a part of the response is covered within the observed gradient range.


Hierarchical logistic regression models offer a flexible way to efficiently fit species response data. They propose a sound theoretical background for ecological interpretation. Extended HOF models as presented here are judged as an effective tool for univariate species response modelling.