Generalized Functional Responses in Habitat Selection Fitted by Decision Trees and Random Forests

Species Distribution Models (SDMs) are important regression tools in the ecological sciences that can support distribution predictions using different environmental variables. Most of the research in the area of SDMs has assumed that regression coefficients in these models are fixed. However, species respond differently to different habitats depending on the habitat availability, meaning that regression coefficients change as functions of habitat availability, a phenomenon known as a functional response in habitat selection. The generalized functional response (GFR) is a varying-coefficient extension of the basic SDM framework, designed for more robust forecasts of species distributions in a rapidly changing world. The original GFR model formulated the varying regression coefficients using a polynomial function approach, which led to improvements of forecasting performance in many applications. The purpose of this paper is to improve the out-of-sample performance of the GFR model using a decision tree and Breiman's random forest algorithm. We compare the original GFR model with a decision tree and random forests using the GFR model by applying both models to a real population dataset on house sparrows. The results revealed a noticeable improvement in terms of out-of-sample R² in the decision tree and the random forest approaches over the original GFR model.