According to ecological niche theory, species response curves are unimodal with respect to environmental gradients. A variety of statistical methods have been developed for species distribution modelling. A general problem with most of these habitat modelling approaches is that the estimated response curves can display biologically implausible shapes which do not respect ecological niche theory. This work proposes using shape-constrained generalized additive models (SC-GAMs) to build species distribution models under the ecological niche theory framework, imposing concavity constraints in the linear predictor scale. Based on a simulation study and a real data application, we compared performance with respect to other regression models without shape-constraints (such as standard GLMs and GAMs with varying degrees of freedom) and also to models based on so-called "Plateau" climate-envelopes. The imposition of concavity for response curves resulted in a good balance between the goodness of fit (GOF) and agreement with ecological niche theory. The approach has been applied to fit distribution models for three fish species given several environmental variables.
Modelling species presence-absence in the ecological niche theory framework using shape-constrained generalized additive models
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