Fuzzy species distributionmodels: a way to represent plant communities spatially

Vegetation composition is fuzzy by its very nature. Classification approaches, despite their robustness, will always lead to a degradation of the original information (Palmer et al. 2002). Palmer (2007) explicitly states that: ‘we have no comprehensive theory governing the geometry of environmental variation. Some environmental gradients vary smoothly and linearly [...]. Other gradients may be more spatially unpredictable.’ Such unpredictability is related to the uncertainty of representing nature using pre-defined deterministic laws. In this case, uncertainty is particular and important information that deserves to be maintained and spatially represented, instead of being abruptly cut off. Thomas J. Duff and colleagues (Duff et al. 2014) attempt to describe vegetation classes relying on fuzzy set theory, leading to what I call ‘fuzzy species distribution models’, to represent their continuous variation over space. For the sake of clarity, mathematically speaking, let U denote a universe of entities u; hence, the fuzzy set F is