Résumé
Simulations of virtual species (i.e. species for which the environment–occupancy relationships are known) are increasingly being used to test the effects of different aspects of modelling and sampling strategy on performance of species distribution models (SDMs). Here we discuss an important step of the simulation process: the translation of simulated probabilities of occurrence into patterns of presence and absence. Often a threshold strategy is used to generate virtual occurrences, where presence always occurs above a specific simulated probability value and never below. This procedure effectively translates any shape of simulated species response into a threshold one and eliminates any stochasticity from the species occupancy pattern. We argue that a probabilistic approach should be preferred instead because the threshold response can be treated as a particular case within this framework. This also allows one to address questions relating to the shape of functional responses and avoids convergence issues with some of the most common SDMs. Furthermore, threshold- based virtual species studies generate over-optimistic performance measures that lack classification error or incorporate error from a mixture of sampling and modelling choices. Incorrect use of a threshold approach can have significant consequences for the practising biogeographer. For example, low model performance may be interpreted as due to sample bias or poor model choice, rather than being related to fundamental biological responses to environmental gradients. We exemplify these shortcomings with a case study where we compare results from threshold and probabilistic simulation approaches.