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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 …