||Species distribution models (SDMs) have been widely used in ecology, biogeography, and conservation. Although ecological theory predicts that species occupancy is dynamic, the outputs of SDMs are generally converted into a single occurrence map, and model performance is evaluated in terms of success to predict presences and absences. The aim of this study was to characterize the effects of a gradual response in species occupancy to environmental gradients into the performance of SDMs. First we outline guidelines for the appropriate simulation of artificial species that allows controlling for gradualism and prevalence in the occupancy patterns over an environmental gradient. Second, we derive theoretical expected values for success measures based on presence-absence predictions (AUC, Kappa, sensitivity and specificity). And finally we used artificial species to exemplify and test the effect of a gradual probabilistic occupancy response to environmental gradients on SDM performance. Our results show that when a species responds gradually to an environmental gradient, conventional measures of SDM predictive success based on presence-absence cannot be expected to attain currently accepted performance values considered as good, even for a model that recovers perfectly well the true probability of occurrence. A gradual response imposes a theoretical expected value for these measures of performance that can be calculated from the species properties. However, irrespective of the statistical modeling strategy used and of how gradual the species response is, one can recover the true probability of occurrence as a function of environmental variables provided that species and sample prevalence are similar. Therefore, model performance based on presence-absence should be judged against the theoretical expected value rather than to absolute values currently in use such as AUC \textgreater 0.8. Overall, we advocate for a wider use of the probability of occurrence and emphasize the need for further technical developments in this sense.