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Climate suitability models are used to make projections of species’ potential future distribution under climate change. When studying the species richness with such modeling methods, the extent of the study range is of particular importance, especially when the full range of occurrence is not considered for some species, often because of geographical or political limits. Here we examine biases induced by the use of range-restricted occurrence data on predicted changes in species richness and predicted extinction rates, at study area margins. We compared projections of future suitable climate space for 179 bird species breeding in Iberia and North Africa (27 of them breeding only in North Africa though potential colonizers in Europe), using occurrence data from the full Western Palaearctic (WP) species range and from the often-considered European-restricted range. Current and future suitable climatic spaces were modeled using an ensemble forecast technique applied to five general circulation models and three climate scenarios, with eight climatic variables and eight modeling techniques. The use of range-restricted compared to the full WP occurrence data of a species led to an underestimate of its suitable climatic space. The projected changes in species richness across the focus area (Iberia) varied considerably according to the occurrence data we used, with higher local extinction rates with European-restricted data (on average 38 vs 12% for WP data). Modeling results for species currently breeding only in North Africa revealed potential colonization of the Iberian Peninsula (from a climatic point of view), which highlights the necessity to consider species outside the focus area if interested in forecasted changes in species richness. Therefore, the modeling of current and future species richness can lead to misleading conclusions when data from a restricted range of occurrence is used. Consequently, climate suitability models should use occurrence data from the complete distribution range of species, or at least within biogeographical areas.