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Aim Tropical species are thought to experience and be adapted to narrow ranges of abiotic conditions. This idea has been invoked to explain a broad array of biological phenomena, including the latitudinal diversity gradient and differential rates of speciation and extinction. However, debate continues regarding the broad-scale applicability of this pattern and potential processes responsible. Here, we use a simulation approach to test two propositions: (a) strong geographical patterns in realized niche breadth variation can arise in the absence of variance in fundamental niche breadth size, and (b) realized niche breadths can show latitudinal patterns as a consequence of spatio-temporal climate change, even when fundamental niche breadths are unrelated to latitude and dispersal abilities are held constant. Location Global. Time period Simulations were conducted using climate models from over the last 120 ka, with trait dynamics captured at 95 ka and in the Modern. Major taxa studied We used virtual species with traits based loosely on plants. Methods We simulated latitudinal trends of niche breadth and range size for virtual species using a cellular automaton algorithm that linked a gridded geographical domain with a three-dimensional environmental landscape. Results In all simulations, strong spatial patterns in realized niches were obtained in the absence of niche evolution, and realized niches showed geographical patterns deriving only from realistic, spatio-temporal variation in climate. We noted contrasting patterns of niche breadth in different environmental dimensions, with temperature breadth increasing with latitude, but precipitation breadth decreasing with latitude. Overall, simulation outcomes mimicked the real-world pattern of latitudinal range extent co-varying with amount of land area. Main conclusions Tropical species can have narrower niche breadths for maximum and minimum temperature ranges compared with temperate species solely as the result of the spatial arrangement of environments. We therefore suggest that the complex spatio-temporal distribution of global abiotic environments has strong potential for structuring observed latitudinal gradients of niche breadths.