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Species distribution models (SDMs) are widely used to explain and predict species ranges and environmental niches. They are most commonly constructed by inferring species' occurrence–environment relationships using statistical and machine‐learning methods. The variety of methods that can be used to construct SDMs (e.g. generalized linear/additive models, tree‐based models, maximum entropy, etc.), and the variety of ways that such models can be implemented, permits substantial flexibility in SDM complexity. Building models with an appropriate amount of complexity for the study objectives is critical for robust inference. We characterize complexity as the shape of the inferred occurrence–environment relationships and the number of parameters used to describe them, and search for insights into whether additional complexity is informative or superfluous. By building ‘under fit’ models, having insufficient …