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Bacterial cells come in a huge variety of shapes, but we have yet to understand the importance of these shapes for biofilm biology. How are multi-species biofilms affected by the morphologies of constituent cells? Which morphologies might the biofilm environment select for in turn? To address these questions, we combine individual-based modelling and experiments to investigate the effects of cell shape on patterning and evolution within bacterial biofilms. We have developed a flexible hybrid simulation framework, coupling a continuum model of the biofilm chemical environment to a cellular-level description of biofilm growth mechanics. Improving on previous ad-hoc models, this system allows competitions between different bacterial cell shapes to be rapidly simulated and explored.We show that cell shape can strongly affect patterning within bacterial biofilms. Rod cells do better at colonising surfaces and the expanding edges of colonies, while round cells are better at dominating the biofilm surface. Our predictions are supported by experiments with Pseudomonas aeruginosa, which show that elongated cells gain a competitive advantage at the colony edge. We argue that cell shape is a major neglected determinant of patterning and evolutionary fitness within bacterial biofilms.