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Summary Several models explain how a complex integrated system like the rodent mandible can arise from multiple developmental modules. The models propose various integrating mechanisms, including epigenetic effects of muscles on bones. We test five for their ability to predict correlations found in the individual (symmetric) and fluctuating asymmetric (FA) components of shape variation. We also use exploratory methods to discern patterns unanticipated by any model. Two models fit observed correlation matrices from both components: (1) parts originating in same mesenchymal condensation are integrated, (2) parts developmentally dependent on the same muscle form an integrated complex as do those dependent on teeth. Another fits the correlations observed in FA: each muscle insertion site is an integrated unit. However, no model fits well, and none predicts the complex structure found in the exploratory analyses, best described as a reticulated network. Furthermore, no model predicts the correlation between proximal parts of the condyloid and coronoid, which can exceed the correlations between proximal and distal parts of the same process. Additionally, no model predicts the correlation between molar alveolus and ramus and/or angular process, one of the highest correlations found in the FA component. That correlation contradicts the basic premise of all five developmental models, yet it should be anticipated from the epigenetic effects of mastication, possibly the primary morphogenetic process integrating the jaw coupling forces generated by muscle contraction with those experienced at teeth.