Supplementary material: Early Tetrapod Jaw Outline Data - The evolution of herbivory, not terrestrialization, drove morphological change in the mandibles of Palaeozoic tetrapods

<b>Abstract</b>The radiation of tetrapods during the Devonian and Early Carboniferous was associated with a transition from aquatic to terrestrial environments, with attendant changes in feeding ecology. Despite this, evidence suggests that feeding morphology remained relatively static throughout this transition, until morphological disparity eventually rose later in the Carboniferous and Permian. Using a theoretical morphospace and functional optimality approach, we characterize the functional evolution of tetrapod mandibles, finding an antagonistic relationship between the strength, rotational efficiency, mechanical advantage and height of jaw morphologies. We further show that the regions of morphospace occupied by the jaws of aquatic and faunivorous terrestrial tetrapods are optimised within this trade-off. As terrestrial herbivores radiated, they explored broader regions of jaw morphospace characterised by deeper, stronger jaw shapes, driving the delayed spike in jaw disparity. We interpret this as a release of functional constraint on the jaw morphology by the evolution of herbivory, with new functional demands driving evolutionary innovation. While feeding in aquatic and terrestrial environments is fundamentally different, the criteria for functional optimality in the lower jaw did not change across this transition. Instead, access to terrestrial plant-based diets drove mandibular change.