Open palates with large interpterygoid vacuities are a diagnostic characteristic of temnospondyl amphibians, the most species-rich group of early tetrapods. Aside from their functional roles, several other aspects of such vacuities, such as their variation and spatial relationships relative to the orbits, have received only scarce attention. The present work examines patterns of shape and size changes in the orbits and vacuities of temnospondyls using a time-calibrated phylogeny of 69 temnospondyl taxa and 13 additional early tetrapod ‘outgroups' (colosteids, an embolomere, ‘microsaurs' and nectrideans). Orbit and vacuity outlines are quantified in a comparative framework using standard eigenshape analyses. In addition, we employ a series of ratios of linear measurements of both orbits and vacuities, and subject them to a phylogenetic principal component analysis in order to evaluate their proportional changes relative to the skull and to one another. Finally, we examine rates of evolutionary change and their associated shifts for shape and size for both structures, and assess the strength and significance of the correlations between these two variables using phylogenetic generalised least squares analyses. Although orbits and vacuities have fairly simple outlines, they both reveal complex models of proportional change across the temnospondyl phylogeny. These changes exhibit strong phylogenetic signal, that is, trait covariance among taxa is predicted by tree topology. We discuss the hypothesis that, early in tetrapod evolution, the functional role of the vacuities was related to the accommodation of the anterior jaw muscles. Only later in evolution did such vacuities serve to accommodate the eye muscles only.
