Temnospondyls—a major component of Permian and Carboniferous terrestrial ecosystems—display great diversity in skull shapes and proportions. To quantify and interpret this diversity, we conducted a geometric morphometric analysis using 45 landmarks on the dorsal skull surface of 90 species with well-represented cranial material. Results show a correlation between morphospace occupation and phylogenetic proximity of taxa for trees in which dvinosaurs and dissorophoids are sister groups and join an edopoid-–eryopoid–basal archegosauriform clade. Most large groups of Carboniferous and Permian temnospondyls occupy specific areas of morphospace. Nearest-neighbor analyses reveal significantly greater taxon clustering than expected under either uniform or Gaussian null models. Size correlates strongly with shape across the whole data set, highlighting the association of some features (short, broad snout; large orbits) with small size. A significant relationship between size and shape is not observed in clades such as branchiosaurids, dvinosaurs, and olsoniforms (the clade encompassing trematopids plus dissorophids). This suggests that evolutionary allometry patterns vary across temnospondyls. In the case of branchiosaurids, this pattern may be explained by the similar sizes and relatively conservative morphologies of the constituent species. Distance-based disparity measures indicate that edopoids, eryopoids, and basal archegosauriforms make the largest contributions to total disparity (reflecting the peripheral locations of some of the constituent taxa in morphospace), whereas amphibamids, dissorophids, and trematopids make the smallest contributions. Disparity correlates strongly with diversity within groups, suggesting that skull shape was not subject to character state exhaustion (decrease or cessation in the acquisition of novel morphological conditions during clade evolution). The Kasimovian, Roadian, Wordian, and Changhsingian are time intervals of high disparity despite their low diversity. We hypothesize that this pattern stems from the fact that times of high diversity are characterized by larger areas of morphospace, which results in mean shapes being located relatively close to the grand mean; in contrast, mean shapes for low-diversity stages are based on incomplete morphospace samples. Many of these patterns are similar to those observed in previous analyses of stereospondyls, suggesting that similar controls on skull shape may have operated throughout the history of temnospondyls.
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