Seemingly consistent proportional differences in several palatal structures have been noted between Permian and Triassic anomodont therapsids for nearly a century. These patterns have been cited as evidence in support of a decline in atmospheric oxygen concentrations that may have contributed to end-Permian terrestrial extinctions. However, it is not known whether the observed differences are significant, or whether they stem from continued directional selection. If they are not significant, or if their timing does not match that proposed for the oxygen decline, support for the hypoxia-based extinction scenario would be weakened. We tested whether the internal nares and bony secondary palate, two palatal features proposed to be related to respiratory efficiency, are significantly larger in Triassic anomodonts, and whether the variation can be attributed to a long-term tendency for increase. Results based on raw data indicate that Triassic anomodonts have significantly larger secondary palates than Permian anomodonts. They also have significantly larger internal nares, but only when primitive, morphologically-divergent specimens are not considered. Although nares and palate size are correlated with stratigraphic occurrence, available data reject the hypothesis that the observed differences were the result of a long-term trend. Most of these findings are consistent with the predictions of the hypoxia scenario. However, removing the effects of body size and phylogeny causes some of the differences to break down, indicating that if selection for increased respiratory efficiency affected these characters, it was most likely not the only factor to do so. Therefore, the characters provide only weak evidence in support of the hypoxia scenario, and we recommend against their use for this purpose. Our results emphasize the need for caution when invoking presumed differences between Permian and Triassic vertebrates as support for hypoxia, or other extinction scenarios, without a rigorous study of the character(s) in question.

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