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THOMAS L. STUBBS AND MICHAEL J. BENTON Stratigraphic assignments were based on the
primary literature, previous compendia of marine reptile diversity, and the Paleobiology Database (
paleodb.org) (Benson et al. 2010; Young et al. 2010; Benton et al. 2013; Kelley et al. 2014). Species-level stratigraphic assignments were used in most cases, but in the disparity analyses there were a number of instances in which species could not be sampled in a time bin due to inadequately preserved material. In these cases, the stratigraphic range of a representative taxon belonging to the same genus was extended to account for that taxon’s absence (Supplemen- tary Data). There were two instances in which taxa could not have their absence accounted for by amember of the same genus, both of them in the Norian time bin. Because it is important to represent all forms at a given time, we decided to represent their ecomorphological characteristics with a closely related species; we used Psephochelys polyosteoderma to represent the placodont species Psephoderma alpinum (and placodonts in general), and we used Guanlingsaurus liangae to represent the large edentulous ichthyosaur Shonisaurus sikanniensis. Disparity Sensitivity Analyses.—To scrutinize
temporal trends of marine reptile disparity we performed sensitivity tests using alternative protocols and data subsets. First, disparity was recalculated based onwithin-binmean pairwise dissimilarity fromthe originalGower intertaxon distance matrix for all 206 taxa (without PCOa ordination; e.g., Close et al. 2015). Second, disparity analyses were undertaken based solely on the nine continuous functional metrics (C1–C9) measured across all taxa, to ensure that the calculated trajectory of marine reptile disparity through time was not simply the result of overwhelming dominance from binary characters. The ichthyosaur Thalattoarchon was removed, because it could not be scored for enough continuous characters. Because size can dominate data sets based on linear measurements and ratios, additional tests were run on eight continuous variables minus the character total mandibular length (C9). For both cases, the z-transformed continuous characters were converted into a variance-covariance matrix and subjected to principal components analysis (PCA) to derive multivariate ordination axes and the
corresponding PC scores for all 205 taxa. Missing values were accounted for using iterative imputation with 10,000 bootstrap replicates (Ilin and Raiko 2010). Seven ordination axes were retained from the nine- character analysis (accounting for 98.9% of variance), and six axes were retained from the analysis with size removed (accounting for 98.7% variance). Following the protocol discussed above, disparity based on the sum of variances and sum of ranges was calculated in the 16Mesozoic time intervals. Skull-Size Trends.—To complement the
disparity analyses, we also examined patterns of skull-size evolution in all Mesozoic marine reptiles. Skull size represents an ecomorpho- logical characteristic that can be compared broadly across all marine reptile clades and used to identify patterns of phenotypic diversity. In 354 marine reptile species, maximum skull length (MSL) was measured from the anterior tip of the premaxilla to the posterior margin of the squamosal. Data were collected during museum visits and from published tables and figures (Supplementary Data). For incomplete specimens, MSL was estimated based on cranial proportions of closely related species or total mandible length (required for <5% of taxa). Juvenile specimens, identified based on discussions in the literature, were not included in the data set. Temporal trends of skull-size evolution were explored by plotting log10-transformed MSL against geological time based on the stratigraphic range midpoints of all species. Univariate disparity, based on the range and interquartile range, was examined in the same time bins as the multivariate disparity analyses. Comparative Disparity and Diversity
Analyses.—To test whether all marine reptile clades have similar trajectories of disparity through time, we compared the temporal disparity profiles of sauropterygians, eosauro- pterygians, ichthyosauromorphs, thalatto- suchians, and mosasauroids. These analyses were based on subsets of the primary data set (both continuous and binary characters). Some characters became redundant in the individual analyses and were removed, and the data subsets were then separately z-transformed
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