MESOZOIC MARINE REPTILE DISPARITY


and ordinated using PCOa. Taxa were assigned to new time bins covering the full duration of each clade (Supplementary Table 1). For each clade, disparity calculations were based on the binned PCOa scores of taxa from the ordination axes that accounted for more than 1% of absolute variance. The number of axes used for each clade is as follows: Sauropterygia (10), Eosauropterygia (11), Ichthyosauromorpha (7), Thalattosuchia (8), and Mosasauroidea (9). Once again, two disparity metrics were examined: the sum of variances and rarefied sum of ranges. We also calculated phylogenetic diversity estimates (PDE) for each group to explore the pattern of numerical diversification (cladogenesis). PDE incorporate both taxon occurrences and ghost lineages inferred from time-calibrated trees. Diversity counts were made in 5Myr intervals spanning the duration of each of the five groups. To account for phylogenetic uncertainty within each tree, unresolved nodes were randomly resolved and 100 trees were used to calculate PDE. The median of the 100 topologies was plotted along with confidence intervals based on two- tailed 95% lower and upper quantiles. Calcu- lations were performed using the R package paleotree, Version 1.4 (Bapst 2012). Time-scaled Phylogenies.—Phylogenetic compa-


rative methods were used to quantify the tempo and mode of phenotypic evolution in sauropterygians, eosauropterygians, ichthyosau- romorphs, thalattosuchians, and mosasauroids. Informal composite supertrees were first constructed for each clade (see description in Supplementary Text and Supplementary Figs. 2–5). All trees had unresolved nodes, reflecting phylogenetic uncertainty. These nodes were randomly resolved prior to analyses, and to test for consistency, 50 alternative fully resolved topologies were retained for Ichthyosauromorpha, Thalatto- suchia, and Mosasauroidea, while 100 topologies were analyzed for Sauropterygia and Eosauropterygia. Branch durations in all trees were estimated by assigning taxa a point age, drawn randomly from a uniform distribution between their first appearance dates (FAD) and last appearance dates (LAD).Absolute ages for FADs and LADs are from Gradstein


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et al. (2012) (Supplementary Data). Zero-length branches were lengthened by sharing duration equally with preceding non-zero-length branches, after setting a time of root divergence (equal method; Brusatte et al. 2008). Sensitivity analyses were conducted with enforced 1Myr minimum branch lengths (mbl method; Laurin 2004). Finally, prior to analyses, the taxa in each fully resolved time-calibrated tree that lacked the appropriate trait data (see “Maximum-Likelihood Evolutionary Models” below) were removed. All dating procedures were implemented using the functiontimePaleoPhy in theRpackagepaleotree, Version 1.4 (Bapst 2012). Maximum-Likelihood Evolutionary Models.—


Maximum-likelihood models were fitted to trait data on the time-calibrated phylogenies for each marine reptile clade, using the R package Geiger, Version 1.99-3 (Harmon et al. 2008). PC scores from axes of variation were used as continuous trait data to explore the tempo and mode of functional evolution in the jaws and dentition (e.g., Sallan and Friedman 2012). The PC scores were taken from the separate multivariate analyses of each clade used to investigate disparity through time. Because no single ordination axis accounts for all functional disparity, we fitted models to multiple axes independently. The axes utilized, and their relative contributions to overall absolute variance, are: Sauropterygia PC1 (47.8%), PC2 (11.6%), and PC3 (5.7%); Eosauropterygia PC1 (30.5%), PC2 (13.7%), and PC3 (8.9%); Ichthyosauromorpha PC1 (28.5%), PC2 (21.1%), and PC3 (13.2%); Thalattosuchia PC1 (44.6%), PC2 (18.1%), and PC3 (10.2%); and Mosasauroidea PC1 (30.6%), PC2 (24.8%), and PC3 (10.5%). Skull-size trends were also explored utilizing the log10-transformed MSL data. We focus on three models that explicitly test


for rate heterogeneity in a temporal context; Brownian motion (BM), early burst (EB), and Pagel’s δ (delta). BM is a time-homogeneous process, equivalent to a random walk with constant variance and evolutionary rates per unit time. Under BM, increases and decreases in trait values are equiprobable, and trait covariance is proportional to the duration of shared ancestry. The EB model presumes higher rates of evolution early in a clade’s


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