MESOZOIC MARINE REPTILE DISPARITY
reptile disparity was quantified using the PCOa scores of taxa from the first 11 ordination axes (Table 2), based on the sum of variances and the sum of ranges metrics. To derive a trajectory of disparity through time, we performed calculations on taxa binned in
variation. The scores (coordinates) of the taxa on PC axes 1, 2, and 3 were used to construct morphospaces because these axes contribute the most to overall absolute variance. Only the first 11 axes were retained for statistical tests and disparity calculations, because higher axes were associated with negligible amounts of absolute variance (<1%) or negative eigen- values (Table 2). To ensure that the presence of negative eigenvalues did not distort the ordinated dissimilarity among forms, we performed correlation tests on the computed intertaxon distances and ordination distances (Friedman 2012). Results show strong correlation between the distance measures (Pearson’s product-moment correlation: r=0.982, p<0.001), suggesting the PCOa accurately preserves most of the underlying distances between taxa without major distortion (Supplementary Fig. 1). Nonparametric multivariate analyses of variance (NPMANOVA) were carried out on the 11 retained PCOa axes to test for separation by temporal and group bins in morphospace (Ruta et al. 2013). The above-described procedureswere repeated separately for each of the five major clades to generate multivariate axes of variation for subsequent disparity calculations in each group (see below). Temporal Disparity Calculations.—Marine
551
16 Mesozoic time intervals. The sum of ranges calculations were rarefied to account for differing sample sizes, using both the average sample size of all bins (n=17) and the smallest sample size (n=5). Statistical tests for differences in disparity between time bins are based on 95% confidence intervals, paired- sample t-tests based on multivariate variance (Anderson et al. 2011), and ratios of marginal likelihoods for variance (Finarelli and Flynn 2007). Confidence intervals associated with calculated disparity values were generated by bootstrapping with 10,000 replications. Ratios of marginal likelihoods were used exclusively to identify shifts in disparity between successive time intervals based on the procedure outlined in Finarelli and Flynn (2007) and Anderson et al. (2011). We assessed the statistical dependence between bin sample size and disparity by applying generalized differencing and assessing the strength and significance of correlations (e.g., Ruta et al. 2013). Partial disparity for each marine reptile group was also examined to see how they contribute to overall disparity through the Mesozoic (Foote 1993). All disparity calculations and significance tests were performed using the MDA Matlab® package (Navarro 2003) and in R (R Development Core Team 2011). Stratigraphic Binning.—For temporal disparity
TABLE 2. Eigenvalues and percentages of variance associated with each PCO axis from themultivariate analysis. The primary analysis is based on all 18 characters.
PC 1
2 3 4 5 6 7 8 9
10 11
Principal coordinate analysis Eigenvalue 2.6051
1.1496 1.0131
0.77706 0.32332 0.26086 0.15826 0.13675 0.13178 0.11304 0.094332
% variance 27.42
12.10 10.66 8.18 3.40 2.75 1.67 1.44 1.39 1.19 0.99
calculations and morphospace plots, taxa were binned in 16 Mesozoic time intervals. We used a combination of stage-level and composite bins, with ages in Myr: Olenekian (250–247.1), Anisian (247.1–241.5), Ladinian (241.5–237), Carnian (237–228.4), Norian (228.4–209.5), Hettangian– Sinemurian (201.3–190.8), Pliensbachian– Toarcian (190.8–174.1), Aalenian–Bathonian (174.1–166.1), Callovian–Oxfordian (166.1– 157.3), Kimmeridgian–Tithonian (157.3–145), Berriasian–Barremian (145–126.3), Aptian– Albian (126.3–100.5), Cenomanian–Turonian (100.5–89.8), Coniacian–Santonian (89.77–83.6), Campanian (83.6–72.1), and Maastrichtian (72.1–66). A Rhaetian bin was not included due to the lack of marine reptile fossils during this interval. Absolute ages for the stratigraphic stages are from Gradstein et al. (2012). The mean bin duration is 11Myr and the range is 22.9Myr.
Page 1 |
Page 2 |
Page 3 |
Page 4 |
Page 5 |
Page 6 |
Page 7 |
Page 8 |
Page 9 |
Page 10 |
Page 11 |
Page 12 |
Page 13 |
Page 14 |
Page 15 |
Page 16 |
Page 17 |
Page 18 |
Page 19 |
Page 20 |
Page 21 |
Page 22 |
Page 23 |
Page 24 |
Page 25 |
Page 26 |
Page 27 |
Page 28 |
Page 29 |
Page 30 |
Page 31 |
Page 32 |
Page 33 |
Page 34 |
Page 35 |
Page 36 |
Page 37 |
Page 38 |
Page 39 |
Page 40 |
Page 41 |
Page 42 |
Page 43 |
Page 44 |
Page 45 |
Page 46 |
Page 47 |
Page 48 |
Page 49 |
Page 50 |
Page 51 |
Page 52 |
Page 53 |
Page 54 |
Page 55 |
Page 56 |
Page 57 |
Page 58 |
Page 59 |
Page 60 |
Page 61 |
Page 62 |
Page 63 |
Page 64 |
Page 65 |
Page 66 |
Page 67 |
Page 68 |
Page 69 |
Page 70 |
Page 71 |
Page 72 |
Page 73 |
Page 74 |
Page 75 |
Page 76 |
Page 77 |
Page 78 |
Page 79 |
Page 80 |
Page 81 |
Page 82 |
Page 83 |
Page 84 |
Page 85 |
Page 86 |
Page 87 |
Page 88 |
Page 89 |
Page 90 |
Page 91 |
Page 92 |
Page 93 |
Page 94 |
Page 95 |
Page 96 |
Page 97 |
Page 98 |
Page 99 |
Page 100 |
Page 101 |
Page 102 |
Page 103 |
Page 104 |
Page 105 |
Page 106 |
Page 107 |
Page 108 |
Page 109 |
Page 110 |
Page 111 |
Page 112 |
Page 113 |
Page 114 |
Page 115 |
Page 116 |
Page 117 |
Page 118 |
Page 119 |
Page 120 |
Page 121 |
Page 122 |
Page 123 |
Page 124 |
Page 125 |
Page 126 |
Page 127 |
Page 128 |
Page 129 |
Page 130 |
Page 131 |
Page 132 |
Page 133 |
Page 134 |
Page 135 |
Page 136 |
Page 137 |
Page 138 |
Page 139 |
Page 140 |
Page 141 |
Page 142 |
Page 143 |
Page 144 |
Page 145 |
Page 146 |
Page 147 |
Page 148 |
Page 149 |
Page 150 |
Page 151 |
Page 152 |
Page 153 |
Page 154 |
Page 155 |
Page 156 |
Page 157 |
Page 158 |
Page 159 |
Page 160 |
Page 161 |
Page 162 |
Page 163 |
Page 164 |
Page 165 |
Page 166 |
Page 167 |
Page 168 |
Page 169 |
Page 170 |
Page 171 |
Page 172 |
Page 173 |
Page 174 |
Page 175 |
Page 176 |
Page 177 |
Page 178 |
Page 179 |
Page 180 |
Page 181 |
Page 182 |
Page 183 |
Page 184 |
Page 185 |
Page 186 |
Page 187 |
Page 188 |
Page 189 |
Page 190 |
Page 191 |
Page 192
