We compared subsampled genus biodiversities at a quorum of 0.4 to δ18O palaeotemperature proxies and sequence stratigraphic eustatic sea level estimates in two sets of analyses: (1) terrestrial pseudosuchian biodiversity in North America and Europe were each compared to the Zachos et al.17 (link) compendium of benthic foraminifera isotopic values (Supplementary Data 5 ), which spans the latest Maastrichtian to Cenozoic; and (2) global marine pseudosuchian genus biodiversity was compared to the eustatic sea level estimates of Miller et al.18 (link) (Supplementary Data 6 ) and δ18O from the Prokoph et al.40 compendium (Supplementary Data 7 ), which includes Jurassic–Recent temperate palaeolatitudinal sea surface isotopic values from a range of marine organisms, adjusted for vital effects.
Although a contentious issue in crocodylomorph phylogeny, we follow the most recent placement of Thalattosuchia as a basal clade outside of Crocodyliformes63 (link), rather than within Neosuchia (for example, ref. 26 (link)). Consequently, we consider crocodylomorphs to have independently become adapted to marine life in the Jurassic (Thalattosuchia) and Cretaceous (pholidosaurids, dyrosaurids and eusuchians), representing separate temporal and evolutionary replicates that are characterised by distinct groups with possible different biodiversity dynamics. We therefore also analysed relationships between marine biodiversity and climatic variables including a binary variable denoting ‘1' for Jurassic–Hauterivian (mid-Early Cretaceous) intervals and ‘2' for stratigraphically younger intervals.Supplementary Figure 6 shows the palaeotemperature and sea level curves with the weighted means used in our time series regressions. Supplementary Fig. 7 shows plots of subsampled marine biodiversity versus δ18O and sea level, with and without the application of first differencing.
The similarity of these independent isotopic databases17 (link)40 for the overlapping portion of geological time suggests that both capture broad patterns of global climate change. Martin et al.16 (link) compared Jurassic–late Eocene marine crocodylomorph biodiversity with a sea surface temperature (SST) curve established from δ18O values of fish teeth from the Western Tethys. One potential problem with this method is that the fish teeth are from a variety of different species and genera, with Lécuyer et al.64 noting that species-specific differences in fractionation of δ18O can occur. In addition, there might be differences between the isotopic fractionation that occurs between phosphate and water, and that which takes place in the fish teeth64 . Despite these potential issues, their SST curve broadly follows the δ18O curves of Prokoph et al.40 and Zachos et al.17 (link), suggesting that the overall pattern between them is congruent. However, the benthic δ18O dataset for deep sea palaeotemperatures of Zachos et al.17 (link) is much better resolved than that of the SST curve, and the Prokoph et al.40 data set spans a larger time interval. Consequently, we consider these two datasets17 (link)40 better suited to testing for a correlation between palaeotemperature and biodiversity than the SST curve16 (link)64 . Time-weighted mean values of each of these two data sets were calculated and used in the regression analyses below.
Statistical comparison was made using time series approaches, specifically generalised least squares (GLS) regression incorporating a first-order autoregressive model (for example, refs 22 , 65 , 66 (link)), and implemented in the R package nlme, using the gls() function67 . This estimates the strength of serial correlation in the relationship between variables using maximum likelihood during the regression model-fitting process, correcting for the non-independence of adjacent points within a time series. We compared the results to those of ordinary least squares regression using untransformed data, which assumes serial correlation=0. Because intervals lacking marine pseudosuchians, and intervals that did not meet our quorum level due to data deficiency were excluded, our regression analyses ask whether pseudosuchian diversity was correlated to environmental variables when pseudosuchians were present at all.
All analyses were performed in R version 3.0.2 (ref. 68 ) and using a customized PERL script provided by J. Alroy. Additional information is provided in theSupplementary Methods .
Although a contentious issue in crocodylomorph phylogeny, we follow the most recent placement of Thalattosuchia as a basal clade outside of Crocodyliformes63 (link), rather than within Neosuchia (for example, ref. 26 (link)). Consequently, we consider crocodylomorphs to have independently become adapted to marine life in the Jurassic (Thalattosuchia) and Cretaceous (pholidosaurids, dyrosaurids and eusuchians), representing separate temporal and evolutionary replicates that are characterised by distinct groups with possible different biodiversity dynamics. We therefore also analysed relationships between marine biodiversity and climatic variables including a binary variable denoting ‘1' for Jurassic–Hauterivian (mid-Early Cretaceous) intervals and ‘2' for stratigraphically younger intervals.
The similarity of these independent isotopic databases17 (link)40 for the overlapping portion of geological time suggests that both capture broad patterns of global climate change. Martin et al.16 (link) compared Jurassic–late Eocene marine crocodylomorph biodiversity with a sea surface temperature (SST) curve established from δ18O values of fish teeth from the Western Tethys. One potential problem with this method is that the fish teeth are from a variety of different species and genera, with Lécuyer et al.64 noting that species-specific differences in fractionation of δ18O can occur. In addition, there might be differences between the isotopic fractionation that occurs between phosphate and water, and that which takes place in the fish teeth64 . Despite these potential issues, their SST curve broadly follows the δ18O curves of Prokoph et al.40 and Zachos et al.17 (link), suggesting that the overall pattern between them is congruent. However, the benthic δ18O dataset for deep sea palaeotemperatures of Zachos et al.17 (link) is much better resolved than that of the SST curve, and the Prokoph et al.40 data set spans a larger time interval. Consequently, we consider these two datasets17 (link)40 better suited to testing for a correlation between palaeotemperature and biodiversity than the SST curve16 (link)64 . Time-weighted mean values of each of these two data sets were calculated and used in the regression analyses below.
Statistical comparison was made using time series approaches, specifically generalised least squares (GLS) regression incorporating a first-order autoregressive model (for example, refs 22 , 65 , 66 (link)), and implemented in the R package nlme, using the gls() function67 . This estimates the strength of serial correlation in the relationship between variables using maximum likelihood during the regression model-fitting process, correcting for the non-independence of adjacent points within a time series. We compared the results to those of ordinary least squares regression using untransformed data, which assumes serial correlation=0. Because intervals lacking marine pseudosuchians, and intervals that did not meet our quorum level due to data deficiency were excluded, our regression analyses ask whether pseudosuchian diversity was correlated to environmental variables when pseudosuchians were present at all.
All analyses were performed in R version 3.0.2 (ref. 68 ) and using a customized PERL script provided by J. Alroy. Additional information is provided in the
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