Foraminifera

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 the Supplementary Methods.

Samples were collected along a transect from Hawaii to Alaska during August 2017 as part of the CDisK-IV (KM1712) cruise on R/V Kilo Moana (Fig. 1). The five stations along the transect were designed to sample subtropical, transition zone, and subpolar waters. A rosette of Niskin bottles equipped with CTD (conductivity, temperature, depth) and other sensors for coccolithophore and biogeochemical parameters and a vertically integrated plankton tow were collected at each station. Further plankton tows were conducted at four additional intermediate stations (Supplementary material).
A 0.5 m diameter net with 90 µm mesh size was used throughout; based on previous work this mesh size should provide a good estimate of both pteropod^{18 (link),77} and foraminiferal⁷⁸ biomass. The sampling strategy was designed to capture an integrated sample of all foraminifera, pteropods, and heteropods from juveniles to adults living throughout the upper water column. The net was towed from the surface down to a specified maximum depth within the water column, and then back to the surface in a continuous manner following an oblique trajectory through the water column. The maximum depth was determined from the fluorescence profile of the preceding CTD cast, and was selected to ensure the net sampling captured well below the base of the chlorophyll maximum and ranged from 150 m in the most northerly subpolar sites to 300 m in the subtropical region (Tables S1, S2). The volume of water represented by each net tow sample was calculated by multiplying the net area by the distance traveled as determined by a flowmeter. For the vertically integrated values, the integration is carried out from the surface to the maximum depth of the tow.
After collection, samples were preserved in a 4% formalin seawater solution, buffered to a pH of ~8.1 with hexamethylenetetramine^{73 (link)}. Samples were split with a Folsom splitter or a McLane rotary splitter (splitting error <4%). Large pteropods and heteropods (>1 mm) were picked and quantified before splitting. Half of the split sample was transferred into ethanol solution in the laboratory for the analysis of pteropods and heteropods.
Water samples from rosettes of Niskin bottles equipped with CTD (Sea-Bird SBE 9) were collected at different depths throughout the photic zone and including the chlorophyll maximum depth.

We converted the measured CaCO₃ concentrations (i.e. CaCO₃ standing stock, CaCO₃ biomass) into production rate, using estimates of the turnover time for each group (that is, the typical lifespan of an individual; Table 1): for foraminifera we used a range of 10–30 days^{90 (link)–93 (link)}, noting that more slowly reproducing deep-dwelling species make up only a very small fraction of the assemblages in our tows^{31 (link)}. For pteropods and heteropods we used a range of 5–16 days (although we note their lifespan may be much longer than this^{94 (link)}). Pteropods and heteropod turnover time was calculated as turnover time (days) =1/G, where G is the average instantaneous growth rates expressed as mg Ca deposited (on mg Ca shell)⁻¹ day⁻¹ ref. ^{57 (link),58 (link)}. We assume that growth rates do not vary with shell size; this approximation is supported by a previous study⁷⁷ , who found no significant difference in the shell growth rates of small and large sizes of any of the four pteropod species the author examined.
For coccolithophores we used a range of 0.1–1.5 cell division day⁻¹ (1.5–10 days) (Table 1). This range is derived from laboratory field estimates and simulated by a generalized coccolithophore model for equatorial to North Pacific Ocean^{59 (link)}. We are aware that cell growth phase differs for small cells with few coccoliths produced during exponential growth phase (normal, rapid division) and larger cells with more coccoliths produced during early stationary phase (slowed cell division).
Given the large range in the turnover rate of coccolithophores, foraminifera, pteropoda, and heteropoda, we apply a probabilistic approach to determine the production rate and propagate the uncertainties in turnover time through to our estimates of total production using a flat probability distribution i.e. for foraminifera there is equal chance of the average lifespan being 10 days as it is 30 days (this highly conservative approach thus results in larger total uncertainties in production rate). The production (mg m^-2 day^-1) is then given as the CaCO₃ standing stock (in mg m^-2) divided by the turnover time (days), ${\mathrm{CaCO}}_3\mathrm{production}\left(\mathrm{mg}{\mathrm{m}}^{-2}{\mathrm{day}}^{-1}\right)={\mathrm{CaCO}}_3\mathrm{standing}\mathrm{stock}\left(\mathrm{mg}{\mathrm{m}}^{-2}\right)/\mathrm{turnover}\mathrm{time}\left(\mathrm{days}\right)$
Our approach assumes that all of the organisms we sampled are living. This assumption is valid for foraminifera and pteropods as they sink individually, and relatively quickly upon death. For coccolithophores this assumption is valid as we only consider intact coccospheres, which mostly disaggregate quickly upon death. Annual estimates were then calculated by multiplying the daily estimates by 365 accounting for the seasonal bias at the time of sampling using PIC/chlorophyll_a/zooplankton time series (see below).
The data and R code to perform the calculation of CaCO₃ production including error propagation and seasonal bias correction (see below) is available at 10.5281/zenodo.7458132.