Philippa Kaur

Hart, M. B. et al. The search for the origin of the planktic foraminifera. J. Geol. Soc. Lond. 160, 341–343 (2003).Article 

Google Scholar 
Aze, T. et al. A phylogeny of Cenozoic macroperforate planktonic foraminifera from fossil data. Biol. Rev. 86, 900–927 (2011).Article 
PubMed 

Google Scholar 
Gradstein, F., Waskowska, A. & Glinskikh, L. The first 40 million years of planktonic foraminifera. Geosci 11, 1–25 (2021).Article 

Google Scholar 
Ujiié, Y., Kimoto, K. & Pawlowski, J. Molecular evidence for an independent origin of modern triserial planktonic foraminifera from benthic ancestors. Mar. Micropaleontol. 69, 334–340 (2008).Article 
ADS 

Google Scholar 
Darling, K. F. et al. Surviving mass extinction by bridging the benthic/planktic divide. Proc. Natl Acad. Sci. USA 106, 12629–33 (2009).Article 
ADS 
PubMed 
PubMed Central 
CAS 

Google Scholar 
Kucera, M. et al. Caught in the act: anatomy of an ongoing benthic–planktonic transition in a marine protist. J. Plankton Res. 39, 436–449 (2017).
Google Scholar 
Ezard, T. H. G., Aze, T., Pearson, P. N. & Purvis, A. Interplay between changing climate and species’ ecology drives macroevolutionary dynamics. Science 332, 349–352 (2011).Article 
ADS 
PubMed 
CAS 

Google Scholar 
Lowery, C. M., Bown, P. R., Fraass, A. J. & Hull, P. M. Ecological response of plankton to environmental change: thresholds for extinction. Annu. Rev. Earth Planet. Sci. 48, 403–429 (2020).Article 
ADS 
CAS 

Google Scholar 
Pawlowski, J., Holzmann, M. & Tyszka, J. New supraordinal classification of foraminifera: molecules meet morphology. Mar. Micropaleontol. 100, 1–10 (2013).Article 
ADS 

Google Scholar 
Lecroq, B. et al. Ultra-deep sequencing of foraminiferal microbarcodes unveils hidden richness of early monothalamous lineages in deep-sea sediments. Proc. Natl Acad. Sci. USA 108, 13177–13182 (2011).Article 
ADS 
PubMed 
PubMed Central 
CAS 

Google Scholar 
Pawlowski, J. et al. The evolution of early foraminifera. Proc. Natl Acad. Sci. USA 100, 11494–8 (2003).Article 
ADS 
PubMed 
PubMed Central 
CAS 

Google Scholar 
Vachard, D. Macroevolution and biostratigraphy of paleozoic foraminifers. in Stratigraphy and Timescales (Ed. Montenari, M.) Vol. 1, 257–323 (Academic Press, 2016).Ibarbalz, F. M. et al. Global trends in marine plankton diversity across kingdoms of life. Cell 179, 1084–1097.e21 (2019).Article 
PubMed 
PubMed Central 
CAS 

Google Scholar 
Guillou, L. et al. The Protist Ribosomal Reference database (PR2): a catalog of unicellular eukaryote Small Sub-Unit rRNA sequences with curated taxonomy. Nucleic Acids Res. 41, D597–D604 (2013).Article 
PubMed 
CAS 

Google Scholar 
Holzmann, M. & Pawlowski, J. An updated classification of rotaliid foraminifera based on ribosomal DNA phylogeny. Mar. Micropaleontol. 132, 18–34 (2017).Article 
ADS 

Google Scholar 
John, A. W. G. The regular occurrence of Reophax Scottie Chaster, a benthic foraminiferan, in plankton samples from the North Sea. J. Micropalaeontol. 6, 61–63 (1987).Article 

Google Scholar 
Kucera, M. et al. Caught in the act: anatomy of an ongoing benthic-planktonic transition in a marine protist. J. Plankton Res. 39, 436–449 (2017).Darling, K. F., Wade, C. M., Kroon, D. & Brown, A. J. L. Planktic foraminiferal molecular evolution and their polyphyletic origins from benthic taxa. Mar. Micropaleontol. 30, 251–266 (1997).Article 
ADS 

Google Scholar 
Church, S. H., Ryan, J. F. & Dunn, C. W. Automation and evaluation of the SOWH test with SOWHAT. Syst. Biol. 64, 1048–1058 (2015).Article 
PubMed 
PubMed Central 

Google Scholar 
Shimodaira, H. An approximately unbiased test of phylogenetic tree selection. Syst. Biol. 51, 492–508 (2002).Article 
PubMed 

Google Scholar 
Pawlowski, J. et al. Extreme differences in rates of molecular evolution of foraminifera revealed by comparison of ribosomal DNA sequences and the fossil record. Mol. Biol. Evol. 14, 498–505 (1997).Article 
PubMed 
CAS 

Google Scholar 
Peijnenburg, K. T. C. A. et al. The origin and diversification of pteropods precede past perturbations in the Earth’s carbon cycle. Proc. Natl Acad. Sci. USA 117, 25609–25617 (2020).Article 
ADS 
PubMed 
PubMed Central 
CAS 

Google Scholar 
O’Brien, C. L. et al. Cretaceous sea-surface temperature evolution: constraints from TEX86 and planktonic foraminiferal oxygen isotopes. Earth-Sci. Rev. 172, 224–247 (2017).Article 
ADS 

Google Scholar 
Olsson, R. K., Berggren, W. A., Hemleben, C. & Huber, B. T. Atlas of Paleocene planktonic foraminifera. Smithson. Contrib. Paleobiol. 1–252 https://doi.org/10.5479/si.00810266.85.1 (1999).Arenillas, I. & Arz, J. A. Benthic origin and earliest evolution of the first planktonic foraminifera after the Cretaceous/Palaeogene boundary mass extinction. Hist. Biol. 29, 25–42 (2017).Article 

Google Scholar 
Huber, B. T., Petrizzo, M. R. & MacLeod, K. G. Planktonic foraminiferal endemism at southern high latitudes following the terminal cretaceous extinction. J. Foraminifer. Res. 50, 382–402 (2020).Article 

Google Scholar 
Arenillas, I., Arz, J. A. & Gilabert, V. An updated suprageneric classification of planktic foraminifera after growing evidence of multiple benthic-planktic transitions. Spanish J. Palaeontol. https://doi.org/10.7203/sjp.22189 (2022).Culver, S. J. Benthic foraminifera across the Cretaceous–Tertiary (K–T) boundary: a review. Mar. Micropaleontol. 47, 177–226 (2003).Article 
ADS 

Google Scholar 
Widmark, J. G. V. & Malmgren, B. A. Benthic foraminiferal changes across the Cretaceous/Tertiary boundary in the deep sea; DSDP sites 525, 527, and 465. J. Foraminifer. Res. 22, 81–113 (1992).Article 

Google Scholar 
Rigaud, S., Martini, R. & Vachard, D. Early evolution and new classification of the order Robertinida (foraminifera). J. Foraminifer. Res. 45, 3–28 (2015).Article 

Google Scholar 
Rigaud, S., Granier, B. & Masse, J. P. Aragonitic foraminifers: an unsuspected wall diversity. J. Syst. Palaeontol. 19, 461–488 (2021).Article 

Google Scholar 
Hull, P. M. et al. On impact and volcanism across the Cretaceous-Paleogene boundary. Science 367, 266–272 (2020).Article 
ADS 
PubMed 
CAS 

Google Scholar 
Morard, R. et al. PFR2: a curated database of planktonic foraminifera 18S ribosomal DNA as a resource for studies of plankton ecology, biogeography and evolution. Mol. Ecol. Resour. 15, 1472–1485 (2015).Article 
PubMed 
CAS 

Google Scholar 
Morard, R. et al. Genetic and morphological divergence in the warm-water planktonic foraminifera genus Globigerinoides. PLoS ONE 14, 1–30 (2019).Article 

Google Scholar 
Morard, R., Vollmar, N. M., Greco, M. & Kucera, M. Unassigned diversity of planktonic foraminifera from environmental sequencing revealed as known but neglected species. PLoS ONE 14, e0213936 (2019).Article 
PubMed 
PubMed Central 
CAS 

Google Scholar 
Camacho, C. et al. BLAST+: Architecture and applications. BMC Bioinforma. 10, 1–9 (2009).Article 

Google Scholar 
R Development Core Team. R: A Language and Environment for Statistical Computing (R Foundation for Statistical Computing, 2014).Liaw, A. & Wiener, M. Classification and Regression by randomForest. R. N. 2, 18–22 (2002).
Google Scholar 
Lang, M. et al. mlr3: a modern object-oriented machine learning framework in R. J. Open Source Softw. 4, 1903 (2019).Article 
ADS 

Google Scholar 
Katoh, K. & Standley, D. M. MAFFT multiple sequence alignment software version 7: improvements in performance and usability. Mol. Biol. Evol. 30, 772–780 (2013).Article 
PubMed 
PubMed Central 
CAS 

Google Scholar 
Darriba, D. et al. ModelTest-NG: a new and scalable tool for the selection of DNA and protein evolutionary models. Mol. Biol. Evol. 37, 291–294 (2020).Article 
MathSciNet 
PubMed 
CAS 

Google Scholar 
Kozlov, A. M. et al. RAxML-NG: a fast, scalable and user-friendly tool for maximum likelihood phylogenetic inference. Bioinformatics 35, 4453–4455 (2019).Article 
PubMed 
PubMed Central 
CAS 

Google Scholar 
Barbera, P. et al. EPA-ng: massively parallel evolutionary placement of genetic sequences. Syst. Biol. 68, 365–369 (2019).Article 
MathSciNet 
PubMed 

Google Scholar 
Letunic, I. & Bork, P. Interactive tree of life (iTOL) v5: an online tool for phylogenetic tree display and annotation. Nucleic Acids Res. 49, 293–296 (2021).Article 

Google Scholar 
Löytynoja, A. & Goldman, N. WebPRANK: a phylogeny-aware multiple sequence aligner with interactive alignment browser. BMC Bioinform. 11, 1–7 (2010).Ronquist, F. et al. MrBayes 3. 2: efficient Bayesian phylogenetic inference and model choice across a large model space. Syst. Biol. 61, 539–542 (2012).Article 
PubMed 
PubMed Central 

Google Scholar 
Minh, B. Q. et al. IQ-TREE 2: new models and efficient methods for phylogenetic inference in the genomic era. Mol. Biol. Evol. 37, 1530–1534 (2020).Article 
PubMed 
PubMed Central 
CAS 

Google Scholar 
Dos Reis, M., Donoghue, P. C. J. & Yang, Z. Bayesian molecular clock dating of species divergences in the genomics era. Nat. Rev. Genet. 17, 71–80 (2016).Article 
PubMed 

Google Scholar 
Song, H., Tong, J. & Chen, Z. Q. Evolutionary dynamics of the Permian-Triassic foraminifer size: Evidence for Lilliput effect in the end-Permian mass extinction and its aftermath. Palaeogeogr. Palaeoclimatol. Palaeoecol. 308, 98–110 (2011).Article 

Google Scholar 
Copestake, P. & Johnson, B. Lower Jurassic Foraminifera from the Llanbedr (Mochras Farm) Borehole, North Wales, UK. Monogr. Palaeontogr. Soc. 167, 1–403 (2013).Article 

Google Scholar 
Rigaud, S. & Blau, J. New Robertinid Foraminifers from the Early Jurassic of Adnet, Austria and Their Evolutionary Importance. Acta Palaeontol. Pol. 61, 721–734 (2016).Article 

Google Scholar 
Boudagher-fadel, M. K. Evolution and Geological Significance of Larger Benthic Foraminifera. Evolution and Geological Significance of Larger Benthic Foraminifera (UCL Press, 2018).Piuz, A. & Meister, C. Cenomanian rotaliids (Foraminiferida) from Oman and Morocco. Swiss J. Palaeontol. 132, 81–97 (2013).Article 

Google Scholar 
Kucera, M. & Schönfeld, J. The origin of modern oceanic foraminiferal faunas and Neogene climate change. in Deep-Time Perspectives on Climate Change: Marrying the Signal from Computer Models and Biological Proxies. (ed. The Micropalaeontological Society, S. P.) 409–425 (The Geological Society, 2007).Drummond, A. J. & Suchard, M. A. Bayesian random local clocks, or one rate to rule them all. BMC Biol. 8, 114 (2010).Article 
PubMed 
PubMed Central 

Google Scholar 
Rambaut, A. FigTree version 1.3.1. http://tree.bio.ed.ac.uk (2009).Groussin, M., Pawlowski, J. & Yang, Z. Bayesian relaxed clock estimation of divergence times in foraminifera. Mol. Phylogenet. Evol. 61, 157–166 (2011).Article 
PubMed 

Google Scholar 
Loeblich Jr, A. R. & Tappan, H. Foraminiferal Genera and Their Classification (Springer, 1988). More

MaterialsTrunk wash was collected from one male (Tembo, born 1985) and five female (Tonga, 1984; Numbi, 1992; Mongu, 2003; Iqhwa, 2013; Kibali, 2019) African elephants at the Vienna Zoo during routine procedures. Briefly, 100 mL of a sterile 0.9% saline solution is injected in each nostril of the trunk, which is kept in a lifted position, so that the solution is running up to the base of the trunk. The mixture of the solution and trunk mucus is collected in sterile plastic bags by active blowing of the elephant. Chemicals were all from Merck, Austria, unless otherwise stated. Restriction enzymes and kits for DNA extraction and purification were from New England Biolabs, USA. Oligonucleotides and synthetic genes were custom synthesised at Eurofins Genomics, Germany.Ethics declarationWe confirm that the trunk wash performed to provide a sample of the mucus was carried out as a routine procedure to monitor the health of elephants at the Vienna Zoo and in accordance with relevant guidelines and regulations.Trunk wash fractionationTrunk wash was centrifuged for 1 h at 10,000 g, the supernatant was dialyzed against 50 mM Tris–HCl buffer, pH 7.4 and concentrated by ultrafiltration in the Amicon stirred cell, then fractionated by anion-exchange chromatography on HiPrep-Q 16/10 column, 20 mL (Bio-Rad), along with standard protocols.Protein alkylation and digestion, and mass spectrometry analysisSDS-PAGE gel portions of proteins from whole elephant trunk wash (for component identification), chromatographic fractions of the elephant trunk wash (for PTMs analysis) or SDS-PAGE gel bands of LafrOBP1 expressed in P. pastoris were in parallel triturated, washed with water, in gel-reduced, S-alkylated, and digested with trypsin (Sigma, sequencing grade). Resulting peptide mixtures were desalted by μZip-TipC18 (Millipore) using 50% (v/v) acetonitrile, 5% (v/v) formic acid as eluent, vacuum-dried by SpeedVac (Thermo Fisher Scientific, USA), and then dissolved in 20 μL of aqueous 0.1% (v/v) formic acid for subsequent MS analyses by means of a nanoLC-ESI-Q-Orbitrap-MS/MS system, comprising an UltiMate 3000 HPLC RSLC nano-chromatographer (Thermo Fisher Scientific) interfaced with a Q-ExactivePlus mass spectrometer (Thermo Fisher Scientific) mounting a nano-Spray ion source (Thermo Fisher Scientific). Chromatographic separations were obtained on an Acclaim PepMap RSLC C18 column (150 mm × 75 μm ID; 2 μm particle size; 100 Å pore size, Thermo Fisher Scientific), eluting the peptide mixtures with a gradient of solvent B (19.92/80/0.08 v/v/v water/acetonitrile/formic acid) in solvent A (99.9/0.1 v/v water/formic acid), at a flow rate of 300 nL/min. In particular, solvent B started at 3%, increased linearly to 40% in 45 min, then achieved 80% in 5 min, remaining at this percentage for 4 min, and finally returned to 3% in 1 min. The mass spectrometer operated in data-dependent mode in positive polarity, carrying out a full MS1 scan in the range m/z 345–1350, at a nominal resolution of 70,000, followed by MS/MS scans of the 10 most abundant ions in high energy collisional dissociation (HCD) mode. Tandem mass spectra were acquired in a dynamic m/z range, with a nominal resolution of 17,500, a normalized collision energy of 28%, an automatic gain control target of 50,000, a maximum ion injection time of 110 ms, and an isolation window of 1.2 m/z. Dynamic exclusion was set to 20 s36.Bioinformatics for peptide identification and post-translational modification assignmentRaw mass data files were searched by Proteome Discoverer v. 2.4 package (Thermo Fisher Scientific), running the search engine Mascot v. 2.6.1 (Matrix Science, UK), Byonic™ v. 2.6.46 (Protein Metrics, USA) and Peaks Studio 8.0 (BSI, Waterloo, Ontario, Canada) software, both for peptide assignment/protein identification and for post-translational modification analysis.In the first case, analyses were carried out against a customized database containing protein sequences downloaded from NCBI (https://www.ncbi.nlm.nih.gov/) for superorder Afrotheria (consisting of 192,838 protein sequences, December 2021) plus the most common protein contaminants and trypsin. Parameters for database searching were fixed carbamidomethylation at Cys, and variable oxidation at Met, deamidation at Asn/Gln, and pyroglutamate formation at Gln. Mass tolerance was set to ± 10 ppm for precursors and to ± 0.05 Da for MS/MS fragments. Proteolytic enzyme and maximum number of missed cleavages were set to trypsin and 3, respectively. All other parameters were kept at default values. In the latter case, raw mass data were analyzed against a customized database containing LafrOBP1 (XP_023395442.1) protein sequence plus the most common protein contaminants and trypsin, allowing to search Lys-acetylation (Δm =  + 42.01), Ser/Thr/Tyr-phosphorylation (Δm =  + 79.97), and the most common mammals N-linked glycans at Asn and O-linked glycans at Ser/Thr/Tyr, using the same parameters previously set. The max PTM sites per peptide was set to 2.Proteome Discoverer peptide candidates were considered confidently identified only when the following criteria were satisfied: (i) protein and peptide false discovery rate (FDR) confidence: high; (ii) peptide Mascot score:  > 30; (iii) peptide spectrum matches (PSMs): unambiguous; (iv) peptide rank (rank of the peptide match): 1; (v) Delta CN (normalized score difference between the selected PSM and the highest-scoring PSM for that spectrum): 0. Byonic peptide candidates were considered confidently identified only when the following criteria were satisfied: (i) PEP 2D and PEP 1D:  More

Data sourcesData for the trophic parameters and data categories listed in Tables 1 and 2 were gathered from peer-reviewed scientific publications, grey literature (e.g., agency reports, theses, and dissertations) and unpublished data by the authors of this paper. Data compilation on stomach contents, stable isotopes, FATM, and trophic positions, focussed on mesopelagic organisms, their potential prey and predators. For major and trace elements, energy density and estimates of diet proportions, our search concentrated on mesopelagic taxa. Nevertheless, we also gathered information from small or intermediate-sized epi-, bathy- or benthopelagic species found in the compiled data sources. These species were included because they play key roles in most marine ecosystems, both as important consumers of phytoplankton and zooplankton, and prey for many top predators, and can represent alternative energy pathways to mesopelagic organisms. However, we stress that the data coverage for these species in the current version of the database is very incomplete. Our main interest was on data from the central and eastern North Atlantic, and the Mediterranean, corresponding to the study regions of the SUMMER project. When we could not find suitable data within this region, we extended the geographic scope of our literature search to the western North Atlantic. We did not search for datasets in open access repositories since those data can be easily accessed and extracted. However, some of the data provided by the authors of this paper have been previously deposited in PANGAEA.DNA sequencing-based methods, such as metabarcoding and direct shotgun sequencing, are emerging as promising tools in dietary analyses due to the high resolution in taxonomic identification of many prey simultaneously, and the potential to provide quantitative diet estimates from relative read abundance29. However, recent studies have shown that various methodological and biological factors can break the correlation between the number and abundance of ingested prey and the prey DNA present in the sample, and lead to biased estimates of taxonomic diversity and composition of diet29,30. Given the uncertainties remaining in the interpretation of DNA sequencing-based diet data, we decided not to include these data in MesopTroph until additional research demonstrates that these techniques can be confidently applied for quantitative diet assessment.We identified available data sources in the literature through systematic searches on Web of Science, Google Scholar, ResearchGate, and the Google search engine. We used multiple combinations of terms related to specific data categories (Table 3), in conjunction with the common or scientific taxon names (from genus to order), and the ocean basin. For example, the search for stomach content data of fishes belonging to the family Myctophidae was undertaken using the following terms: “stomach content” OR “gut content” OR “prey composition” OR “diet composition”, AND “mesopelagic fish” OR “myctophid” OR “Myctophiformes” OR “Myctophidae”, AND “Atlantic” or “Mediterranean”. For the mesopelagic and predator species known to be numerically abundant in the SUMMER study regions, we performed a second literature search using the common or scientific name of the species, along with the terms “diet”, “feeding habits”, “trophic ecology”, “trophic markers”, or “food web”. We also examined the literature cited within each collected publication to locate additional data sources.Table 3 Terms used in the literature search for each data category.Full size tableWe next screened the full text of the compiled studies and retained data sources that: (1) were collected within the region of interest, (2) reported quantitative data for the trophic parameters of interest, (3) reported the number of samples for pooled or aggregated data, and (4) provided sufficient details on the methodology to enable a quality check. In the case of stable isotope data, we only included data sources reporting both δ13C and δ15N measurements.Data extraction, cleaning, and formattingWe created a template table for each data category in Microsoft Excel to assemble all datasets into a single file, and to facilitate cleaning and standardization of data records. We added a large number of metadata fields to the tables to annotate details about the sampling (e.g., location, date, methods), sampled specimen(s) (e.g., taxonomy, number and size of individuals, number of replicates, tissue analysed), and data source (e.g., full reference, DOI) for every record.Data contributors formatted and incorporated their datasets directly into the tables. For published sources, the data and associated metadata were extracted manually or digitized from the article text, tables, or supplementary material into the tables. Extraneous or hidden characters, and values such as “NA” (Not Available) or “ND” (Not Determined), were deleted from the parameter and metadata fields. Measurements of trophic parameters were standardized to the same units (see Tables 1 and 2). Parameter values that were clearly incorrect (e.g., δ15N  > 20, or the frequency of occurrence of a prey higher than the number of stomachs sampled) were corrected by searching for the value within the data source. When values could not be corrected, we deleted that data record.When available, we extracted information at the individual level. However, most studies reported data obtained from pooled samples of the same species. In some cases (e.g., small specimens such as planktonic organisms), a minimum and maximum number of individuals in the sample was provided instead of the actual number of individuals sampled. We added two columns to the tables presenting the minimum and maximum number of individuals in the sample. By filtering the column “Ind No (maximum per sample)” for values >1, users can easily identify records with aggregated data and differentiate them from records where information was drawn from a single individual (i.e., where “Ind No (maximum per sample)” =1). In addition, the tables Stomach contents and Estimates of diet proportions include a field “Sample ID” with a unique identifier of the sample. If data are reported at the individual level (i.e., “Ind No (maximum per sample)” =1) then Sample ID is the individual animal ID. If the data are from a group of individuals (i.e., “Ind No (maximum per sample)” >1), then Sample ID identifies that group.We standardized the taxonomic classification and nomenclature of fishes and elasmobranchs following the Eschmeyer’s Catalog of Fishes (http://researcharchive.calacademy.org/research/ichthyology/catalog/fishcatmain.asp)31,32. For the remaining taxa, we used the World Register of Marine Species (http://www.marinespecies.org/)33. Unaccepted or alternate taxon names were replaced by the most up-to-date valid name. When the identification of a taxon was uncertain, the taxonomic level of identification was decreased to a satisfactory level. For example, prey reported as “Cephalopods” were changed to “Cephalopoda”, “Sepiolids” to “Sepiolidae”, and “Myctophum punctatum?” to the genus “Myctophum”.Stomach contentsStomach contents analysis is a standard dietary assessment method that potentially enables quantifying diet components with high taxonomic resolution34. Three parameters are typically used to describe diet composition from stomach contents: the number of individuals of a prey type as a proportion of the total number of prey items (%N), the proportion of a prey item by weight or volume (%W), and the proportion of stomachs containing a particular prey item (i.e., percent frequency of occurrence, %F)35. When available, we collected data on the three parameters, as well as on the absolute number, weight, and frequency of occurrence of each prey type in the stomachs of each sampled individual or group of individuals. If stated in the data source, we indicate if prey weights were directly measured or reconstructed from hard remains (fish otoliths and vertebrae, cephalopod beaks), and if they represent dry or wet weight. Some datasets contained records of prey items without corresponding weights or numbers. As a result, the cumulative percent of all prey items did not sum to 100%. This occurred in 11 data records for the cumulative %W, and nine for the cumulative %N. While we checked the accuracy of percentage values and adjusted rounding errors, we did not attempt to fill in missing values nor did we remove records with missing values. When prey values were reported by an upper bound (e.g., “ More

Prosser JI, Hink L, Gubry-Rangin C, Nicol GW. Nitrous oxide production by ammonia oxidizers: Physiological diversity, niche differentiation and potential mitigation strategies. Glob Chang Biol. 2020;26:103–18.Article 
PubMed 

Google Scholar 
Huang L, Chakrabarti S, Cooper J, Perez A, John SM, Daroub SH, et al. Ammonia-oxidizing archaea are integral to nitrogen cycling in a highly fertile agricultural soil. ISME Commun. 2021;1:19.Article 

Google Scholar 
Hink L, Gubry-Rangin C, Nicol GW, Prosser JI. The consequences of niche and physiological differentiation of archaeal and bacterial ammonia oxidisers for nitrous oxide emissions. ISME J. 2018;12:1084–93.Article 
PubMed 
PubMed Central 
CAS 

Google Scholar 
Li Y, Chapman SJ, Nicol GW, Yao H. Nitrification and nitrifiers in acidic soils. Soil Biol Biochem. 2018;116:290–301.Article 
CAS 

Google Scholar 
Ahlgren NA, Fuchsman CA, Rocap G, Fuhrman JA. Discovery of several novel, widespread, and ecologically distinct marine Thaumarchaeota viruses that encode amoC nitrification genes. ISME J 2019;13:618–31.Article 
PubMed 
CAS 

Google Scholar 
Kim J-G, Kim S-J, Cvirkaite-Krupovic V, Yu W-J, Gwak J-H, López-Pérez M, et al. Spindle-shaped viruses infect marine ammonia-oxidizing thaumarchaea. Proc Natl Acad Sci USA. 2019;116:15645–50.Article 
PubMed 
PubMed Central 
CAS 

Google Scholar 
Emerson JB. Soil Viruses: A New Hope. mSystems 2019;4:e00120–19.Article 
PubMed 
PubMed Central 
CAS 

Google Scholar 
Santos-Medellín C, Estera-Molina K, Yuan M, Pett-Ridge J, Firestone MK, Emerson JB. Spatial turnover of soil viral populations and genotypes overlain by cohesive responses to moisture in grasslands. Proc Natl Acad Sci USA. 2022;119:e2209132119.Article 
PubMed 
PubMed Central 

Google Scholar 
Wu R, Davison MR, Gao Y, Nicora CD, Mcdermott JE, Burnum-Johnson KE, et al. Moisture modulates soil reservoirs of active DNA and RNA viruses. Commun Biol. 2021;4:992.Article 
PubMed 
PubMed Central 
CAS 

Google Scholar 
Braga LPP, Spor A, Kot W, Breuil M-C, Hansen LH, Setubal JC, et al. Impact of phages on soil bacterial communities and nitrogen availability under different assembly scenarios. Microbiome 2020;8:52.Article 
PubMed 
PubMed Central 
CAS 

Google Scholar 
Albright MBN, Gallegos-Graves LV, Feeser KL, Montoya K, Emerson JB, Shakya M, et al. Experimental evidence for the impact of soil viruses on carbon cycling during surface plant litter decomposition. ISME Commun. 2022;2:24.Article 

Google Scholar 
Starr EP, Shi S, Blazewicz SJ, Koch BJ, Probst AJ, Hungate BA, et al. Stable-isotope-informed, genome-resolved metagenomics uncovers potential cross-kingdom interactions in rhizosphere soil. mSphere 2021;6:e0008521.Article 
PubMed 

Google Scholar 
Trubl G, Kimbrel JA, Liquet-Gonzalez J, Nuccio EE, Weber PK, Pett-Ridge J, et al. Active virus-host interactions at sub-freezing temperatures in Arctic peat soil. Microbiome 2021;9:208.Article 
PubMed 
PubMed Central 
CAS 

Google Scholar 
Lee S, Sieradzki ET, Nicolas AM, Walker RL, Firestone MK, Hazard C, et al. Methane-derived carbon flows into host–virus networks at different trophic levels in soil. Proc Natl Acad Sci USA. 2021;118:e2105124118.Article 
PubMed 
PubMed Central 
CAS 

Google Scholar 
Nicol GW, Leininger S, Schleper C, Prosser JI. The influence of soil pH on the diversity, abundance and transcriptional activity of ammonia oxidizing archaea and bacteria. Environ Microbiol. 2008;10:2966–78.Article 
PubMed 
CAS 

Google Scholar 
Chaumeil P-A, Mussig AJ, Hugenholtz P, Parks DH. GTDB-Tk: a toolkit to classify genomes with the Genome Taxonomy Database. Bioinformatics 2020;36:1925–7.CAS 

Google Scholar 
Alves RJE, Minh BQ, Urich T, von Haeseler A, Schleper C. Unifying the global phylogeny and environmental distribution of ammonia-oxidising archaea based on amoA genes. Nat Commun. 2018;9:1517.Article 
PubMed 
PubMed Central 

Google Scholar 
Cardinale DJ, Duffy S. Single-stranded genomic architecture constrains optimal codon usage. Bacteriophage 2011;1:219–24.Article 
PubMed 
PubMed Central 

Google Scholar 
Lee S, Sorensen JW, Walker RL, Emerson JB, Nicol GW, Hazard C. Soil pH influences the structure of virus communities at local and global scales. Soil Biol Biochem. 2022;166:108569.Article 
CAS 

Google Scholar 
Jang HB, Bolduc B, Zablocki O, Kuhn JH, Roux S, Adriaenssens EM, et al. Taxonomic assignment of uncultivated prokaryotic virus genomes is enabled by gene-sharing networks. Nat Biotechnol. 2019;37:632–9.Article 

Google Scholar 
Nishimura Y, Yoshida T, Kuronishi M, Uehara H, Ogata H, Goto S. ViPTree: the viral proteomic tree server. Bioinformatics 2017;33:2379–80.Article 
PubMed 
CAS 

Google Scholar 
Kerou M, Offre P, Valledor L, Abby SS, Melcher M, Nagler M, et al. Proteomics and comparative genomics of Nitrososphaera viennensis reveal the core genome and adaptations of archaeal ammonia oxidizers. Proc Natl Acad Sci Usa 2016;113:7937–46.Article 

Google Scholar 
Reyes C, Hodgskiss LH, Kerou M, Pribasnig T, Abby SS, Bayer B, et al. Genome wide transcriptomic analysis of the soil ammonia oxidizing archaeon Nitrososphaera viennensis upon exposure to copper limitation. ISME J 2020;14:2659–74.Article 
PubMed 
PubMed Central 
CAS 

Google Scholar 
Sieradzki ET, Greenlon A, Nicolas AM, Firestone MK, Pett-Ridge J, Blazewicz SJ, et al. Functional succession of actively growing soil microorganisms during rewetting is shaped by precipitation history. bioRxiv. 2022; 2022.06.28.498032. More

HFRS distribution in China, 2004–2018From January 1, 2004 to December 31, 2018, 190 203 cases of HFRS were reported nationwide in China, with an average annual incidence rate of 0.950 per 100,000 people, with the highest incidence in 2004 (1.926 per 100,000) and the lowest in 2018 (0.86 per 100,000) (Fig. 1A), and the cases showed obvious seasonal fluctuations (Fig. 1B). HFRS cases existed every month and showed an obvious dual-season mode every year, with a spring peak from May to June and a winter peak from November to December. The highest number of cases were in May and November, with the composition ratios accounting of 9.51% and 17.06%, respectively (Fig. 1B).Figure 1The incidence and number of HFRS cases reported in China, 2004–2018. (A) Number of cases and incidence by year. Trend of the incidence rate of HFRS between 2004 and 2018 shown by the joinpoint regression (upper right corner). The red squares represent the observed crude incidence of HFRS and the lines represent the slope of the annual percentage change (APC). (B) The pink line represents the monthly incidence of HFRS. The bar chart shows the number of cases at peak and trough.Full size imageThe incidence of HFRS in northern regions was higher than that in the south, especially in Heilongjiang, Liaoning, Jining, Shaanxi, Shandong and Hebei provinces. Relatively few cases existed in south China, which were mainly concentrated in Jiangxi, Zhejiang, Hunan and Fujian (Figs. S1 and S2). Spatial autocorrelation analysis indicated that HFRS cases were positively correlated (Moran’s I = 0.09, p  More

Laine RA. A calculation of all possible oligosaccharide isomers both branched and linear yields 1.05 x 10(12) structures for a reducing hexasaccharide: the Isomer Barrier to development of single-method saccharide sequencing or synthesis systems. Glycobiology. 1994;4:759–67.PubMed 

Google Scholar 
Becker S, Tebben J, Coffinet S, Wiltshire K, Iversen MH, Harder T, et al. Laminarin is a major molecule in the marine carbon cycle. Proc Natl Acad Sci. 2020;117:6599.PubMed 
PubMed Central 

Google Scholar 
Pauly M, Gille S, Liu L, Mansoori N, Souza A, de, Schultink A, et al. Hemicellulose biosynthesis. Planta. 2013;238:627–42.PubMed 

Google Scholar 
Domozych D. Algal Cell Walls. In: Lauc G, Wuhrer M High-throughput glycomics and glycoproteomics. Humana Press, New York, 2016. pp 1–11.Donlan RM. Biofilms: microbial life on surfaces. Emerg Infect Dis. 2002;8:881–90.PubMed 
PubMed Central 

Google Scholar 
Popper ZA, Michel G, Hervé C, Domozych DS, Willats WGT, Tuohy MG, et al. Evolution and diversity of plant cell walls: from algae to flowering plants. Annu Rev Plant Biol. 2011;62:567–90.PubMed 

Google Scholar 
Henrissat B. A classification of glycosyl hydrolases based on amino acid sequence similarities. Biochem J. 1991;280:309–16.PubMed 
PubMed Central 

Google Scholar 
Martens EC, Koropatkin NM, Smith TJ, Gordon JI. Complex glycan catabolism by the human gut microbiota: the Bacteroidetes Sus-like paradigm. J Biol Chem. 2009;284:24673–7.PubMed 
PubMed Central 

Google Scholar 
Cuskin F, Lowe EC, Temple MJ, Zhu Y, Cameron E, Pudlo NA, et al. Human gut Bacteroidetes can utilize yeast mannan through a selfish mechanism. Nature. 2015;517:165–9.PubMed 
PubMed Central 

Google Scholar 
Falkowski PG, Barber RT, Smetacek VV. Biogeochemical Controls and Feedbacks on Ocean Primary Production. Science. 1998;281:200–7.PubMed 

Google Scholar 
Smetacek V. Seeing is Believing: Diatoms and the Ocean Carbon Cycle Revisited. Protist. 2018;169:791–802.PubMed 

Google Scholar 
Teeling H, Fuchs BM, Becher D, Klockow C, Gardebrecht A, Bennke CM, et al. Substrate-controlled succession of marine bacterioplankton populations induced by a phytoplankton bloom. Science. 2012;336:608–11.PubMed 

Google Scholar 
Teeling H, Fuchs BM, Bennke CM, Krüger K, Chafee M, Kappelmann L, et al. Recurring patterns in bacterioplankton dynamics during coastal spring algae blooms. Elife. 2016;5:e11888.PubMed 
PubMed Central 

Google Scholar 
Kappelmann L, Krüger K, Hehemann J-H, Harder J, Markert S, Unfried F, et al. Polysaccharide utilization loci of North Sea Flavobacteriia as basis for using SusC/D-protein expression for predicting major phytoplankton glycans. ISME J. 2019;13:76–91.PubMed 

Google Scholar 
Vidal-Melgosa S, Sichert A, Francis TB, Bartosik D, Niggemann J, Wichels A, et al. Diatom fucan polysaccharide precipitates carbon during algal blooms. Nat Commun. 2021;12:1150.PubMed 
PubMed Central 

Google Scholar 
Chanzy H, Dube M, Marchessault RH, Revol JF. Single crystals and oriented crystallization of ivory nut mannan. Biopolymers 1979;18:887–98.
Google Scholar 
Katsuraya K, Okuyama K, Hatanaka K, Oshima R, Sato T, Matsuzaki K. Constitution of konjac glucomannan: chemical analysis and 13C NMR spectroscopy. Carbohydr Polym. 2003;53:183–9.
Google Scholar 
Melton L, Smith BG, Ibrahim R, Schröder R, Harris P, Schmitt U. Mannans in primary and secondary plant cell walls. NZ J forestry Sci. 2009;39:153–60.
Google Scholar 
Hannuksela T, Du Hervé Penhoat C. NMR structural determination of dissolved O-acetylated galactoglucomannan isolated from spruce thermomechanical pulp. Carbohydr Res. 2004;339:301–12.PubMed 

Google Scholar 
Gilbert HJ, Stålbrand H, Brumer H. How the walls come crumbling down: recent structural biochemistry of plant polysaccharide degradation. Curr Opin Plant Biol. 2008;11:338–48.PubMed 

Google Scholar 
Bågenholm V, Reddy SK, Bouraoui H, Morrill J, Kulcinskaja E, Bahr CM, et al. Galactomannan catabolism conferred by a polysaccharide utilization locus of Bacteroides ovatus: Enzyme synergy and crystal structure of a β-mannanase. J Biol Chem. 2017;292:229–43.PubMed 

Google Scholar 
Chen J, Robb CS, Unfried F, Kappelmann L, Markert S, Song T, et al. Alpha- and beta-mannan utilization by marine Bacteroidetes. Environ Microbiol. 2018;20:4127–40.PubMed 

Google Scholar 
Klemetsen T, Raknes IA, Fu J, Agafonov A, Balasundaram SV, Tartari G, et al. The MAR databases: development and implementation of databases specific for marine metagenomics. Nucl Acids Res. 2018;46:D692–99.PubMed 

Google Scholar 
Sayers EW, Bolton EE, Brister JR, Canese K, Chan J, Comeau DC, et al. Database resources of the national center for biotechnology information. Nucl Acids Res. 2022;50:D20–26.PubMed 

Google Scholar 
Gilchrist CL, Booth TJ, van Wersch B, van Grieken L, Medema MH, Chooi Y-H. cblaster: a remote search tool for rapid identification and visualisation of homologous gene clusters. Bioinformatics Advances. 2021;1:016.Zhang H, Yohe T, Huang L, Entwistle S, Wu P, Yang Z, et al. dbCAN2: a meta server for automated carbohydrate-active enzyme annotation. Nucl Acids Res. 2018;46:W95–W101.PubMed 
PubMed Central 

Google Scholar 
Altschul SF, Madden TL, Schäffer AA, Zhang J, Zhang Z, Miller W, et al. Gapped BLAST and PSI-BLAST: a new generation of protein database search programs. Nucl Acids Res. 1997;25:3389–402.PubMed 
PubMed Central 

Google Scholar 
Krüger K, Chafee M, Ben Francis T, Del Glavina Rio T, Becher D, Schweder T, et al. In marine Bacteroidetes the bulk of glycan degradation during algae blooms is mediated by few clades using a restricted set of genes. ISME J. 2019;13:2800–16.PubMed 
PubMed Central 

Google Scholar 
Francis TB, Bartosik D, Sura T, Sichert A, Hehemann J-H, Markert S, et al. Changing expression patterns of TonB-dependent transporters suggest shifts in polysaccharide consumption over the course of a spring phytoplankton bloom. ISME J. 2021;15:2336–50.PubMed 
PubMed Central 

Google Scholar 
Lex A, Gehlenborg N, Strobelt H, Vuillemot R, Pfister H. UpSet: Visualization of Intersecting Sets. IEEE Trans Vis Comput Graph. 2014;20:1983–92.PubMed 
PubMed Central 

Google Scholar 
Conway JR, Lex A, Gehlenborg N. UpSetR: an R package for the visualization of intersecting sets and their properties. Bioinformatics. 2017;33:2938–40.PubMed 
PubMed Central 

Google Scholar 
Krzywinski M, Schein J, Birol I, Connors J, Gascoyne R, Horsman D, et al. Circos: an information aesthetic for comparative genomics. Genome Res. 2009;19:1639–45.PubMed 
PubMed Central 

Google Scholar 
Madeira F, Pearce M, Tivey ARN, Basutkar P, Lee J, Edbali O, et al. Search and sequence analysis tools services from EMBL-EBI in 2022. Nucl Acids Res. 2022;50(W1):W276–79.Guindon S, Dufayard J-F, Lefort V, Anisimova M, Hordijk W, Gascuel O. New Algorithms and Methods to Estimate Maximum-Likelihood Phylogenies: Assessing the Performance of PhyML 3.0. Syst Biol. 2010;59:307–21.PubMed 

Google Scholar 
Lefort V, Longueville J-E, Gascuel O. SMS: Smart Model Selection in PhyML. Mol Biol Evol. 2017;34:2422–4.PubMed 
PubMed Central 

Google Scholar 
Letunic I, Bork P. Interactive Tree Of Life (iTOL) v4: recent updates and new developments. Nucleic Acids Res. 2019;47:W256–59.PubMed 
PubMed Central 

Google Scholar 
Hahnke RL, Harder J. Phylogenetic diversity of Flavobacteria isolated from the North Sea on solid media. Syst Appl Microbiol. 2013;36:497–504.PubMed 

Google Scholar 
Schut F, Vries EJ, de, Gottschal JC, Robertson BR, Harder W, Prins RA, et al. Isolation of Typical Marine Bacteria by Dilution Culture: Growth, Maintenance, and Characteristics of Isolates under Laboratory Conditions. Appl Environ Microbiol. 1993;59:2150–60.PubMed 
PubMed Central 

Google Scholar 
Otto A, Bernhardt J, Meyer H, Schaffer M, Herbst F-A, Siebourg J, et al. Systems-wide temporal proteomic profiling in glucose-starved Bacillus subtilis. Nat Commun. 2010;1:137.PubMed 

Google Scholar 
Cox J, Mann M. MaxQuant enables high peptide identification rates, individualized p.p.b.-range mass accuracies and proteome-wide protein quantification. Nat Biotechnol. 2008;26:1367–72.PubMed 

Google Scholar 
Tyanova S, Temu T, Sinitcyn P, Carlson A, Hein MY, Geiger T, et al. The Perseus computational platform for comprehensive analysis of (prote)omics data. Nat Methods. 2016;13:731–40.PubMed 

Google Scholar 
Yu NY, Wagner JR, Laird MR, Melli G, Rey S, Lo R, et al. PSORTb 3.0: improved protein subcellular localization prediction with refined localization subcategories and predictive capabilities for all prokaryotes. Bioinformatics. 2010;26:1608–15.PubMed 
PubMed Central 

Google Scholar 
Yu C-S, Lin C-J, Hwang J-K. Predicting subcellular localization of proteins for Gram-negative bacteria by support vector machines based on n-peptide compositions. Protein Sci. 2004;13:1402–6.PubMed 
PubMed Central 

Google Scholar 
Perez-Riverol Y, Bai J, Bandla C, García-Seisdedos D, Hewapathirana S, Kamatchinathan S, et al. The PRIDE database resources in 2022: a hub for mass spectrometry-based proteomics evidences. Nucl Acids Res. 2022;50:D543–52.PubMed 

Google Scholar 
Studier F. Protein production by auto-induction in high density shaking cultures. Protein Expr. Purif. 2005;41:207–34.The CCP4 suite: programs for protein crystallography. Acta Crystallogr D Biol Crystallogr. 1994;50:760–3.Kabsch W. XDS. Acta Crystallogr D Biol Crystallogr. 2010;66:125–32.PubMed 
PubMed Central 

Google Scholar 
Cartmell A, Topakas E, Ducros VM-A, Suits MDL, Davies GJ, Gilbert HJ. The Cellvibrio japonicus mannanase CjMan26C displays a unique exo-mode of action that is conferred by subtle changes to the distal region of the active site. J Biol Chem. 2008;283:34403–13.PubMed 
PubMed Central 

Google Scholar 
Couturier M, Roussel A, Rosengren A, Leone P, Stålbrand H, Berrin J-G. Structural and Biochemical Analyses of Glycoside Hydrolase Families 5 and 26 β-(1,4)-Mannanases from Podospora anserina Reveal Differences upon Manno-oligosaccharide Catalysis*. J Biol Chem. 2013;288:14624–35.PubMed 
PubMed Central 

Google Scholar 
Afonine PV, Grosse-Kunstleve RW, Echols N, Headd JJ, Moriarty NW, Mustyakimov M, et al. Towards automated crystallographic structure refinement with phenix.refine. Acta Crystallogr D Biol Crystallogr. 2012;68:352–67.PubMed 
PubMed Central 

Google Scholar 
Murshudov GN, Skubák P, Lebedev AA, Pannu NS, Steiner RA, Nicholls RA, et al. REFMAC5 for the refinement of macromolecular crystal structures. Acta Crystallogr D Biol Crystallogr. 2011;67:355–67.PubMed 
PubMed Central 

Google Scholar 
Emsley P, Lohkamp B, Scott WG, Cowtan K. Features and development of Coot.Acta Crystallogr D Biol Crystallogr. 2010;66:486–501.PubMed 
PubMed Central 

Google Scholar 
Cowtan K. The Buccaneer software for automated model building. 1. Tracing protein chains. Acta Crystallogr D Biol Crystallogr. 2006;62:1002–11.PubMed 

Google Scholar 
DeLano WL. The PyMOL Molecular Graphics System Version 2.3.4. Schrödinger, LLC, New York; 2010.Fontes CM, Clarke JH, Hazlewood GP, Fernandes TH, Gilbert HJ, Ferreira LM. Possible roles for a non-modular, thermostable and proteinase-resistant cellulase from the mesophilic aerobic soil bacterium Cellvibrio mixtus. Appl Microbiol Biotechnol. 1997;48:473–9.PubMed 

Google Scholar 
Brändén C-I. The TIM barrel—the most frequently occurring folding motif in proteins: Current Opinion in Structural Biology. 1991;1:978–83.Marcus SE, Blake AW, Benians TAS, Lee KJD, Poyser C, Donaldson L, et al. Restricted access of proteins to mannan polysaccharides in intact plant cell walls. Plant J. 2010;64:191–203.PubMed 

Google Scholar 
Meikle PJ, Hoogenraad NJ, Bonig I, Clarke AE, Stone BA. A (1-3,1-4)-beta-glucan-specific monoclonal antibody and its use in the quantitation and immunocytochemical location of (1-3,1-4)-beta-glucans. Plant J. 1994;5:1–9.PubMed 

Google Scholar 
Kračun SK, Fangel JU, Rydahl MG, Pedersen HL, Vidal-Melgosa S, Willats WGT. Carbohydrate microarray technology applied to high-throughput mapping of plant cell wall glycans using comprehensive microarray polymer profiling (CoMPP). In: High-Throughput Glycomics and Glycoproteomics. Humana Press, New York, NY, 2017;1503:147–65.Moller I, Sørensen I, Bernal AJ, Blaukopf C, Lee K, Øbro J, et al. High-throughput mapping of cell-wall polymers within and between plants using novel microarrays. Plant J. 2007;50:1118–28.PubMed 

Google Scholar 
Yan X-X, An X-M, Gui L-L, Liang D-C. From structure to function: insights into the catalytic substrate specificity and thermostability displayed by Bacillus subtilis mannanase BCman. J Mol Biol. 2008;379:535–44.PubMed 

Google Scholar 
Tailford LE, Ducros VM-A, Flint JE, Roberts SM, Morland C, Zechel DL, et al. Understanding how diverse beta-mannanases recognize heterogeneous substrates. Biochemistry. 2009;48:7009–18.PubMed 

Google Scholar 
Nakae S, Ito S, Higa M, Senoura T, Wasaki J, Hijikata A, et al. Structure of Novel Enzyme in Mannan Biodegradation Process 4-O-β-d-Mannosyl-d-Glucose Phosphorylase MGP. J Mol Biol. 2013;425:4468–78.PubMed 

Google Scholar 
Scheller HV, Ulvskov P. Hemicelluloses. Annu Rev Plant Biol. 2010;61:263–89.PubMed 

Google Scholar 
Varki A, Cummings RD, Aebi M, Packer NH, Seeberger PH, Esko JD, et al. Symbol Nomenclature for Graphical Representations of Glycans. Glycobiology. 2015;25:1323–4.PubMed 
PubMed Central 

Google Scholar 
Altschul SF, Gish W, Miller W, Myers EW, Lipman DJ. Basic local alignment search tool. J Mol Biol. 1990;215:403–10.PubMed 

Google Scholar 
Finn RD, Clements J, Eddy SR. HMMER web server: interactive sequence similarity searching. Nucleic Acids Res. 2011;39:W29–W37.PubMed 
PubMed Central 

Google Scholar  More

We incorporated a macromolecular model of phytoplankton (CFM-Phyto) into the global ocean model (MITgcm). This combined model predicts cellular growth rate based on the macromolecular allocation, which in turn is used to determine the elemental stoichiometry of phytoplankton for the next model time step.The phytoplankton component of the model is executed using the following algorithm, which is illustrated graphically in Extended Data Fig. 2: (1) relate the growth rate and elemental stoichiometry of phytoplankton based on the macromolecular allocation; (2) evaluate the possible growth rates under four different limiting nutrient assumptions and select the lowest rate: Liebig’s Law of the Minimum; (3) evaluate storage of non-limiting elements; (4) evaluate excess of non-limiting elements relative to maximum quotas; (5) based on that excess, evaluate effective nutrient uptake rate; and (6) evaluate the change in the elemental stoichiometry based on the balance between the growth rate and effective nutrient uptake rate. We describe the procedural details in the following text. Parameter values are listed in Extended Data Table 1. See ref. 21 for further details and justification of each equation in CFM-Phyto; here we repeat equations essential to explain the model used in the current study.Connecting the elemental stoichiometry and the growth rateThe first step of the algorithm is to obtain the relationship between the current elemental stoichiometry and the growth rate (μ). To do that, we use CFM-Phyto21 (Extended Data Fig. 1). The model is based on the assumption of pseudo-steady state with respect to macromolecular allocation; in other words, the cellular-scale acclimation occurs rapidly relative to environmental changes. Laboratory studies show that macromolecular re-allocation occurs on the timescale of hours to days19. This is fast relative to the rates of environmental change in our coarse-resolution ocean simulations and so steady state solutions21 are used to relate growth rate, macromolecular allocation and elemental stoichiometry, as described in detail below. We first describe the case of N quota (here defined as QN; moles cellular N per mole cellular C) in detail, and then we briefly explain the case of P and C quotas as the overall procedures are similar. After that, we describe the case with Fe quota, which extends the previously published model21 for this study.Relating N quota and growth rateCFM-Phyto describes the allocation of N quota as follows, focusing on the quantitatively major molecules:$$Q_{mathrm{N}} = Q_{mathrm{N}}^{{mathrm{Pro}}} + Q_{mathrm{N}}^{{mathrm{RNA}}} + Q_{mathrm{N}}^{{mathrm{DNA}}} + Q_{mathrm{N}}^{{mathrm{Chl}}} + Q_{mathrm{N}}^{{mathrm{Sto}}}$$
(2)
where QN is total N quota (per cellular C: mol N (mol C)−1), the terms on the right-hand side are the contributions from protein, RNA, DNA, chlorophyll and N storage. We use empirically determined fixed elemental stoichiometry of macromolecules21 (Extended Data Table 1) to connect the macromolecular contributions of different elements (here C and P):$$Q_{mathrm{N}} = Q_{mathrm{C}}^{{mathrm{Pro}}}Y_{{mathrm{Pro}}}^{{mathrm{N:C}}} + Q_{mathrm{P}}^{{mathrm{RNA}}}Y_{{mathrm{RNA}}}^{{mathrm{N:P}}} + Q_{mathrm{C}}^{{mathrm{DNA}}}Y_{{mathrm{DNA}}}^{{mathrm{N:C}}} + Q_{mathrm{C}}^{{mathrm{Chl}}}Y_{{mathrm{Chl}}}^{{mathrm{N:C}}} + Q_{mathrm{N}}^{{mathrm{Nsto}}}$$
(3)
Here (Y_l^{j:k}) represents the imposed elemental ratio (elements j and k) for each macromolecular pool (l). (Q_{mathrm{C}}^x) and (Q_{mathrm{P}}^x) describe the contributions of macromolecule x to the total C quota (mol C (mol C)−1) and P quota (mol P (mol C)−1), respectively.CFM-Phyto uses the following empirically supported relationship to describe (Q_{mathrm{P}}^{{mathrm{RNA}}}) (ref. 21):$$Q_{mathrm{P}}^{{mathrm{RNA}}} = A_{{mathrm{RNA}}}^{mathrm{P}}mu Q_{mathrm{C}}^{{mathrm{Pro}}} + Q_{{mathrm{P,min}}}^{{mathrm{RNA}}}$$
(4)
where (A_{{mathrm{RNA}}}^{mathrm{P}}) is constant (below, A values represent constant except (A_{{mathrm{Chl}}}); see below), μ is growth rate (d−1) and (Q_{{mathrm{P,min}}}^{{mathrm{RNA}}}) represents the minimum amount of RNA in phosphorus per cellular C (mol P (mol C)−1). Substituting this equation into equation (3) gives:$$begin{array}{l}Q_{mathrm{N}} = Q_{mathrm{C}}^{{mathrm{Pro}}}Y_{{mathrm{Pro}}}^{{mathrm{N:C}}} + left( {A_{{mathrm{RNA}}}^{mathrm{P}}mu Q_{mathrm{C}}^{{mathrm{Pro}}} + Q_{{mathrm{P,min}}}^{{mathrm{RNA}}}} right)\Y_{{mathrm{RNA}}}^{{mathrm{N:P}}} + Q_{mathrm{C}}^{{mathrm{DNA}}}Y_{{mathrm{DNA}}}^{{mathrm{N:C}}} + Q_{mathrm{C}}^{{mathrm{Chl}}}Y_{{mathrm{Chl}}}^{{mathrm{N:C}}} + Q_{mathrm{N}}^{{mathrm{Nsto}}}end{array}$$
(5)
In CFM-Phyto, we resolve three types of protein, photosynthetic, biosynthetic and other:$$Q_{mathrm{C}}^{{mathrm{Pro}}} = Q_{mathrm{C}}^{{mathrm{Pro}}_{mathrm{Pho}}} + Q_{mathrm{C}}^{{mathrm{Pro}}_{mathrm{Bio}}} + Q_{mathrm{C}}^{{mathrm{Pro}}_{mathrm{Other}}}$$
(6)
Photosynthetic proteins represent those in chloroplasts largely responsible for light harvesting and electron transport. The model assumes a constant composition of chloroplasts; thus, the amount of photosynthetic protein is proportional to the amount of chlorophyll21:$$Q_{mathrm{C}}^{{mathrm{Pro}}_{mathrm{Pho}}} = A_{{mathrm{Pho}}}Q_{mathrm{C}}^{{mathrm{Chl}}}$$
(7)
Biosynthetic proteins represent proteins related to producing new material such as proteins, carbohydrates, lipids, RNAs, DNAs and other molecules. The models use the following empirically derived relationship21:$$Q_{mathrm{C}}^{{mathrm{Pro}}_{mathrm{Bio}}} = A_{{mathrm{Bio}}}mu$$
(8)
Substituting equations (6)–(8) (in this order) into equation (5) leads to the following equation:$$begin{array}{l}Q_{mathrm{N}} = left( {A_{{mathrm{Pho}}}Q_{mathrm{C}}^{{mathrm{Chl}}} + A_{{mathrm{Bio}}}mu + Q_{mathrm{C}}^{{mathrm{Pro}}_{mathrm{Other}}}} right)Y_{{mathrm{Pro}}}^{{mathrm{N:C}}}\ + left( {A_{{mathrm{RNA}}}^{mathrm{P}}mu left( {A_{{mathrm{Pho}}}Q_{mathrm{C}}^{{mathrm{Chl}}} + A_{{mathrm{Bio}}}mu + Q_{mathrm{C}}^{{mathrm{Pro}}_{mathrm{Other}}}} right) + Q_{{mathrm{P,min}}}^{{mathrm{RNA}}}} right)Y_{{mathrm{RNA}}}^{{mathrm{N:P}}}\ + Q_{mathrm{C}}^{{mathrm{DNA}}}Y_{{mathrm{DNA}}}^{{mathrm{N:C}}} + Q_{mathrm{C}}^{{mathrm{Chl}}}Y_{{mathrm{Chl}}}^{{mathrm{N:C}}} + Q_{mathrm{N}}^{{mathrm{Sto}}}end{array}$$
(9)
Empirically, chlorophyll depends on the growth rate and equation (10) accurately describes the relationship between the growth-rate dependences of chlorophyll under different light intensities21:$$Q_{mathrm{C}}^{{mathrm{Chl}}} = A_{{mathrm{Chl}}}mu + B_{{mathrm{Chl}}}$$
(10)
with (A_{{mathrm{Chl}}} = left( {1 + E} right)/v_I) and (B_{Chl} = m/v_I) with E (dimensionless) as a constant representing growth-rate-dependent respiration, and m (d−1) describing maintenance respiration. vI (mol C (mol C in Chl)−1 d−1) represents chlorophyll-specific photosynthesis rate based on an established function of light intensity I (μmol m−2 s−1)21,57:$$v_I = v_I^{{mathrm{max}}}left( {1 – e^{A_II}} right)$$
(11)
where (v_I^{{mathrm{max}}}) is the maximum chlorophyll-specific photosynthesis rate, e is the natural base and AI is a combined coefficient for absorption cross-section and turnover time. Substitution of equation (10) into equation (9) leads to the following quadratic relationship between QN and μ:$$Q_{mathrm{N}} = a_{mathrm{N}}mu ^2 + b_{mathrm{N}}mu + c_{mathrm{N}} + Q_{mathrm{N}}^{{mathrm{Sto}}}$$
(12)
where$$begin{array}{l}a_{mathrm{N}} = A_{{mathrm{RNA}}}^{mathrm{P}}left( {A_{{mathrm{Pho}}}A_{{mathrm{Chl}}} + A_{{mathrm{Bio}}}} right)Y_{{mathrm{RNA}}}^{{mathrm{N:P}}}\ b_{mathrm{N}} = left( {A_{{mathrm{Pho}}}A_{{mathrm{Chl}}} + A_{{mathrm{Bio}}}} right)Y_{{mathrm{Pro}}}^{{mathrm{N:C}}} + A_{{mathrm{Chl}}}Y_{{mathrm{Chl}}}^{{mathrm{N:C}}} + A_{{mathrm{RNA}}}^{mathrm{P}}left( {A_{{mathrm{Pho}}}B_{{mathrm{Chl}}} + Q_{mathrm{C}}^{{mathrm{Pro}}_{mathrm{Other}}}} right)Y_{mathrm{{RNA}}}^{{mathrm{N:P}}}\ c_{mathrm{N}} = B_{{mathrm{Chl}}}Y_{{mathrm{Chl}}}^{{mathrm{N:C}}} + left( {A_{{mathrm{Pho}}}B_{{mathrm{Chl}}} + Q_{mathrm{C}}^{{mathrm{Pro}}_{mathrm{Other}}}} right)Y_{{mathrm{Pro}}}^{{mathrm{N:C}}}\ + Q_{{mathrm{P}},{mathrm{min}}}^{{mathrm{RNA}}}Y_{{mathrm{RNA}}}^{{mathrm{N:P}}} + Q_{mathrm{C}}^{{mathrm{DNA}}}Y_{{mathrm{DNA}}}^{{mathrm{N:C}}}end{array}$$Relating P quota and growth rateSimilarly, CFM-Phyto describes the relationship between the current P quota QP and μ. P is allocated to its major molecular reservoirs:$$Q_{mathrm{P}} = Q_{mathrm{P}}^{{mathrm{RNA}}} + Q_{mathrm{C}}^{{mathrm{DNA}}}Y_{{mathrm{DNA}}}^{{mathrm{P:C}}} + Q_{mathrm{P}}^{{mathrm{Thy}}} + Q_{mathrm{P}}^{{mathrm{Other}}} + Q_{mathrm{P}}^{{mathrm{Sto}}}$$
(13)
Similar to equation (7), with the assumption of the constant composition of photosynthetic apparatus, the model connects the amount of the chlorophyll to phosphorus in thylakoid membranes:$$Q_{mathrm{P}}^{{mathrm{Thy}}} = A_{{mathrm{Pho}}}^{{mathrm{P:Chl}}}Q_{mathrm{C}}^{{mathrm{Chl}}}$$
(14)
As for N allocation, substitution of equations (14), (4), (6), (7), (8) and (10) (in this order) into equation (13) leads to a quadratic relationship between QP and μ:$$Q_{mathrm{P}} = a_{mathrm{P}}mu ^2 + b_{mathrm{P}}mu + c_{mathrm{P}} + Q_{mathrm{P}}^{{mathrm{Sto}}}$$
(15)
where$$begin{array}{l}a_{mathrm{P}} = A_{{mathrm{RNA}}}^{mathrm{P}}left( {A_{{mathrm{Pho}}}A_{{mathrm{Chl}}} + A_{{mathrm{Bio}}}} right)\ b_{mathrm{P}} = A_{{mathrm{RNA}}}^{mathrm{P}}left( {A_{{mathrm{Pho}}}B_{{mathrm{Chl}}} + Q_{mathrm{C}}^{{mathrm{Pro}}_{mathrm{Other}}}} right)Y_{{mathrm{RNA}}}^{{mathrm{N:P}}} + A_{{mathrm{Pho}}}^{{mathrm{P:Chl}}}A_{{mathrm{Chl}}}\ c_{mathrm{P}} = Q_{{mathrm{P,min}}}^{{mathrm{RNA}}} + Q_{mathrm{C}}^{{mathrm{DNA}}}Y_{{mathrm{DNA}}}^{{mathrm{P:C}}} + A_{{mathrm{Pho}}}^{{mathrm{P:Chl}}}B_{{mathrm{Chl}}} + Q_{mathrm{P}}^{{mathrm{Other}}}end{array}$$Relating C quota and growth rateSimilarly, CFM-Phyto describes C allocation as follows:$$begin{array}{l}Q_{mathrm{C}} = 1 = Q_{mathrm{C}}^{{mathrm{Pro}}} + Q_{mathrm{C}}^{{mathrm{RNA}}} + Q_{mathrm{C}}^{{mathrm{DNA}}} + Q_{mathrm{C}}^{{mathrm{Other}}} + Q_{mathrm{C}}^{{mathrm{Plip}} – {mathrm{Thy}}}\qquad + Q_{mathrm{C}}^{{mathrm{Csto}}} + Q_{mathrm{C}}^{{mathrm{Nsto}}}end{array}$$
(16)
where Plip−Thy indicates P lipid in thylakoid membranes. The equation represents the allocation per total cellular C in mol C (mol C)−1, so the sum of the macromolecules in C (QC) becomes 1. Using the imposed elemental ratios of macromolecular pools ((Y_l^{j:k})) we relate the elemental contributions:$$Q_{mathrm{C}} = Q_{mathrm{C}}^{{mathrm{Pro}}} + Q_{mathrm{P}}^{{mathrm{RNA}}}Y_{{mathrm{RNA}}}^{{mathrm{C:P}}} + Q_{mathrm{C}}^{{mathrm{DNA}}} + Q_{mathrm{C}}^{{mathrm{Other}}} + Q_{mathrm{P}}^{{mathrm{Thy}}}Y_{{mathrm{Plip}}}^{{mathrm{C:P}}} + Q_{mathrm{C}}^{{mathrm{Sto}}} + Q_{mathrm{N}}^{{mathrm{Sto}}}Y_{{mathrm{Nsto}}}^{{mathrm{C:N}}}$$
(17)
Following the steps similar to those for the N and P allocations, substituting equations (14), (4), (6), (7), (8) and (10) (in this order) into equation (17) leads to the following quadratic relationship between cellular C quota QC (=1 mol C (mol C)−1) and μ:$$Q_{mathrm{C}} = a_{mathrm{C}}mu ^2 + b_{mathrm{C}}mu + c_{mathrm{C}} + Q_{mathrm{C}}^{{mathrm{Sto}}} + Q_{mathrm{N}}^{{mathrm{Sto}}}Y_{{mathrm{Nsto}}}^{{mathrm{C:N}}}$$
(18)
where$$begin{array}{l}a_{mathrm{C}} = A_{{mathrm{RNA}}}^{mathrm{P}}left( {A_{{mathrm{Pho}}}A_{{mathrm{Chl}}} + A_{{mathrm{Bio}}}} right)Y_{{mathrm{RNA}}}^{{mathrm{C:P}}}\ b_{mathrm{C}} = A_{{mathrm{Chl}}}left( {1 + A_{{mathrm{Pho}}} + A_{{mathrm{Pho}}}^{{mathrm{P:Chl}}}Y_{{mathrm{Plip}}}^{{mathrm{C:P}}}} right) + A_{{mathrm{Bio}}} + A_{{mathrm{RNA}}}^{mathrm{P}}left( {A_{{mathrm{Pho}}}B_{{mathrm{Chl}}} + Q_{mathrm{C}}^{{mathrm{Pro}}_{mathrm{Other}}}} right)Y_{{mathrm{RNA}}}^{{mathrm{C:P}}}\ c_{mathrm{C}} = left( {1 + A_{{mathrm{Pho}}} + A_{{mathrm{Pho}}}^{{mathrm{P:Chl}}}Y_{{mathrm{Plip}}}^{{mathrm{C:P}}}} right)B_{{mathrm{Chl}}} + Q_{mathrm{C}}^{{mathrm{Pro}}_{rm{Other}}}\ + Q_{{mathrm{P}},{mathrm{min}}}^{{mathrm{RNA}}}Y_{{mathrm{RNA}}}^{{mathrm{C:P}}} + Q_{mathrm{C}}^{{mathrm{DNA}}} + Q_{mathrm{C}}^{{mathrm{Other}}}end{array}$$Relating Fe quota and growth rateIn order to capture global scale biogeochemical dynamics including the iron-limited high-nitrogen, low chlorophyll regimes, CFM-Phyto21 is extended to resolve Fe quota and allocation. The model is guided by a laboratory proteomic study58 in which the major Fe allocations are to photosystems, storage and nitrogen-fixing enzymes (nitrogenase). As we do not resolve nitrogen-fixing organisms here, Fe allocation (mol Fe (mol C)−1) represents only the first two:$$Q_{{mathrm{Fe}}} = Q_{{mathrm{Fe}}}^{{mathrm{Pho}}} + Q_{{mathrm{Fe}}}^{{mathrm{Sto}}}$$
(19)
As for equation (7) and equation (14), we relate the allocation of Fe to photosystems to the investment in chlorophyll, (Q_{mathrm{C}}^{{mathrm{Chl}}}):$$Q_{{mathrm{Fe}}}^{{mathrm{Pho}}} = A_{{mathrm{Pho}}}^{{mathrm{Fe}}}Q_{mathrm{C}}^{{mathrm{Chl}}}$$
(20)
This is a strong simplification because the pigment to photosystem ratio is observed to vary59, but enables an explicit, mechanistically motivated representation of Fe limitation, which, a posteriori, results in global scale regimes of iron limitation that resemble those observed43 (Extended Data Fig. 4). With equations (10), (19) and (20), we obtain the following relationship between QFe and μ:$$Q_{{mathrm{Fe}}} = A_{{mathrm{Pho}}}^{{mathrm{Fe}}}A_{{mathrm{Chl}}}mu + A_{{mathrm{Pho}}}^{{mathrm{Fe}}}B_{{mathrm{Chl}}} + Q_{{mathrm{Fe}}}^{{mathrm{Sto}}}$$
(21)
Evaluating the growth rateWe assume that the cellular growth rate is constrained by the most limiting element within the cell (and its associated functional macromolecules). Thus, at each time step and location, and for each cell type, the evaluation of growth rate is based on the following two steps: (1) computation of the growth rate for each element without storage; that is, the case when all of the elemental quotas are allocated to functional macromolecules; and (2) selection of the lowest growth rate among these; Liebig’s Law of the Minimum. For the first step, we define (mu _i) (i = C, N, P, Fe) as the growth rate, assuming that nutrient i is limiting. Under this condition, (Q_i^{{mathrm{Sto}}}) should be small as element i is allocated to other essential molecules. We assume that (Q_{mathrm{N}}^{{mathrm{Sto}}}) is also small under C limitation because N storage molecules are rich in carbon. With these assumptions, the solution for (mu _i) is obtained by solving the standard quadratic relationships of equations (12), (15) and (18) for N, P and C, respectively, neglecting any (Q_i^{{mathrm{Sto}}}) terms:$$mu _i = frac{{ – b_i + sqrt {b_i^2 – 4a_ileft( {c_i – Q_i} right)} }}{{2a_i}}$$
(22)
where QC = 1. For μFe, equation (21) without (Q_{{mathrm{Fe}}}^{{mathrm{Sto}}}) leads to$$mu _{{mathrm{Fe}}} = frac{{Q_{{mathrm{Fe}}} – A_{{mathrm{Pho}}}^{{mathrm{Fe}}}B_{{mathrm{Chl}}}}}{{A_{{mathrm{Pho}}}^{{mathrm{Fe}}}A_{{mathrm{Chl}}}}}$$
(23)
Once the μi values are obtained, we determine the effective growth rate, μ, based on the lowest value, which identifies the limiting element based on current intracellular quotas:$$mu = {mathrm{min}}left( {mu _{mathrm{N}},mu _{mathrm{P}},mu _{mathrm{C}},mu _{{mathrm{Fe}}}} right)$$
(24)
Evaluating nutrient storageIn CFM-Phyto, non-limiting nutrients can be stored in an intracellular reserve21, reflecting commonly observed luxury uptake. Storage is evaluated as the difference between the total elemental quota (updated later) and the functionally allocated portion of that element:$$Q_i^{{mathrm{Sto}}} = Q_i – Q_i^{{mathrm{Non}}_{mathrm{Sto}}}$$
(25)
Here (Q_i^{{mathrm{Non}}_{mathrm{Sto}}}) represents the contribution to element i by functional, non-storage molecules. For N, P and C, (Q_i^{{mathrm{Non}}_{mathrm{Sto}}}) is represented by the non-(Q_i^{{mathrm{Sto}}}) terms on the right-hand side in equations (12), (15) and (18), respectively:$$Q_i^{{mathrm{Non}}_{mathrm{Sto}}} = a_imu ^2 + b_imu + c_i$$
(26)
Similarly, for Fe, from equation (21):$$Q_{{mathrm{Fe}}}^{{mathrm{Non}}_{mathrm{Sto}}} = A_{{mathrm{Pho}}}^{{mathrm{Fe}}}A_{{mathrm{Chl}}}mu + A_{{mathrm{Pho}}}^{{mathrm{Fe}}}B_{{mathrm{Chl}}}$$
(27)
When there is N storage, (Q_{mathrm{C}}^{{mathrm{Sto}}}) must be recomputed to consider the allocation of C to it:$$Q_{mathrm{C}}^{{mathrm{Sto}}} = Q_{mathrm{C}} – Q_{mathrm{C}}^{{mathrm{Non}}_{mathrm{Sto}}} – Q_{mathrm{N}}^{{mathrm{Sto}}}Y_{{mathrm{Nsto}}}^{{mathrm{C:N}}}$$
(28)
Evaluating the excess nutrientStorage capacity for any element is finite and we define excess nutrient as a nutrient (N, P, Fe) that is in beyond an empirically informed, imposed maximum phytoplankton storage capacity. Excess nutrient is assumed to be excreted (see below). Excess of element i ((Q_i^{{mathrm{Exc}}})) is computed:$$Q_i^{{mathrm{Exc}}} = {mathrm{max}}left( {Q_i – Q_i^{{mathrm{max}}},0} right)$$
(29)
where (Q_i^{{mathrm{max}}}) is maximum capacity for nutrient i. For N, CFM-Phyto computes (Q_i^{{mathrm{max}}}) as a sum of non-storage molecules and prescribed maximum nutrient storing capacity according to model–data comparison21:$$Q_i^{{mathrm{max}}} = Q_i^{{mathrm{Non}}_{mathrm{Sto}}} + Q_i^{{mathrm{Sto}}_{mathrm{max}}}$$
(30)
Laboratory studies suggest that when P is not limiting, the phosphorus quota maximizes to a value that is almost independent of growth rate21,39,44. Storage of each element is finite and the upper limit to storage is imposed by specifying the maximum cellular quotas ((Q_{mathrm{P}}^{{mathrm{max}}}) (ref. 21) and also (Q_{{mathrm{Fe}}}^{{mathrm{max}}})) with size and taxonomic dependencies (for example, refs. 27,41). Thus, the maximum storage is represented by the difference between the prescribed maximum quota and the actual quota21:$$Q_i^{{mathrm{Sto}}_{mathrm{max}}} = Q_i^{{mathrm{max}}} – Q_i$$
(31)
In the case where (Q_i^{{mathrm{Sto}}}) computed in the previous section exceeds (Q_i^{{mathrm{Sto}}_{mathrm{max}}}), the value of (Q_i^{{mathrm{Sto}}}) is replaced by (Q_i^{{mathrm{Sto}}_{mathrm{max}}}) and the difference is placed in the excess pool, (Q_i^{{mathrm{Exc}}}).Computing effective nutrient uptake rateOne factor that influences the cellular elemental quota is the effective nutrient uptake rate (mol i (mol C)−1 d−1) of N, P and Fe, which we define as follows:$$V_i^{{mathrm{Eff}}} = V_i – frac{{Q_i^{{mathrm{Exc}}}}}{{tau _i^{{mathrm{Exu}}}}}$$
(32)
where Vi (mol i (mol C)−1 d−1) is nutrient uptake rate and the second term represents the exudation of the excess nutrient based on the timescale (tau _i^{{mathrm{Exu}}}) (d−1). For Vi, we use Monod kinetics60,61:$$V_i = V_i^{{mathrm{max}}}frac{{[i]}}{{left[ i right] + K_i}}$$
(33)
where (V_i^{{mathrm{max}}}) is maximum nutrient uptake, [i] (mmol m−3) is the environmental concentration of nutrient i and Ki (mmol m−3) is the half-saturation constant of i. Previous models have resolved the relationship between nutrient uptake and allocation to transporters31,62. Here we do not explicitly resolve allocation to transporters, as proteomic studies indicate that it is a relatively minor component of the proteome compared with photosystems and biosynthesis in phytoplankton63. Transporter proteins could be represented in a model with a finer-scale resolution of the proteome64.Differentiating small and large phytoplanktonIn this model, ‘small’ phytoplankton broadly represent picocyanobacteria, which have high nutrient affinities and low maximum growth rates (for example, Prochlorococcus), whereas ‘large’ phytoplankton represent eukaryotes with higher maximum growth rates (for example, diatoms). The former are associated with a gleaner strategy adapted to oligotrophic regimes, while the latter are opportunistic, adapted to variable and nutrient-enriched regimes. To encapsulate this, the large phytoplankton have overall higher imposed (V_i^{{mathrm{max}}}) (~µmaxQi), Ki and (v_I^{mathrm{max}}) than for the small phytoplankton (Extended Data Table 1), consistent with the previous models (for example, ref. 10). In addition, the larger cells are assigned a higher (Q_{mathrm{P}}^{{mathrm{max}}}) following the observed trends (Fig. 1 and Extended Data Table 1).Computing the change in the elemental stoichiometryThe computation of the change in the elemental quotas is done based on the balance between the effective nutrient uptake rate and the loss of nutrient to the new cells:$$frac{{{mathrm{d}}Q_i}}{{{mathrm{d}}t}} = V_i^{{mathrm{Eff}}} – mu Q_i$$
(34)
This change in the elemental quotas based on the cellular processes and the passive transport of elements in phytoplankton by the flow field created by MITgcm governs the elemental stoichiometry of the next time step at a specific grid box, as in other versions of ecological models with MITgcm10.Calculation of CV valuesWe computed the CV values based on the following equation:$${mathrm{CV}} = frac{sigma }{{bar x}}$$
(35)
where σ is the standard deviation and (bar x) is the mean. The purpose of this computation is to quantify the latitudinal variation of the averaged elemental stoichiometry. Thus, we used the averaged values for each latitude (as plotted in Fig. 2) for the calculation of σ and (bar x).MITgcm-CFMThe biogeochemical and ecological component of the model resolves the cycling of C, P, N and Fe through inorganic, living, dissolved and particulate organic phases. The biogeochemical and biological tracers are transported and mixed by the MIT general circulation model (MITgcm)35,36, constrained to be consistent with altimetric and hydrographic observations (the ECCO-GODAE state estimates)65. This three-dimensional configuration has a coarse resolution (1° × 1° horizontally) and 23 depth levels ranging from 5 m at the surface to 5450 m at depth. The model was run for three years, and the results of the third year were analysed, by which time the modelled plankton distribution becomes quasi-stable. Equations for the biogeochemical processes are as described by equations and parameters in previous studies10,38. Here, however, we include only nitrate for inorganic nitrogen, and do not resolve the silica cycle. We simulated eukaryotic and prokaryotic analogues of phytoplankton (as ‘large’ and ‘small’ phytoplankton). The eukaryotic analogue has a higher maximum C fixation rate for the same macromolecular composition and higher maximum nutrient uptake rates, but also has overall higher half-saturation constants for nutrient uptake. We used light absorption spectra of picoeukaryotes, which sits in-between small prokaryotes and large eukaryotes10. In MITgcm, the mortality of phytoplankton is represented by the sum of a linear term (ml), representing sinking and maintenance losses, and quadratic terms representing the action of unresolved next-trophic levels66,67, implicitly assuming that the higher-trophic-level biomass scales with that of its prey. We assumed that the latter term is small to avoid introducing additional uncertainties. Similarly, we do not resolve the stoichiometric effects of prey selection due to the nutritional status of prey, or viral partitioning of nutrients in the environment50. Atmospheric iron deposition varies by orders of magnitude around the globe and has a large margin of uncertainty, including the bio-availability of the deposited iron, which in turn depends on the source and chemical history of the deposited material68. To realize a realistic global net primary production, we doubled the atmospheric iron input from ref. 10; this factor is well within the uncertainty of the iron supply estimates. Each of the two phytoplankton groups has variable C:N:P:Fe as determined by the component macromolecules at each time step. The pools of C, N, P and Fe are tracked within the modelled three-dimensional flow fields. More

Tallis, H. M. et al. Front. Ecol. Environ. 16, 563–570 (2018).Article 

Google Scholar 
Tu, C. et al. Nat. Sustain. https://doi.org/10.1038/s41893-022-01008-1 (2022).Article 

Google Scholar 
Lloyd, W. F. Two lectures on the checks to population (S. Collingwood, The University of Oxford, 1833).Gordon, H. S. J. Polit. Econ. 62, 124–142 (1954).Article 

Google Scholar 
Nash, J. F. Jr Proc. Natl Acad. Sci. USA 36, 48–49 (1950).Article 
CAS 

Google Scholar 
Hardin, G. Science 162, 1243–1248 (1968).Article 
CAS 

Google Scholar 
Ostrom, E. Governing the Commons: The Evolution of Institutions for Collective Action (Cambridge University Press, 1990).Sethi, R. & Somanathan, E. Am. Econ. Rev. 86, 766–788 (1996).
Google Scholar 
Schill, C. et al. Nat. Sustain. 2, 1075–1082 (2019).Article 

Google Scholar 
Levin, S. Philos. Trans R. Soc. B Biol. Sci. 365, 13–18 (2010).Article 

Google Scholar  More