Ecology

DNA sample collectionTo analyze the population structure of wild medaka populations, we selected samples from the DNA collection of Takehana et al.29, deposited in University of Shizuoka. The original DNA collection had been made throughout 1980s and 2000s. The selected samples covered the major mitotypes and contained more than three individuals of each population (Table S11, Fig. 3), which were collected from three collection sites for O. sakaizumii and 12 collection sites for O. latipes. We also examined several artificial strains: HNI and Hd-rR, which are inbred strains derived from O. sakaizumii and O. latipes, respectively, and four Himedaka individuals from commercial stock (Uruma city, Okinawa Prefecture, Japan).In addition, samples were newly collected at Kunigami Village, Okinawa Prefecture. Live fish were anesthetized with MS-222 (aminobenzene methanesulfonate, FUJIFILM Wako Pure Chemical Corporation, Osaka, Japan) and then fixed in 99% ethanol. Genomic DNA was extracted using a DNeasy kit (Qiagen Inc., Hilden, Germany) from ethanol-fixed pectoral fin samples according to the manufacturer’s protocol. The DNA concentration was measured using a spectrophotometer (Nanodrop 1000, Thermo Fisher Scientific, Waltham, Massachusetts, USA), and the DNA was diluted with PCR-grade water to a concentration of c.a. 10 ng/µl (UltraPure™ DNase/RNase-Free Distilled Water, Thermo Fisher Scientific).Ethic statementAll methods were carried out in accordance with the Regulation for Animal Experiments at University of the Ryukyus for handling live fish. All experiments were approved by the Animal Care Ethics Committee of University of the Ryukyus (R2019035). All experimental methods are reported in accordance with ARRIVE guidelines.PCR primer designThe following steps were used to select primers for MAAS (Fig. 1). (1) All possible 10-mer sequence combinations (i.e., 410 = 1,048,576 sequences) were generated in silico. (2) The sequences containing simple sequence repeats, some of which had been used in the MIG-seq method17, were excluded. (3) Sequences containing a functional motif, such as a transcription factor-binding site, were also excluded because they may not be suitable for examining neutral genetic markers. We obtained a catalog of motifs from the JASPAR CORE40 (http://jaspar.genereg.net). (4) To avoid taxon-dependency in primer performance, we used information about the k-mer (k = 10) frequency of reference genomes from multiple phyla. Sequences that showed marked differences in frequency among taxa were excluded. The frequencies of each 10-mer sequence in the reference genomes of 17 species belonging to 12 phyla of metazoa were counted (Table S12) using the “oligonucleotideFrequency” function in the “Biostrings” package ver. 2.441. In each of these taxa, the frequencies of sequences were stratified into three grades ( 103). We then selected the sequences that showed the same grade in more than 80% (14/17) of the species. (5) To avoid synthesizing primer dimers, self-complementary sequences were excluded, taking Illumina adapter sequences (5′-CGCTCTTCCGATCT-3′ and 5′-TGCTCTTCCGATCT-3′) into account. Self-complementation of two bases at the 3′-end or every three continuous bases in primer sequences was then evaluated using a custom script in R ver. 3.5.0 (R Development Core Team, http://cran.r-project.org). Based on the selected 10-mer sequences (i.e., 129 sequences, Fig. 1), 7-mer primer sequences were designed by removing the 3 bases at the 3′ end. Finally, we selected 24 candidate sequences for both 10-mer and 7-mer primers for the subsequent step (Table S1).The primer sequence consisted of three parts17: partial sequence of the Illimina adapter, 7 N bases, and a short priming sequence, e.g., 5′-CGCTCTTCCGATCTNNNNNNNGTCGCCC-3′. PCR amplification was performed using the candidate primers using the first PCR protocol described below (Table S1). Banding patterns were observed by electrophoresis on 1% agarose gels (agarose S; TaKaRa, Japan). Of the candidate primers, we selected four 7-mer primers and four 10-mer primers that each gave a smeared banding pattern with amplification products ranging from 500 to 2000 bp, indicating uniform amplification of multiple target sequences (Table S1).Library construction and sequencingThe library was constructed by a two-step PCR approach using a modification of a MIG-seq protocol14. In the first PCR step, multiple regions of genomic DNA were amplified using a cocktail of primers with a Multiplex PCR Assay Kit Ver.2 (TaKaRa) (Table 1). The volume of the PCR reaction mixture was 7 μl, containing 1 μl of template DNA, 2 μM of each PCR primer, 3.5 μl of 2 × Multiplex PCR Buffer, and 0.035 μl of Multiplex PCR Enzyme Mix. PCR was performed under the following conditions: denaturation at 94 °C for 1 min; 25 cycles of 94 °C for 30 s, 38 °C for 1 min, and 72 °C for 1 min, followed by a final extension step at 72 °C for 10 min.The primers in the second PCR step contained the Illumina sequencing adapter and an index sequence to identify each sample. Following the Truseq indexes, we used the combinations of eight forward indexes (i5) and 12 reverse indexes (i7), which resulted in a total of 96 combinations. To be used as a template for the second PCR, the first PCR product from each sample was diluted 50 times with PCR-grade water. The second PCR was performed in a 15-μl reaction mixture containing, 3 μl of diluted first PCR product, 3 μl of 5 × PrimeSTAR GXL Buffer, 200 μM of each dNTP, 0.2 μM of forward index primer and reverse index primer, 0.375 U of PrimeSTAR GXL DNA Polymerase (TaKaRa). The PCR conditions were as follows: 12 cycles at 98 °C for 10 s, 54 °C for 15 s, and 68 °C for 30 s.The second PCR product of each sample was pooled by equal volume and size-selected from 600 to 1000 bp using solid phase reversible immobilization (SPRI) select beads (Beckman Coulter Inc, Brea, California, USA) according to the manufacturer’s protocol. The DNA concentration of the pooled library was measured using a Qubit fluorometer (Thermo Fisher Scientific). We sequenced the libraries using two NGS platforms, MiSeq (Illumina, MiSeq Reagent Kit v2 Micro, Paired-End (PE), 150 bp) and HiSeq X (Illumina, PE, 150 bp). Sequencing using the HiSeq X platform was performed by Macrogen Japan (Tokyo, Japan).To compare primer performance, the DNA libraries constructed using the 7-mer and 10-mer primers for one individual were sequenced using MiSeq. Then, a 7-mer primer cocktail containing four sets of mixed primers was used for the subsequent analyses (Table 1). We also constructed DNA libraries using 7-mer and MIG-seq primer cocktails for three individuals and sequenced them using the HiSeq X platform. Finally, we constructed DNA libraries using 7-mer primer cocktails for 67 wild individuals and six artificial strain individuals for population genetics analyses (Table S11, Fig. 3).Mapping and SNV callingGenotyping was conducted using the following BWA-GATK best-practices pipeline for each sample42. Primer sequences were removed using cutadapt with the –b option selected43. The Illumina adapter sequences were also removed and quality filtering was performed using fastp ver. 0.20.0 with the “–detect_adapter_for_pe, –cut_front” option selected44. The remaining reads were mapped on the reference genome of medaka, Hd-rR strain, GCA_002234675.1; ASM223467v127 using Burrows-Wheeler Alignment tool, BWA mem ver. 0.7.1745. After mapping, output files were converted to Binary Alignment/Map (BAM) format using SAMtools ver. 1.746. SNVs and InDels in the sample were determined following the best practice guidelines set out in the Genome Analysis Tool Kit (GATK ver. 3.8.0)42. We then filtered out SNVs and InDels based on the following criteria: “QD  60.0 || MQ  More

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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

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