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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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

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Among the 325 municipalities in Greece during the period 2010–2021, WNV events, defined as the occurrence of at least one laboratory-confirmed human WNV case during a specific year, were reported in 154 (47%) municipalities, while the remaining 171 did not report any WNV case. WNV events were reported for a period ranging from one to eight years: 54 (35%) municipalities reported laboratory-confirmed WNV cases in only one year, 38 (25%) in two years, 30 (19%) in three years, 12 (8%) in four years, 10 (6%) in five years, 6 (4%) in six years, 1 (1%) in seven years, and 3 (2%) in eight years. This means that in 60% of the positive areas (82 municipalities out of 154), WNV appeared at most for two years, in 27% (42 out of 154) between three and four years, and in the remaining 13% (20 out of 154) for five years or more. Considering the total number of reported laboratory-confirmed human WNV cases across the twelve years (Fig. 1), in approximately 50% of the positive municipalities (78 out of 154), at most 4 cases were reported: 1, 2, 3, and 4 WNV cases were reported in 24, 32, 11, and 11 municipalities, respectively. Overall, 39 municipalities recorded a number of WNV cases ranging from 5 to 10 (third quartile), 34 a number ranging from 11 to 46, while the remaining 3 municipalities recorded a number of WNV cases equal to 56, 71 and 94.Figure 1(a) Map of Greece with total numbers of laboratory-confirmed human WNV cases throughout the 12-year period 2010–2021, with breakdowns by municipality. White denotes municipalities where no human cases were observed. (b) Map of Greece with total numbers of modelled human WNV cases throughout the 12-year period 2010–2021, with breakdowns by municipality. White denotes municipalities where no human cases were modelled.Full size imageModel evaluation and comparison with MIMESISWe investigated the ability of the MIMESIS-2 model to correctly identify the occurrence of WNV events, both in space and time, and its capacity to quantify the annual number of human WNV cases and the timing of the first WNV event in the year. The performance of many quantities of interest, such as the severity and timing of occurrence of human WNV cases, was also compared output from the original MIMESIS model26.Occurrence of WNV eventsStarting with the spatial analysis, we considered the fit of the model to replicate the observed 385 WNV events out of 3,900 (325*12) possible events across municipalities. MIMESIS-2 was able to correctly identify 356 of them, generated only one false alarm, and correctly modelled 3,514 true negatives.The performance of MIMESIS-2 was then evaluated according to four indices: the probability of detection (POD), false alarm rate (FAR), miss rate (MIS), and critical success index (CSI), described in the Methods section. For the POD, MIS and CSI, we considered the 154 municipalities with at least one reported and laboratory-confirmed human WNV case over the 12-year period, while for the FAR, we considered the 153 municipalities where at least one human WNV case was modelled over the same period. We split the (0.0–1.0) index interval into five equally sized bins to derive for each index, the fraction of municipalities falling into each bin. Both the POD and CSI were above 0.8 for 139 municipalities out of 154, while the MIS was below 0.2 for 142 municipalities (out of 154) and the FAR was always below 0.2, with one false alarm produced in a municipality where WNV events were observed in eight out of twelve years (Table 1).Table 1 Capacity of the MIMESIS-2 model to correctly model laboratory-confirmed human WNV cases.Full size tableWe also analysed how the model performed in different years by studying the multiannual evolution of the indices. Both the aggregated POD and CSI were equal to 0.92, with annual variations ranging from 0.72 (2021) to 1 (2011 and 2014). The aggregated MIS was 0.08, ranging from 0.0 (2011 and 2014) to 0.28 (2021). The FAR was virtually 0, being always equal to 0.0, with the only exception being 2017, when it was 0.1 (Table 2).Table 2 Capacity of the MIMESIS-2 model to correctly model laboratory-confirmed human WNV cases by year and in the whole observed time period.Full size tableMagnitude and timing of WNV events: performance and comparison with MIMESISTo evaluate the ability of MIMESIS-2 to capture the magnitude and timing of WNV events, we first considered the discrepancy between the overall number of observed and modelled WNV cases during the 12-year period for each municipality. Out of the 153 municipalities where at least one case was modelled across the 12 years, 76 (50%) had at most 4 modelled cases of WNV: 1, 2, 3, and 4 WNV cases were modelled in 22, 31, 13, and 10 municipalities, respectively. In 42 municipalities, the number of modelled cases ranged from 5 to 10 (which, as for the observed WNV cases, coincided with the third quartile), and in 32 municipalities, the number ranged from 11 to 47, while the remaining 3 municipalities had 55, 70, and 99 modelled cases (Fig. 1).The MIMESIS-2 model closely replicated the total number of laboratory-confirmed WNV cases during the 12-year period. When considering only the 154 municipalities that recorded at least one WNV event during the considered period (excluding the true negatives), for 140 of them, the modelled number of cases fell within a ± 10% error range of the observed value, whereas for 149 the modelled number of cases fell within the ± 25% error margin. Only two municipalities showed a percent error above 50%. These were particular instances where only one WNV case was reported throughout the considered period, while MIMESIS-2 fitted zero human cases. For the original MIMESIS model, 63 and 84 municipalities fell within the ± 10% and ± 25% error margins, respectively, while 31 municipalities—mainly those where few cases were observed— had a relative error ≥ 100% (Fig. 2).Figure 2(a) For MIMESIS-2, modelled (IHMOD) vs. observed (IHOBS) human WNV cases in each municipality in the period 2010–2021. The inner black line represents the main diagonal where ideally the points would lie in case of perfect fit, while the dashed green, black and red lines represent, respectively, the ± 10%, ± 25% and ± 50% error margin. (b) Same quantities for MIMESIS. (c). Breakdown of the week of first WNV incidence by year. Plotted are the modelled quantities (WYMOD) for each of the 325 municipalities on the y-axis and the observed quantities (WYOBS) on the x-axis. The continuous line represents the main diagonal where ideally the points would lie in case of perfect fit, while the dashed lines represent the ± 4-week error margins.Full size imageTo further evaluate the bias of the model across all municipalities and years, we explored the difference between the yearly modelled and observed human WNV cases both with MIMESIS-2 and the original MIMESIS (IHMOD-IHOBS) across municipalities. In MIMESIS-2, we excluded 3,514 true negative cases to avoid distorted conclusions. For the remaining 386 cases, the mean bias was -0.04 indicating a possibly unbiased model, with the standard deviation (SD) of the residuals equal to 0.66 (original MIMESIS: mean bias 0.33, SD 2.07, after removing 3,387 true negatives) (Supplementary Fig. 1).Across the 325 municipalities and the 12 years, 385 WNV events were observed, while on 3,515 occasions, no laboratory-confirmed human WNV cases were reported; on 162 occurrences, 1 case was reported, and on 67 and 39 occasions, 2 and 3 cases were reported, respectively. The maximum yearly number of human WNV cases observed in a single municipality was 38. Considering the modelled human WNV cases with MIMESIS-2, the distribution of the 356 hits ranged between 1 and 37 modelled cases, closely mimicking the distribution of the observed cases, since 1, 2 and 3 human WNV cases were modelled on 129, 72 and 37 occasions, respectively. For the 29 misses, the observed numbers of human cases were 1 (24 times), 2 (3 times), or 3 (2 times). The only false alarm was produced in the Pellas municipality, where WNV events were observed in 8 out of the 12 years.We evaluated the timing of the first occurrence of WNV in humans for any municipality and year. Ignoring the municipalities with zero cases, the observed and MIMESIS-2-modelled first WNV cases occurred between weeks 22 and 44 and weeks 24 and 36, respectively. Modelled values tended to be dispersed around the observed ones: excluding the 3514 true negatives, 290 (75.13%) of the remaining 386 cases fell into the ± 4-week error margins from the observed cases (Fig. 2). This translated into a much lower bias of the week of first appearance (WYMOD-WYOBS) with respect to MIMESIS (Supplementary Fig. 2).Case study: The Pellas municipalityIn addition to presenting the overall performance of the model throughout different years and Greek municipalities, we highlight here the capacity of the model to capture population-specific behaviour and epidemiological features, such as the force of infection, that is, the rate at which susceptible humans, birds, and mosquitoes become infected, by presenting a single municipality case study for the municipality of Pellas. The Pellas municipality had the highest number of observed WNV cases over the 12-year period with a total of 94 human WNV cases, 38 in 2010, 16 in 2018, and 13 in 2021, no cases from 2014 to 2017, and between 4 to 8 cases in the remaining years.We considered the impact arising from the changes in parameters defining the forces of infection. In addition to the introduction of bird (({psi }_{B})) and human (({psi }_{H})) host selections, changes included modifications for the mosquito-to-bird (({p}_{M})) and bird-to-mosquito (({p}_{B})) probabilities of transmission, whose values were made temperature-dependent following Vogels et al.21, and the replacement of the mosquito-to-bird (({varphi }_{B})) and mosquito-to-human (({varphi }_{H})) ratios with their dynamic counterparts, ({N}_{M}/{N}_{B}) and ({N}_{M}/{N}_{H}), respectively (Fig. 3). We used the May–October period for the 12 years that were considered, because this is the part of the year when Culex pipiens mosquitoes are reproductively active and the majority of human WNV cases are reported. In each year of the 12-year period, ({p}_{M}) started from 0.02, reached its peak—ranging from 0.16 to 0.25—in midsummer, and then decreased to the initial values (in the original model, ({p}_{M}=0.9)). Similarly, ({p}_{B}) started from 0.28, peaked in the same time interval—with maximal values ranging from 0.51 to 0.56—and then returned to the initial values (in the original model, ({p}_{B}=0.125)). Additionally, the dynamic specifications of ({varphi }_{B}) and ({varphi }_{H}) were shown to play an important role. Whereas in MIMESIS ({varphi }_{B}=30), in MIMESIS-2 the values started at approximately 8.6 and peaked in late summer when more human WNV cases are reported, reaching values of approximately 57, before decreasing to values ranging from 31.15 to 41.60 in late October. In MIMESIS, ({varphi }_{H}) was calibrated at the municipality level, and for Pellas municipality, it was 0.0001, whereas the dynamic counterpart in MIMESIS-2 showed a temporal evolution with a shape (but different scale) similar to that of ({varphi }_{B}), starting from values of approximately 1, peaking in late summer to values of approximately 7, and then decreasing to values of approximately 4 in late October.Figure 3The temporal evolution during May to October of the (a) mosquito-to-bird probability of transmission, ({p}_{M}), (b) bird-to-mosquito probability of transmission, ({p}_{B},) (c) mosquito-to-bird ratio, ({varphi }_{B},) and (d) mosquito-to-human ratio, ({varphi }_{H},) for both MIMESIS-2 across different years and MIMESIS for each of the 12 years from 2010 to 2021. The plots refer to the simulations for the municipality of Pella.Full size imageChanges in these parameters enter into the expression for the forces of infection. It is of major practical interest to investigate how the values for the forces of infection resulting from MIMESIS-2 may vary for different values of the relative abundance of the vectors with respect to the corresponding carrying capacity and the temperature in different months (Fig. 4). As expected, all forces of infection increased with both the temperature and the relative abundance of the infectious vertebrate hosts. It is worth noting the importance of day length, as this affects the fraction of nondiapausing mosquitoes, ({delta }_{M}), and causes the forces of infection, all other things being equal, to be potentially higher in June and July than in the other months. However, in these two months, the modelled forces of infection tend to be smaller than those in August due to the lower abundance of infectious hosts.Figure 4Contour plots of the forces of infection for May to September for different values of the relative abundance of infected hosts/vectors with respect to the carrying capacity and the temperature. All the other quantities were fixed to the amounts obtained in the simulations for Pellas municipality for 2021 at the end of the corresponding month. (a) Bird-to-mosquito force of infection (({lambda }_{BM})) as a function of the relative abundance of infected birds (({I}_{B})) with respect to the bird carrying capacity (({K}_{B})) and temperature. (b) Mosquito-to-bird force of infection (({lambda }_{MB})) as a function of the relative abundance of infected mosquitoes (({I}_{M})) with respect to the mosquito carrying capacity (({K}_{M})) and temperature. (c) Mosquito-to-human force of infection (({lambda }_{MH})) as a function of the relative abundance of infected mosquitoes (({I}_{M})) with respect to the mosquito carrying capacity (({K}_{M})) and temperature. The ranges for ({I}_{B}/{K}_{B}) and ({I}_{M}/{K}_{M}) were fixed, increasing the maximum modelled value by 20% for the considered period, while the range for the temperature was chosen considering that in the period of interest, the average daily temperature ranged from 16.6 to 27.1 degrees Celsius. Black crosses represent the modelled values for 2021.Full size imageThe bird-to-mosquito force of infection, ({uplambda }_{BM}), took values on the order of 10–4, with possible peaks of approximately 7 × 10–4 in the case of high temperature and high prevalence of birds in June and July, which were nevertheless not reached due to a low abundance of infected birds in that period. Considering the months of July and August 2021 for illustrative purposes, the resulting modelled values were 1.20 × 10–4 and 2.19 × 10–4, respectively, with the increase in August explained by a higher abundance of infected birds in that period. It is worth noting that if the infection across birds had a lead period of two weeks, the resulting ({uplambda }_{BM}) in July would become 3.91 × 10–4 (+ 226%), while an increase in the average temperature in August by 1 °C would result in ({uplambda }_{BM})= 2.36 × 10–4 (+ 8%). The mosquito-to-bird, ({uplambda }_{MB}), and mosquito-to-human, ({uplambda }_{MH}), forces of infection showed similar qualitative behaviours, albeit at different scales, and in this case, they were higher in August due to a higher prevalence of infected Culex mosquitoes in that month. More specifically, ({uplambda }_{MB}) equalled 1.06 × 10–3 and 1.22 × 10–3 at the end of July and August, respectively, and an expected two weeks for the infection of mosquitoes would result in ({uplambda }_{MB})=4.15 × 10–3 (+ 292%) at the end of July, while an increase in the average temperature in August by 1 °C would result in ({uplambda }_{MB})= 1.31 × 10–3 (+ 7%) at the end of August. Finally, ({uplambda }_{MH})=2.86 × 10–6 at the end of July, while ({uplambda }_{MH})=3.26 × 10–6 at the end of August, with the anticipation of the infection among mosquitoes by two weeks resulting in ({uplambda }_{MH})=1.12 × 10–5 (+ 290%) and an increase in the average August temperature by 1 °C leading to ({uplambda }_{MH})=3.51 × 10–6 (+ 8%). It is worth recalling that since we calibrated the model on the number of reported laboratory-confirmed human WNV cases, ({uplambda }_{MH}) represents the rate at which susceptible humans contract infection and become symptomatic leading to a recorded human WNV case.We explored changes in the populations of infectious hosts and the total population number for both mosquitoes and birds over 2010–2021 for the period spanning from May to October (Figs. 5 and 6). The population of infected mosquitoes (({I}_{M})) was initialised by calibration (see the Methods section). Each year, after a short period in which the population of infected mosquitoes slightly decreased due to a very small number of infectious birds (({I}_{B})) that prevented the infection from spreading, it started growing substantially during summer, reaching its peak in late summer, coinciding with the period when most human cases were recorded. The observed increase in ({I}_{M}) was combined with the growth ({I}_{B}) at approximately the same time (with a slightly anticipated peak), which had an amplification effect on the spread of the infection. Both ({I}_{M}) and ({I}_{B}) showed significant yearly variation, with higher modelled numbers in years where more human WNV cases were reported. The modelled total population of mosquitoes (({N}_{M})) did not show significant interannual variability, always peaking in late summer. Finally, the overall population of birds (({N}_{B})) did not show any variability in the first part of the year, when an increase due to immigration and offspring generation was observed, whereas it had a moderate interannual variability in the second half of the year. These differences may be due to heterogeneous numbers of observed infected, dead and immune birds.Figure 5The temporal evolution during May to October of (a) the number of infected mosquitoes modelled by MIMESIS-2 (({I}_{M})), (b) the total number of mosquitoes modelled by MIMESIS-2 (({N}_{M}))(,) (c) the number of infected birds modelled by MIMESIS-2 (({I}_{B}))(,) and (d) the total number of birds modelled by MIMESIS-2 (({N}_{B})) for each of the 12 years from 2010 to 2021. The plots refer to the simulations for the municipality of Pella.Full size imageFigure 6The temporal evolution during May to October of (a) the ratio between the number of WNV-infected mosquitoes modelled by MIMESIS-2 (({I}_{M,MIM-2})) and the ratio modelled by MIMESIS (({I}_{M,MIM})), (b) the ratio between the total number of mosquitoes modelled by MIMESIS-2 (({N}_{M,MIM-2})) and the ratio modelled by MIMESIS (({N}_{M,MIM}))(,) (c) the ratio between the number of infected birds modelled by MIMESIS-2 (({I}_{B,MIM-2})) and the ratio modelled by MIMESIS (({I}_{B,MIM}))(,) and (d) the ratio between the total number of birds modelled by MIMESIS-2 (({N}_{B,MIM-2})) and the ratio modelled by MIMESIS (({N}_{B,MIM})) for each of the years from 2010 to 2021. The plots refer to the simulations for the municipality of Pella.Full size imageComparison of these population dynamics with those of MIMESIS revealed interesting patterns (Fig. 6). Considering the relative number of mosquitoes in MIMESIS-2 with respect to MIMESIS, the populations in MIMESIS tended to grow faster due to a higher mosquito carrying capacity (({K}_{M})) in the original model (({K}_{M}) ≈ 8.3 × 105 in MIMESIS versus ({K}_{M}) ≈ 2.4 × 105 in MIMESIS-2), resulting in a decrease in the ratio between the amounts modelled by MIMESIS-2 and the ones modelled by MIMESIS. Significant interannual variability could be seen in the first part of the year for infectious mosquitoes, where different initial calibration values played an important role. For the populations of birds, until midsummer, the overall number modelled by MIMESIS-2 tended to be approximately 1/4 that of MIMESIS, while as of July, different patterns were observed due to the higher mortality of birds in the original MIMESIS model. In years with higher virus spread, higher mortality was reflected in a sharper decrease in bird populations; therefore, the ratio between the population modelled by MIMESIS-2 and that modelled by MIMESIS increased up to approximately 0.6 (2010). More