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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

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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Chironomids have the ability to survive and reproduce in polluted environments, and thus they are included in many ecological studies where approaches may be taxonomic or functional16. The diversity of most macroinvertebrates is controlled by the oxygen level of water, but chironomids may survive in hypoxic conditions where the oxygen concentration may be less than 3 mg l−117. The current study demonstrates that changing seasons, as well as anthropogenic activities, have a significant impact on the levels of DO in aquatic bodies. As observed from the result, DO highly influences the tube length of the chironomid larvae. Since KWC is a wastewater canal, the average oxygen level is lower (5.24 ± 1.14 mg l−1) than KFP (6.63 ± 1.28 mg l−1) which is a normal fish culturing pond. It has also been observed that the average tube length of the chironomid larvae of KWC (8.66 ± 0.88 mm) is higher than KFP (7.68 ± 0.62 mm), which indicates that a low concentration of DO promotes the building of longer tubes in natural conditions. Similar observations were also observed in laboratory conditions. When the oxygen level (7.03 ± 0.41 mg l−1) in the experiment was kept in the normal range, there was negligible variation in tube length (7.61 ± 0.31 mm). But when the concentration of oxygen is gradually reduced by dilution, the tube length starts to increase accordingly, which is explained graphically in Fig. 4. The regression model of both the experimental conditions also supports the hypothesis that the tube length has an inverse relationship with DO. The scatter plot and simple linear regression confirmed the inverse relationship between DO and tube length (Figs. 1 and 2).Chironomid larvae are able to grow in the polluted water of a wastewater pond as dominant macroinvertebrates18. It is observed that those larvae living in the sand tubes are more susceptible to chemical pollutants than the larvae living in silt tubes7. Sand particles are bigger than silt and are not suitable for the survival of larvae19. Chironomus riparius larvae make their tubes from different external particles and their own proteins20. Midge larvae are the inhabitants of sediments, and at the same time, sediment is the depository of different inorganic, organic, and heavy metals. In such cases, the tube of chironomid larvae may act as a defensive structure, which protects them from the adverse effects of undesirable pollutants and may increase their tolerance against such chemicals21,22,23.Larvae can thrive in benthic sediments with high decaying organic content and very low DO concentrations in water bodies24. In poor DO concentration, larvae can survive due to the presence of haemoglobin in their body tissue fluid, which plays an important physiological role in increasing respiratory efficiency, as was observed in Chironomus plumosus. Longer tube length may help larvae generate better respiratory currents so that they can cope with a low DO environment.Tube length is crucial for living in water because primarily tubes protect them from outer environmental factors like predators, and pollution. It was observed during this study that when the DO of water is low, larvae make elongated tubes to reach the upper layer of water, where the DO level is comparatively high. To get their required amount of oxygen, the larvae increase the tube length towards the water surface and increase the DO in tube water by undulating the body and other structures, creating a current inside the tube25,26. On contrary, when the DO level of the surrounding water of chironomid is sufficient, they can manage their normal physiological activities with the available oxygen. They need not to elongate their tube length. That’s why their tube length is inversely related to the DO of their surrounding medium.If tube length does not increase in size in hypoxic water, larvae will not be able to meet their oxygen demand. If the DO of water decreases, tube length will increase and vice versa. Behavioural and physiological adaptations of chironomids larvae make them successful to live in a hypoxic environment. Thus, in hypoxic conditions, larvae with longer tubes are able to gather more oxygen from the upper layer of water and get more space to create a current of water to increase the amount of O2 inside the tube by undulating the preanal papillae, anal gill, ventral gills. This would explain why the tube length of chironomids depends on the DO of water. Hence by measuring the tube length with a standard measuring scale, one may get an idea about the quality of water, especially DO, before doing any chemical analysis. The work seems to be unique and novel for its own kind. More

Study settingUganda covers 241,037 km2 (4° N, 2° S, 29° E, 35° E) and averages 1100 m above sea level25. Uganda has a total population of 34.6 million people, with 7.4 and 27.2 million living in urban and rural areas, respectively26. It borders Lake Victoria and has an equatorial climate. The study area is mainly plateau, with a few mountains. About 20 percent of Uganda’s area is covered by swamps and water bodies, including the four Great Lakes of East Africa (Lake Edward, Lake Victoria, Lake Albert, and Lake Kyoga). The country has ten national parks housing a high diversity of wildlife and endangered species26. By 2009, agriculture ranked as the second leading contributor to the country’s Gross Domestic Product27.Surveillance data of Bacillus anthracis infectionSurveillance data of livestock and human cases from 2018 were provided by the Ministry of Health (MOH) in Uganda through the Field Epidemiology and Laboratory Training Program and the Uganda Ministry of Agriculture, Animal Industry and Fisheries (MAAIF). Geographical coordinates of anthrax cases among wildlife (from 2004 to 2010) in Queen Elizabeth National Park were obtained from a recently published study4. These cases were mapped to show the distribution of anthrax across Uganda (Fig. 1). It is only recently that Uganda has mandated systematic anthrax surveillance across the country following the outbreak that started in 2018. GPS coordinates gathered by field personnel during outbreak responses were used to map outbreak locations. The human anthrax cases were defined based on the CDC’s clinical criteria (signs and symptoms), presumptive laboratory diagnosis (Gram staining), and confirmatory laboratory diagnosis (bacterial culture, immunohistochemistry, ELISA, and PCR)28. The animal anthrax cases were also defined based on the clinical presentation, presumptive laboratory diagnosis, and confirmatory laboratory diagnosis. All cases were classified as either ‘probable’ or ‘confirmed,’ with probable defined as cases that met both the clinical and presumptive laboratory diagnostic criteria and confirmed defined as cases that met the clinical and confirmatory laboratory diagnostic criteria. A total of 497 livestock (n = 171), humans (n = 32), and wildlife cases (n = 294), both confirmed (n = 32) and probable (n = 465), occurring from 2004 to 2018 were compiled. All methods were performed in accordance with the relevant guidelines and regulations.Figure 1Distribution of anthrax presence and pseudo-absence locations across Uganda. The navy-blue circles show wildlife cases (n = 294) used for model training, the blue triangles show livestock cases (n = 171), and the red diamonds represent human cases (n = 32). The blue polygons show the locations of the 50 km, 75 km, and 100 km buffers which were constructed around the wildlife cases with a distance of 10 km between the buffers and the presence locations. The pink dots show the pseudo-absence points selected within the 50 km buffer, the orange dots show the pseudo-absence points selected within the 75 km buffer, and the white dots show the pseudo-absence points selected within the 100 km buffer. Prediction maps were developed using the Quantum Geographic Information System software (QGIS). URL: https://qgis.osgeo.org (2020).Full size imageEnvironmental variable processingCorrelative studies of environmental risk factors for anthrax outbreaks suggest that temperature6,29,30,31,32,33,34,35,36,37, precipitation6,29,30,31,32,33,34,35,36,37,38,39, elevation6,29,31,32,34,35,37,38,39, soil (type, calcium concentration, pH, carbon content, and moisture)6,30,31,33,34,36,37,39,40,41,42,43, vegetation6,29,31,34,36,37,38,39,40,42,43, and hydrology37,44 are some of the major drivers of B. anthracis suitability. A total of 26 environmental predictors (Fig. 2) were selected for this study based on these known variables. These comprised 19 bioclimatic variables (the mean for the years 1970–2000) collected from the WorldClim database version 2 (https://www.worldclim.org/data/worldclim21.html) at a resolution of 30 s (~ 1 km2)45. Four soil variables, including exchangeable calcium at a depth of 0–20 cm, soil water availability, soil pH (10×) in H2O at a depth of 0 cm, and soil organic carbon at a depth of 0–5 cm, were retrieved from the International Soil Reference and Information Centre (ISRIC) data hub at a resolution of 250 m (https://data.isric.org/geonetwork/srv/eng/catalog.search#/home). Distance to permanent water bodies was derived from a global hydrology map provided by ArcGIS online version 10.6.146. Elevation data of 1 km2 in resolution was obtained from the Global Multi-resolution Terrain Elevation Data (GMTED2010) dataset available from the United States Geological Service. Finally, the monthly Enhanced Vegetation Index (EVI) data for the years 2004, 2005, and 2010 (36 tiles in total) were obtained from The Aqua Moderate Resolution Imaging Spectroradiometer (MODIS) Vegetation Indices (MYD13A3 v.6) at a spatial resolution of 1 km (https://lpdaac.usgs.gov/products/myd13a3v006/). The single variable, mean EVI, was calculated in QGIS by averaging all 36 tiles. The EVI minimizes variations in the canopy background and maintains precision over conditions with dense vegetation.Figure 2Results of correlation between covariates using Pearson’s correlation test. Correlation between covariates was shown by red numbers (negative correlation) and blue numbers (positive correlation). BIO1 = Annual Mean Temperature, BIO2 = Mean Diurnal Range, BIO3 = Isothermality, BIO4 = Temperature Seasonality, BIO5 = Max Temperature of Warmest Month, BIO6 = Min Temperature of Coldest Month, BIO7 = Temperature Annual Range, BIO8 = Mean Temperature of Wettest Quarter, BIO9 = Mean Temperature of Driest Quarter, BIO10 = Mean Temperature of Warmest Quarter, BIO11 = Mean Temperature of Coldest Quarter, BIO12 = Annual Precipitation, BIO13 = Precipitation of Wettest Month, BIO14 = Precipitation of Driest Month, BIO15 = Precipitation Seasonality, BIO16 = Precipitation of Wettest Quarter, BIO17 = Precipitation of Driest Quarter, BIO18 = Precipitation of Warmest Quarter, BIO19 = Precipitation of Coldest Quarter.Full size imageAll environmental variables were resampled using the R package ‘Resample’47 to a resolution of 1 km and clipped to the extent of Uganda. Since data sampling for wildlife data (used in model training) was not done systematically across the study area, target backgrounds buffers (polygon buffers created at certain radii from the training points and used for the random selection of pseudo-absences) were created for model calibration to reduce sampling bias. As there was no information on the sampling radius, a sensitivity analysis was conducted by creating target backgrounds using circular buffers of radius 50 km, 75 km, and 100 km around the presence points used for model training, leaving 10 km between the presence points and the various buffers (Fig. 1). Quantum Global Information System (QGIS) version 3.16 (https://qgis.org) software was then used to add 294 random pseudo-absence points within each buffer polygon giving a ratio of 1:1 for the training presences to pseudo-absences. A recent study explored how four approaches of pseudo-absence creation affect the performance of models across different species and three model types by building both terrestrial and marine models using boosted regression trees, generalised additive mixed models, and generalised linear mixed models48. They then tested four methods for generating pseudoabsences across all the different model types: (1) correlated random walks (RW); (2) reverse correlated RW; (3) sampling pseudoabsences within a buffer area surrounding the presence points; (4) background sampling48. The findings of the study suggested that the separation or distance in the environmental space between the presence locations and the pseudoabsences was the most significant driver of the model predictive ability and explanatory power, and thus finding was consistent across the three model types (boosted regression trees, generalised additive mixed models, and generalised linear mixed models) and both the terrestrial and marine habitats48.The values of the environmental variables were then extracted for each presence and pseudo-absence location using the raster package in R. With these, we did an initial data exploration to check for outliers within the covariates, collinearity, and to explore the relationships between the covariates and the response variables (presence or absence of anthrax). Cleveland dot plots were used to check for possible outliers. Following the outlier checks, variance inflation factors (VIF), pairwise plots, and Pearson correlation coefficients with correction for multiple comparisons were used to measure the statistically significant correlation between the covariates (Fig. 2). For variables that were highly correlated (correlation greater than 0.6) or those with high variance inflation (VIF  > 3), only one was used in the modelling process. Five variables were selected following this analysis: Temperature seasonality (BIO4), elevation, distance to water, soil calcium, and soil water (Table 1).Table 1 Summary of the environmental variables used.Full size tableModelling anthrax suitability across UgandaQGIS v.3.16 (https://qgis.org) and the R statistical package version 4.1.049 were used to conduct data visualization, cleaning, and model analysis (R code used available in a Github repository: https://github.com/valentinandolo/Uganda-Spatial_Model/tree/master). The wildlife cases (n = 294) were used for model training and testing. The remaining human (n = 32) and livestock (n = 171) cases were used for model evaluation. Since the wildlife case locations were recorded from 2004 to 2010, while the livestock and human cases were recorded in 2018, the latter locations were both spatially and temporally distinct from the wildlife cases, making an excellent basis for block cross-validation of the final model performance50. Random partitioning of the data into training and testing sets can inflate the performance of a model and underestimate the error in the spatial prediction evaluation50. Block cross-validation uses spatial blocks that separate the testing and training datasets; thus, the method has been suggested to be a good technique for error estimation and a robust approach for measuring a model’s predictive performance50.The INLA package in R was applied to model the suitability of B. anthracis across Uganda. INLA calculates the spatial interaction effects using a Stochastic Partial Differential Equation (SPDE) method, which estimates a continuous Gaussian Markov Random Field (GMRF) where the correlation between two locations in space is specified by the Matérn correlation which is explained in more detail elsewhere51. The initial step in fitting an SPDE model is the creation of a Constrained Refined Delaunay Triangulation or a mesh to illustrate the spatial process51. R-INLA uses a function called ‘inla.mesh.2d()’ that applies a variety of arguments to build the mesh, these include: loc, loc.domain, boundary, max.edge, and cutoff51. The loc argument contains the point locations which provide information about the area of study and are used to create the triangulation nodes. Alternatively, a polygon of the study area can be used to identify the extent of the domain via loc.domain. We applied the point locations using the loc argument. We then specified the boundary of the mesh as a convex hull. We used the max.edge argument to specify the maximum edge length for the inner mesh domain/triangles and the outer triangles. We did this by first studying the distribution of distances between the point locations for the training presences and pseudo-absences. Most points were within a distance of about 90–100 km away from each other, thus, a possible guess for the range at which spatial autocorrelation persists was 100 km. We used a distance of 20 km as a range guess to create a finer mesh which has been shown to produce more precise models. We specified the maximum edge length for the inner triangles as 20 km divided by 5 (4 km) and the maximum edge length for the outer triangles as 20 km. Finally, the cutoff argument sets the minimum distance allowed between point locations. We divided the maximum edge length for the inner triangles by 5 (4 km divided by 5 = 0.8 km), meaning that points that were closer in distance than 0.8 km were replaced by one vertex to avoid the occurrence of small triangles.The spatial effect, which is a numeric vector, then links each observation within the data to a spatial location, thus, accounting for region-specific variation that cannot be accounted for by the covariates. Following the recommendation by Lindgren and Rue52, multivariate Gaussian distributions with means of zero and a spatially defined covariance matrix were used to model the spatial effect. Several versions of Bayesian hierarchical additive models were created by estimating a Bernoulli generalized additive model (GAM) with and without spatially correlated random effects. The Bernoulli GAM is defined as shown in Eqs. (1) and (2)$${C}_{i} sim Bernoulli left({p}_{i}right),$$
(1)
$$logit left({p}_{i}right)= alpha +sum_{j=1}^{m}{beta }_{j}left({X}_{j,i}right)+ sum_{k=1}^{l}{f}_{k}left({X}_{k,i}right)+ {mu }_{i},$$
(2)
where ({C}_{i}) denotes the observed value, such that: B. anthracis presence or absence at a given location i (i = 1, …, n; n = 588) is given as ({C}_{i}), where ({C}_{i}) =1 if B. anthracis was present, and ({C}_{i})=0 if absent. Logit is the link function for binomial family, ({p}_{i}) is the expected value of the response variable (the probability of B. anthracis suitability) at location i, α is the intercept, ({X}_{j,i}) and ({X}_{k,i}) are the j th and the k th covariates at a location i, ({beta }_{j}) are the beta coefficients, ({f}_{k}) are the smooth functions (cubic regression splines) for k th covariates, and ({mu }_{i}) is the spatial random effect at the location i53. The number of variables in linear term (m) and the non-liner term (l) are different because the variables employed in each term are different. We estimated both linear and non-linear effects for the covariates. Our overall database had 294 B. anthracis pseudo-absences generated randomly across the target background buffers to match the number of species presences recorded. Because we had no prior information, a Gaussian prior distribution with a mean of zero (default no effect prior unless data is informative) was applied for all the model parameters. The posterior mean, standard deviation, and 95% credible intervals were estimated for all the parameters.Model selectionSeveral different candidate models were examined. First, a baseline model was built using only the intercept. A second baseline model was then built, which included the intercept and spatial random effects only. Covariates were added to the second baseline model (intercept plus spatial effects model) without any smoothing function (i.e., only linear effects). The contribution of the spatial random effect was then re-examined by taking it out from the model. Smoothing functions were then added to all covariates, and the same procedure was repeated. Model selection was done using this forward stepwise approach. The final model was run using the three different target background buffers to identify the buffer distance with the lowest Deviance Information Criterion (DIC). The various options were assessed using the DIC54, Watanabe-Akaike information criterion (WAIC), and the Conditional Predictive Ordinate (CPO). The DIC and WAIC were chosen because they are commonly used to assess model performance by measuring the compromise between the goodness of fit and complexity. For CPO, the logarithmic score (− mean(log (CPO)) (LCPO) was calculated and used55. CPO can also be used to conduct internal cross-validation of models using a leave-one-out approach to evaluate the predictive performance of the model. Lower LCPO, DIC, and WAIC estimates suggest superior model performance. Thus, the favoured model had the lowest values across the 3 metrics.Model validation and evaluationModel validation for the favoured model was conducted using an independent evaluation dataset comprising of livestock and human outbreaks occurring at different spatial locations and 8 years after the training data. The omission rate, which indicates the proportion of positive test locations that end up in pixels predicted to be unsuitable for B. anthracis56, was used to validate the model. A low omission rate indicates good model performance. The threshold for suitability was the probability threshold that maximized the sensitivity and specificity of the model. The sensitivity was then derived by calculating the proportion of positive test locations that end up in pixels predicted to be suitable for B. anthracis56. A high sensitivity indicates good model performance.Model predictionThe favoured model selected using the criteria described above was used to generate countrywide prediction maps showing the posterior mean values, standard deviation, and the 95% credible intervals of the probability of B. anthracis suitability. The raster package in R was used to make the prediction maps. Bayesian kriging was done by treating all model parameters as random variables to include uncertainty in the prediction57. This kriging is built into the INLA framework via the SPDE, which allows a Delaunay triangulation to be constructed around the presence and absence locations within the sampling frame52. INLA then conducts model inference and prediction at the same time by considering the prediction points as locations missing the response variable (set to NA)51. Following successful model prediction, additional linear interpolation functions then generate the output for the whole study area scaled from 0 to 1.Ethical approvalEthical approval for this study was provided by the Human Biology Research Ethics Committee, University of Cambridge, UK (Ref: HBREC.2019.02) the School of Veterinary Medicine and Animal Resources Institutional Animal Care and Use Committee, Makerere University, Uganda (Ref: SVAREC/21/2019); and the Uganda National Council for Science and Technology. Informed consent was obtained from all subjects and/or their legal guardian(s). All methods were performed in accordance with the relevant guidelines and regulations. More