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Fitting tolerance time versus temperature to build a thermal death time curveThe high coefficients of determination found in the D. melanogaster TDT curves (Fig. 3A) are not uncommon and the exponential relation has consistently been found to provide a good fit of tolerance time vs. temperature in ectotherms3,15,20,22,23,24. Tolerance time vs. temperature data are also well fitted to Arrhenius plots which are based on thermodynamic principles (see for example15,36) and the absence of breakpoints in such plots provides a strong indication (but not direct proof) that the cause of coma/heat failure under the different intensities of acute heat stress is related to the same physiological process regardless whether failure occurs after 10 min or 10 h2,3 (but see “Discussion” section below). Despite the superior theoretical basis of Arrhenius analysis, we proceed with simple linear regressions of log10-transformed tcoma (TDT curve) as this analysis likewise provides a high R2 and is mathematically more straightforward. The physiological cause(s) of ectotherm heat failure are poorly understood37,38 but we argue that they are founded in a common process where heat injury accumulates at a temperature-dependent rate until a species-specific critical dose is attained (area below the curve and above Tc in Fig. 2). Thus, the organism has a fixed amount (dose) of thermally induced stress that it can tolerate before evoking the chosen endpoint. The experienced temperature of the animals then dictates the rate of which this stress is acquired, and accordingly when the endpoint is reached (Fig. 2) It is this reasoning that leads to TDT curves and explains why heat stress can be additive and thus also determines the boundaries of TDT curve modelling.Injury is additive across different stressful assay temperaturesIf heat stress acquired at intense and moderate stress within the span of the TDT curve acts through the same physiological mechanisms or converges to result in the same form of injury, then it is expected that injury is additive at different heat stress intensities. This hypothesis was tested by exposing flies sequentially to two static temperatures (different injury accumulation rates) and observe whether coma occurred as predicted from the summed injury (Fig. 2C). The accumulated heat injury at the two temperatures was found to be additive regardless of the order of temperature exposure (Fig. 3B,C). This finding is consistent with a conceptually similar study using speckled trout which also found strong support for additivity of heat stress at different stressful temperatures13. The exact physiological mechanism of heat injury accumulation is interesting to understand in this perspective, but it is not critical as long as the relation between temperature and injury accumulation rate is known.If injury accumulation is additive irrespective of the order of the heat exposure, we can extend the model to fluctuating temperature conditions. We have previously done this by accurately predicting dynamic CTmax from TDT parameters obtained from static assays for 11 Drosophila species (Fig. 6A, see “Discussion” section below and15). Here we extend this to temperature fluctuations that cannot be described by a simple mathematical ramp function. Specifically, groups of flies were subjected to randomly fluctuating temperatures and the observed tcoma was then compared to tcoma predicted using integration of heat injury based on TDT parameters (Fig. 4). The injury accumulation (Fig. 4C) was calculated by introducing the fluctuating temperature profiles in the associated R-script and the observed and predicted tcoma was found to correlate well (R2  > 0.94) across the 13 groups tested for each sex. These results further support the idea that injury is additive across a range of fluctuating and stressful temperatures and hence that similar physiological perturbations are in play during moderate and intense heat stress. It is important to note that in these experiments, temperatures fluctuated between 34.5 and 42.5 °C and accordingly the flies were never exposed to benign temperatures that could allow repair or hardening (see below).Figure 6adapted from Fig. 4b in15. (B) TDT parameters based on dCTmax from three dynamic tests were used to predict tcoma in static assays. Each point represents an observed vs. predicted value of species- and temperature-specific log10(tcoma). (Inset) Species values of the thermal sensitivity parameter z parameterized from TDT curves based on static assays (x-axis) or dynamic assays (y-axis). The dashed line represents the line of unity in all three panels.Conversion of heat tolerance measures between static and dynamic assays in Drosophila. Data from43. (A) Heat tolerance (dCTmax, d for dynamic assays) plotted against predicted dCTmax derived from species-specific TDT curves created from multiple (9–17) static assays. Data are presented for three different ramping rates (0.05, 0.1 and 0.25 °C min-1). Note that this graph is Full size imageIn conclusion, empirical data (present study;6,13,14,22) support the application of TDT curves to assess heat injury accumulation under fluctuating temperature conditions both in the lab and field for vertebrate and invertebrate ectotherms. Potential applications could be assessment of injury during foraging in extreme and fluctuating environments (e.g. ants in the desert39 or lizards in exposed habitat40) or for other animals experiencing extreme conditions41,42. The associated R-scripts allow assessment of percent lethal damage under such conditions if the model is provided with TDT parameters and information of temperature fluctuations (but see “Discussion” section of model limitations below).Model application for comparison of static versus dynamic dataThere is little consensus on the optimal protocol to assess ectotherm thermal tolerance and many different types of static or dynamic tests have been used to assess heat tolerance. TDT curves represent a mathematical and theoretical approach to reconcile different estimates of tolerance as the derived parameters can subsequently be used to assess heat injury accumulation at different rates (temperatures) and durations13,15,16. Here we provide R-scripts that enable such reconciliation and to demonstrate the ability of the TDT curves to reconcile data from static vs. dynamic assays we used published measurements of heat tolerance for 11 Drosophila species using three dynamic and 9–17 static measurements for each species43. Introducing data from only static assays we derived TDT parameters and subsequently used these to predict dynamic CTmax that were compared to empirically observed CTmax for three ramp rates (Fig. 6A). In a similar analysis, TDT parameters were derived from the three dynamic (ramp) experiments to predict tcoma at different static temperatures which were compared to empirical measures from static assays (Fig. 6B). Both analyses found good correlation between the predicted and observed values regardless whether the TDT curve was parameterized from static or dynamic experiments (Fig. 6). However, predictions from TDT curves based on three dynamic assays were characterised by more variation, particularly when used to assess tolerance time at very short or long durations. Furthermore, D. melanogaster and D. virilis which had the poorest correlation between predicted and observed tcoma in Fig. 6B had values of z from the TDT curves based on dynamic input data that were considerably different from values of z derived from TDT curves based on static assays (Fig. 6B inset). In conclusion TDT curves (and the associated R-scripts) are useful for conversion between static and dynamic assessment of tolerance. The quality of model output depends on the quality and quantity of data used as model input, and in this example the poorer model was parameterized from only three dynamic assays while the stronger model was based on 9–17 static assays (see also “Discussion” section below).Model application for comparison of published dataThermal tolerance is important for defining the fundamental niche of animals1,2,4 and the current anthropogenic changes in climate has reinvigorated the interest in comparative physiology and ecology of thermal limits in ectotherms. Meta-analyses of ectotherm heat tolerance data have provided important physiological, ecological and evolutionary insights5,44,45,46, but such studies are often challenged with comparison of tolerance estimates obtained through very different methodologies.Species tolerance is likely influenced by acclimation, age, sex, diet, etc.47 and also by the endpoint used (onset of spasms, coma, death, etc.27). Nevertheless, we expected heat tolerance of a species to be somewhat constrained45, so here we tested the model by converting literature data for nine species to a single and species-specific estimate of tolerance, sCTmax (1 h), the temperature that causes heat failure in 1 h (Fig. 5). The overwhelming result of this analysis is that TDT parameters are useful to convert static and dynamic heat tolerance measures to a single metric, and accordingly, the TDT model and R-scripts presented here have promising applications for large-scale comparative meta-analyses of ectotherm heat tolerance where a single metric allows for qualified direct comparison of results from different publications and experimental backgrounds. While this is an intriguing and powerful application, we caution that careful consideration should be put into the limitations of this model (see “Discussion” section below).Practical considerations and pitfalls for model interpretationAs shown above it is possible to convert and reconcile different types of heat tolerance measures using TDT parameters and these parameters can also be used to model heat stress under fluctuating field conditions. Modelling and discussion of TDT predictions beyond the boundaries of the input data has recently gained traction (see examples in48,49) but we caution that the potent exponential nature of the TDT curve requires careful consideration as it is both easy and enticing to misuse this model.Input dataThe quality of the model output is dictated by the input used for parameterization. Accordingly, we recommend TDT parameterization using several ( > 5) static experiments that should cover the time and temperature interval of interest, e.g. temperatures resulting in tcoma spanning 10 min to 10 h, thus covering both moderate and intense heat exposure. Such an experimental series can verify TDT curve linearity and allows modelling of temperature impacts across a broad range of temperatures and stress durations13,15,22. It is tempting to use only brief static experiments (high temperatures) for TDT parameterization, but in such cases, we recommend that the resulting TDT curve is only used to describe heat injury accumulation under severe heat stress intensities. Thus, the thermal sensitivity factor z represents a very powerful exponential factor (equivalent to Q10 = 100 to 100,000;15) which should ideally be parametrized over a broad temperature range (see below). We also include a script that allows TDT parametrization from multiple ramping experiments and again we recommend a broad span of ramping rates to cover the time/temperature interval of interest. A drawback of ramping experiments is the relatively large proportion of time spent at benign temperatures where there is no appreciable heat injury accumulation. Thus, dynamic experiments can conveniently use starting temperatures that are close to the temperature where injury accumulation rate surpasses injury repair rate (see “Discussion” section of “true” Tc below, in Supplemental Information and19 for other considerations regarding ramp experiments).A final methodological consideration relates to body-temperature in brief static experiments where the animal will spend a considerable proportion of the experiment in a state of thermal disequilibrium (i.e. it takes time to heat the animal). To avoid this, we recommend direct measurement of body temperature (large animals) or container temperature (small animals), and advise against excessive reliance on data from test temperatures that results in coma in less than 10 min.ExtrapolationMost studies of ectotherm heat tolerance include only a single measure of heat tolerance which is inadequate to parameterize a TDT curve. However, a TDT curve can still be generated from a single measure of tolerance (static or dynamic) if a value of z is assumed (see Supplemental Information). As z differs within species and between phylogenetic groups (Table S115,20), choosing the appropriate value may be difficult and discrepancies between the ‘true’ and assumed z represent a problem that should be approached with care. In Fig. 7A we illustrate this point in a constructed example where a single heat tolerance measurement is sampled from a ‘true’ TDT curve (full line; tcoma = 40 min at 37 °C). Along with this ‘true’ TDT curve we depict the consequences for model predictions if the assumed value of z is misestimated by ± 50%. Extrapolation from the original data point is necessary if an estimate of the temperature that causes coma after 1 h is desired, however due to limited extrapolation (from 40 to 60 min), estimation of sCTmax (1 h) values based on the ‘true’ and z ± 50% are not very different ( 6 h) between heat exposure disrupted additivity, suggesting that injury is repaired at benign temperature50. Injury repair rate is largely understudied but repair rate is generally increasing with temperature51,52,53. It is therefore an intriguing and promising idea to include a temperature-dependent repair function in more advanced modelling of heat injury. Until such repair processes are introduced in the model, we recommend that additivity of heat injury is evaluated critically if it involves periods at temperatures both above and below Tc (i.e. over consecutive days, see also13). An alternative, but not mutually excluding, explanation of increased heat resilience in split-dose experiments relates to the contribution of heat hardening as it is likely that the first heat exposure in a series can induce hardening responses that increase resilience (and thus change the TDT parameters) when a second heat exposure occurs. Such issues of repeated thermal stress have been discussed previously54 but for the purpose of the present study the main conclusion is that simple TDT curve modelling is not applicable to fluctuations bracketing Tc unless this is empirically validated. Future studies could address this issue as inclusion of repair functions would add further promise to the use of TDT curves in modelling of the impacts of temperature fluctuations. More

Physical modelThe physical part of the model is a global Oceanic General Circulation Model, Meteorological Research Institute Community Ocean Model version 3 (MRI.COM3)40. The model has horizontal resolutions of 1° in longitude and 0.5° in latitude south of 64° N, and tripolar coordinates are applied north of 64° N. The model is discretized in 51 vertical layers. In the upper 160 m, tracers are calculated at depths of 2.0, 6.5, 12.25, 19.25, 27.5, 37.75, 50.5, 65.5, 82.25, 100.0, 118.2, 137.5, and 157.75 m, and therefore vertical variation in chlorophyll concentration below the grid-scale is not represented in our model. The model was forced with realistic wind stress, surface heat and freshwater fluxes40.Marine ecosystem modelWe developed a marine ecosystem model composed of phytoplankton, zooplankton, nitrate, ammonia, particulate organic nitrogen, dissolved organic nitrogen, dissolved iron (Fed), and particulate iron. Our model is a 3D version of the FlexPFT model27 and is called the FlexPFT-3D model. The main changes of the FlexPFT-3D from original FlexPFT model are the introduction of iron limitation and substitution of the carbon-based phytoplankton biomass in the original with nitrogen-based biomass herein. The iron cycle is based on the nitrogen-, silicon- and iron-regulated Marine Ecosystem Model41 including the process of scavenging and iron input from dust and sediment. Dissolved iron starts from the distribution calculated by the Biological Elemental Cycling model in Misumi et al.42. Nitrate starts from the distribution of World Ocean Database 199843. After the connection of the physical model, a 20 years of historical simulation (1985–2004) is performed. In addition to the standard case with the chlorophyll-specific initial slope of growth versus irradiance, aI, of 0.35 m2 E−1 mol C (g chl)−1, the case studies with aI of 0.5 and 1.0 m2 E−1 mol C (g chl)−1 were implemented. The case studies are calculated from 2003 to 2004, starting from the distributions of biological variables at the end of 2002 in the standard case.Phytoplankton growthThe procedures of numerical integration of phytoplankton concentration are described here. Readers can construct a numerical model using the following equations. The derivations of the following equations from theories are presented by Smith et al.27 (hereafter Smith2016). Values of biological parameters are described in Supplementary Table 1.In accordance with Pahlow’s resource allocation theory28, the FlexPFT model assumes that resources are allocated among structural material, nutrient uptake and, light harvesting (Supplementary Fig. 1a). The fraction of structural material is assumed to be Qs/Q, where Q is the nitrogen cell quota, which is the intracellular nitrogen to carbon ratio (mol N mol C−1), and Qs is the structural cell quota (mol N mol C−1) given as a fixed parameter. The fraction of nutrient uptake is defined as fV (non-dimensional), so that the residual fraction available for light-harvesting is equal to ((1-frac{{Q}_{{rm{s}}}}{Q}-{f}_{{rm{v}}})). Optimal uptake kinetics further sub-divides the resources allocated to nutrient uptake between surface uptake sites (affinity) and enzymes for assimilation (maximum uptake rate), the fraction of which is given by fA and (1 − fA), respectively. Under nutrient-deficient conditions, the number of surface uptake sites (and hence affinity) increases, while enzyme concentration (hence, maximum uptake rate) decreases. The FlexPFT model assumes instantaneous resource allocation, which means that resource allocation tracks temporal environmental change with no lag time. It has elsewhere been demonstrated that an instantaneous acclimation model provides an accurate approximation of a fully dynamic acclimation model44.We assume that acclimation responds to daily-averaged environmental conditions, which are used to calculate the optimal values of fV, fA, and Q as ({f}_{V}^{o}), ({f}_{A}^{o}), and ({Q}^{o}). The optimal values are estimated at the beginning of a day and are retained for the following 24 h. The daily-averaged environmental variables of the seawater temperature, T (°C), intensity of photosynthetically active radiation, I, nitrogen concentration, [N], which is the sum of nitrate and ammonia concentrations, and dissolved iron concentration, [Fed] are defined as (bar{T}), (bar{I}), ([bar{{rm{N}}}]), and ([{overline{{rm{Fe}}}}_{{rm{d}}}]), respectively. Based on the assumption that diurnal variation of temperature and nutrient are very small, T, [N] and [Fed] at the beginning of a day are used as (bar{T}), ([bar{{rm{N}}}]), and ([{overline{{rm{Fe}}}}_{{rm{d}}}]), respectively. For (bar{I}), we use the average in sunshine duration in a day, which is slightly modified from the daily average in Smith2016.Phytoplankton growth rate per unit carbon biomass (day−1), μ, is given by$$mu ={hat{mu }}^{I}left(1-frac{{Q}_{{rm{s}}}}{{Q}^{o}}-{f}_{V}^{o}right)-{zeta }^{N}{f}_{V}^{o}{hat{V}}^{N},$$
(1)
where ({hat{mu }}^{I}) is the potential carbon fixation rate per unit carbon biomass (day−1), ({zeta }^{N}) is the energetic respiratory cost of assimilating inorganic nitrogen (0.6 mol C mol N−1), and ({hat{V}}^{N}) is the potential nitrogen uptake rate per unit carbon biomass (mol N mol C−1 day−1). Equation (1) represents the balance of net carbon fixation and respiration costs of nitrogen uptake, which are proportional to the fraction of resource allocation. ({hat{V}}^{N}([bar{{rm{N}}}],,bar{T})) is$${hat{V}}^{N}([bar{{rm{N}}}],bar{T})=frac{{hat{V}}_{0}[bar{{rm{N}}}]}{(frac{{hat{V}}_{0}}{{hat{A}}_{0}})+2sqrt{frac{{hat{V}}_{0}[bar{{rm{N}}}]}{{hat{A}}_{0}}}+[bar{{rm{N}}}]},$$
(2)
where ({hat{A}}_{0}) and ({hat{V}}_{0}) are the maximum value of affinity and maximum nitrogen uptake rate.From here, we will explain how the optimized values such as ({f}_{V}^{o}), ({f}_{A}^{o}), and ({Q}^{o}) are calculated. The optimal fraction of resource allocation to affinity, ({f}_{A}^{o}), is given by$${f}_{A}^{o}={[1+sqrt{frac{{hat{A}}_{0}[bar{{rm{N}}}]}{F(bar{T}){hat{V}}_{0}}}]}^{-1},$$
(3)
which is derived by substituting Eqs. (18) and (19) in Smith2016 into Eq. (17). (F(bar{T})) is temperature dependence, defined as$$F(bar{T})=exp {-frac{{E}_{a}}{R}[frac{1}{bar{T}+298}-frac{1}{{T}_{{rm{ref}}}+298}],},$$
(4)
where Ea is the parameter of the activation energy of 4.8 × 104 J mol−1, R is the gas constant of 8.3145 J (mol K)−1, and Tref is the reference temperature of 20 °C.Optimization for light-harvesting is described below. The potential carbon fixation rate per unit carbon biomass (day−1), ({hat{mu }}^{I},)(day−1), in Eq. (1) is$${hat{mu }}^{I}(bar{I},bar{T},[{overline{{rm{Fe}}}}_{{rm{d}}}])={hat{mu }}_{0}frac{[{overline{{rm{Fe}}}}_{{rm{d}}}]}{[{overline{{rm{Fe}}}}_{{rm{d}}}]+{k}_{{rm{Fe}}}}S(bar{I},bar{T},[{overline{{rm{Fe}}}}_{{rm{d}}}])F(bar{T}),$$
(5)
where ({hat{mu }}_{0}) and kFe are the maximum carbon fixation rate and half saturation constant for iron, respectively. S specifies the dependence of light. Defining ({hat{mu }}_{0}^{{rm{limFe}}}={hat{mu }}_{0}frac{[{overline{{rm{Fe}}}}_{{rm{d}}}]}{[{overline{{rm{Fe}}}}_{{rm{d}}}]+{k}_{{rm{Fe}}}}),$${hat{mu }}^{I}(bar{I},bar{T},[{overline{{rm{Fe}}}}_{{rm{d}}}])={hat{mu }}_{0}^{{rm{limFe}}}S(bar{I},bar{T},[{overline{{rm{Fe}}}}_{{rm{d}}}],)F(bar{T}).,$$
(6)
Iron limitation is imposed by substituting ({hat{mu }}_{0}) to ({hat{mu }}_{0}^{{rm{limFe}}}) in all equations in Smith2016. S is defined as$$S(bar{I},bar{T},[{overline{{rm{Fe}}}}_{{rm{d}}}],)=1-exp {frac{-{a}_{I}{hat{Theta }}^{o}bar{I}}{{hat{mu }}_{0}^{{rm{limFe}}}F(bar{T})}},$$
(7)
where ({a}_{I}) is the chlorophyll-specific initial slope of growth versus irradiance. ({hat{Theta }}^{o}), optimal chloroplast chl:phyC (g chl (mol C)−1), is$${hat{Theta }}^{o} = ; frac{1}{{zeta }^{{rm{chl}}}}+frac{{hat{mu }}_{0}^{{rm{limFe}}}}{{a}_{I}bar{I}}{1-{W}_{0}[(1+frac{{R}_{M}^{{rm{chl}}}}{{L}_{{rm{d}}}{hat{mu }}_{0}^{{rm{limFe}}}})exp (1+frac{{a}_{I}bar{I}}{{zeta }^{{rm{chl}}}{hat{mu }}_{0}^{{rm{limFe}}}}),],},(bar{I} > {I}_{0})\ {hat{Theta }}^{o} = ; 0,(bar{I}le {I}_{0}),$$
(8)
where constant parameters ({{rm{zeta }}}^{{rm{chl}}}) and ({R}_{M}^{{rm{chl}}}) are the respiratory cost of photosynthesis (mol C (g chl)−1) and the loss rate of chlorophyll (day−1), respectively. Ld is the fractional day length in 24 h. W0 is the zero-branch of Lambert’s W function. I0 is the threshold irradiance below which the respiratory costs overweight the benefits of producing chlorophyll:$${I}_{0}=frac{{zeta }^{{rm{chl}}}{R}_{M}^{{rm{chl}}}}{{L}_{{rm{d}}}{a}_{I}}.,$$
(9)
The optimal fraction of resource allocation to nutrient uptake, ({f}_{V}^{o}), is$${f}_{V}^{o}=frac{{hat{mu }}^{I}(bar{I},bar{T},[{overline{{rm{Fe}}}}_{{rm{d}}}]){Q}_{{rm{s}}}}{{hat{V}}^{N}([bar{{rm{N}}}],bar{T})}[-1+sqrt{{[{Q}_{{rm{s}}}(frac{{hat{mu }}^{I}(bar{I},bar{T},[{overline{{rm{Fe}}}}_{{rm{d}}}])}{{hat{V}}^{N}([bar{{rm{N}}}],bar{T})}+{zeta }^{N})]}^{-1}+1},]$$
(10)
The optimal nitrogen cell quota, ({Q}^{o}) is$${Q}^{o}={Q}_{{rm{s}}}[1+sqrt{1+{[{Q}_{{rm{s}}}(frac{{hat{mu }}^{I}(bar{I},bar{T},[{overline{{rm{Fe}}}}_{{rm{d}}}])}{{hat{V}}^{N}([bar{{rm{N}}}],bar{T})}+{zeta }^{N})]}^{-1}},]$$
(11)
Optimal cellular chl:phyC (g chl (mol C)−1), ({Theta }^{o}), is$${Theta }^{o}=(1-frac{{Q}_{{rm{s}}}}{{Q}^{o}}-{f}_{V}^{o}){hat{Theta }}^{o}$$
(12)
which is the multiplication of the fraction of resource allocation to light-harvesting and optimal chloroplast chl:phyC. The cellular chl:phyC and chloroplast chl:phyC in Figs. 1 and 2 are optimal cellular chl:phyC, ({Theta }^{o}), and optimal chloroplast chl:phyC, ({hat{Theta }}^{o}), respectively. The relation in Eq. (12) is displayed in Fig. 1i-n. If we artificially turn off the optimization of resource allocation by applying the constant ({Q}^{o}) and ({f}_{V}^{o}) to the all grid points, optimal cellular chl:phyC (Fig. 1i,j) only depends on optimal chloroplast chl:phyC (Fig. 1k, l), and therefore significant variation of SCM depth across the equatorial, subtropical, and subpolar regions is not reproduced.In the above equations, Eqs. (3), (8), (10), (11), and (12), optimized values related to acclimation processes are obtained and then used in calculating the phytoplankton growth rate. Phytoplankton growth rate per unit carbon biomass (day−1), (mu), in Eq. (1) is calculated at each time step:$$mu (I,T,[{rm{N}}],[{{rm{Fe}}}_{{rm{d}}}])=frac{{hat{mu }}^{I}(I,T,[{{rm{Fe}}}_{{rm{d}}}]){f}_{V}^{o}(1-{f}_{A}^{o}){hat{V}}_{0}{f}_{A}^{o}{hat{A}}_{0}[{rm{N}}]}{{hat{mu }}^{I}(I,T,[{{rm{Fe}}}_{{rm{d}}}]){Q}_{0}(1-{f}_{A}^{o}){hat{V}}_{0}+({hat{mu }}^{I}(I,T,[{{rm{Fe}}}_{{rm{d}}}]){Q}_{0}+{f}_{V}^{o}(1-{f}_{A}^{o}){hat{V}}_{0}){f}_{A}^{o}{hat{A}}_{0}[{rm{N}}]},$$
(13)
where ({hat{mu }}^{I}(I,,T,,[{{rm{Fe}}}_{{rm{d}}}])) is obtained by substituting I, T, and [Fed] for (bar{I}), (bar{{rm{T}}}), and ([{overline{{rm{Fe}}}}_{{rm{d}}}]) in Eq. (5), respectively. Note that the model calculates circadian variation in solar irradiance, I, and therefore the phytoplankton growth rate, μ, reaches its maximum at noon local time and is zero during night. On the other hand, phytoplankton optimization is assumed to respond to daily-averaged conditions. The FlexPFT model introduces phytoplankton respiration proportional to chlorophyll content, which is another important originality of Pahlow’s resource allocation theory30,33.The carbon biomass-specific respiratory costs of maintaining chlorophyll, Rchl, is$${R}^{{rm{chl}}}(I,T,[{rm{N}}],[{{rm{Fe}}}_{{rm{d}}}])=({hat{mu }}^{I}(I,T,[{{rm{Fe}}}_{{rm{d}}}])+{R}_{M}^{{rm{chl}}}){{rm{zeta }}}^{{rm{chl}}}{Theta }^{o}.,$$
(14)
The growth rate per unit nitrogen biomass, ({mu }_{{rm{N}}}), is equal to that per unit carbon biomass, μ. Instantaneous acclimation assumes that the quota of nitrogen to carbon biomass obtained by phytoplankton growth is equal to the nitrogen quota in a cell: (frac{{mu }_{{rm{N}}}[{{rm{p}}}^{{rm{N}}}]}{mu [{{rm{p}}}^{{rm{C}}}]}={Q}^{o}), where [pC] and [pN] are phytoplankton carbon and nitrogen concentration in a cell, respectively. Since (frac{[{{rm{p}}}^{{rm{N}}}]}{[{{rm{p}}}^{C}]}={Q}^{o}), ({mu }_{{rm{N}}}=mu). When temporal ({Q}^{o}) change occurs, to satisfy the mass conservation, carbon or nitrogen biomass is adjusted with the other fixed. The FlexPFT fixes carbon biomass, while the FlexPFT-3D fixes nitrogen biomass to the temporal ({Q}^{o}) change.The rate of change in the phytoplankton nitrogen concentration, [pN], except for the advection and diffusion terms is given by the following equation:$$frac{partial [{{rm{p}}}^{{rm{N}}}]}{partial t}=mu [{{rm{p}}}^{{rm{N}}}]-({R}^{{rm{chl}}}+{R}^{{rm{cnst}}})[{{rm{p}}}^{{rm{N}}}]-{M}_{{rm{p}}}{[{{rm{p}}}^{{rm{N}}}]}^{2}-({rm{extracellular}},{rm{excretion}})-({rm{grazing}}),$$
(15)
where Rcnst and Mp are the coefficient of respiration not related to chlorophyll concentration and mortality rate coefficient, respectively. The extracellular excretion is$$({rm{extracellular}},{rm{excretion}})={gamma }_{{rm{ex}}}[(mu -{R}^{{rm{chl}}})[{{rm{p}}}^{{rm{N}}}]],$$
(16)
where ({gamma }_{{rm{ex}}}) is the coefficient of extracellular excretion. The grazing term is represented by$$({rm{grazing}})={G}_{20deg }F(T)[{{rm{z}}}^{{rm{N}}}]frac{{[{{rm{p}}}^{{rm{N}}}]}^{{a}_{{rm{H}}}}}{{({k}_{{rm{H}}})}^{{a}_{{rm{H}}}}+{[{{rm{p}}}^{{rm{N}}}]}^{{a}_{{rm{H}}}}},$$
(17)
where G20deg is the maximum grazing rate at 20 °C, and [zN] is zooplankton concentration. Temperature dependency, F(T), is obtained by substituting T for (bar{T}) in Eq. (4). ({a}_{{rm{H}}}) is the parameter controlling Holling-type grazing, which takes a value from 1 to 2. kH is the grazing coefficient in Holling-type grazing.Once [pN] is calculated, phytoplankton carbon concentration (mol C L−1), and chlorophyll concentration (g chl L−1) are uniquely determined in an environmental condition, without prognostic calculation. Therefore, an instantaneous acclimation model can represent stoichiometric flexibility with lower computational costs compared with a dynamic acclimation model44.Model validationThe spatial pattern of simulated annually mean chlorophyll at the ocean surface agrees with that of satellite observation45 (Supplementary Fig. 3). The model reproduced the contrast of the surface chlorophyll concentration between subtropical and subpolar regions, although simulated surface chlorophyll concentration in subtropical regions is lower than that of the observation partly due to the lack of nitrogen fixers. Nitrogen fixation is estimated to support about 30–50% of carbon export in subtropical regions46,47. Simulated surface chlorophyll distribution in the Pacific equatorial region is close to the observed.Our model properly simulates the meridional distribution of nitrate compared with that of observations48 (Supplementary Fig. 4). The simulated horizontal distribution of primary production is consistent with that estimated by satellite data9,49 (Supplementary Fig. 5), although simulated primary production is underestimated in subtropical regions, associated with the underestimation of surface chlorophyll in these regions (Supplementary Fig. 3). More

eCIS are encoded by 1.9% and 1.2% of sequenced bacteria and archaea, respectively, with a highly biased taxonomic distributionFirst, we were interested in identifying all eCIS loci in a large genomic dataset. We compiled a set of 64,756 microbial isolate genomes retrieved from Integrated Microbial Genomes (Supplementary Data 1)16. To identify core component homologs from known systems, we searched for genes with known eCIS-associated pfam annotations (Supplementary Table 1). To supplement this, we also annotated homologous genes ourselves by searching using the Hidden Markov Model (HMM) profiles from a recent publication1,17. We defined putative eCIS operons as gene cassettes that included these multiple eCIS core genes in close proximity and were not bacteriophage, T6SS, or R-type pyocins (Supplementary Table 1, Methods). Overall, we identified eCIS operons encoded in 1230 (1.9%) bacteria and 19 (1.2%) archaea from our genomic repository (Supplementary Data 2–3). We identified two core genes, Afp8 and Afp11, that co-occur in eCIS operons across 98.7% of loci and used their protein sequences to construct an eCIS phylogenetic gene tree (Fig. 1a, Supplementary Figs. 2–3, Supplementary Data 4). Afp8 and Afp11 alone resulted in phylogenetically similar trees (Supplementary Fig. 4) and the trees agree with eCIS division into subtype I and II that were defined in a previous eCIS analysis17 (Supplementary Fig. 5). eCIS is scattered across the prokaryotic diversity with presence in 14 bacterial phyla and one archaeal phylum. The incongruence between this tree and the genomic phylogeny suggests that eCIS undergo HGT frequently, as was proposed before1,17. The previously experimentally characterized eCISs are located within a narrow clade on the eCIS tree, pointing to the possibility that other eCIS particles may play more diverse ecological roles (Fig. 1a, Supplementary Fig. 2).Fig. 1: Taxonomic Distribution of eCIS-encoding microbes.a A phylogenetic tree of eCIS across the microbial world. eCIS core genes Afp8 and Afp11 from each operon were concatenated, aligned, and used to construct the phylogenetic tree. The Domain and Phylum corresponding to each leaf are indicated in the inner and outer rings, respectively. Scaffolds encoding eCIS that have been predicted to be plasmids using Deeplasmid were marked with black triangles. Previously experimentally investigated eCIS are marked on their respective leaves (2 o’clock). Within the tree MACS, AFP, and PVC are abbreviations for Metamorphosis-associated Contractile Structures, Antifeeding Prophage, and Photorhabdus Virulence Cassettes. b eCIS distribution in different genera. We calculated the eCIS distribution across genera using a Fisher exact test. The Odds Ratio represents the enrichment or depletion magnitude, with hotter colors representing enrichment, and colder colors representing depletion. Calculated p values were corrected for multiple testing using FDR to yield minus log10 q values, shown in shades of gray. Only selected Genera are shown. Source data are provided in Supplementary Data 1–2,5–6.Full size imageNext, we looked for genetic mechanisms that may mediate the eCIS HGT. Using Deeplasmid, a new plasmid prediction tool that we developed18, we identified that 7.6% of eCIS are likely plasmid-borne (Fig. 1a and Supplementary Fig. 6, Supplementary Data 5, Methods). In other cases, we found a clear signature of eCIS operon integration into a specific bacterial chromosome (Supplementary Fig. 7). For example, we identified a likely homologous recombination event between identical tRNA genes, a classical integration site19 (Supplementary Fig. 7b). These genomic integration events and the plasmid-borne eCIS operons shed light on the mechanisms through which eCIS loci have been horizontally propagated in microbial genomes.eCIS displays a highly biased taxonomic distributionGiven the propensity of eCIS to transfer between microbes as phylogenetically distant as bacteria and archaea, we were surprised by its scarcity in microbial genomes. We tested if eCIS loci are homogeneously distributed across microbial taxa and found that eCIS are mostly constrained to particular taxa (Fig. 1b, Supplementary Data 6). Strikingly, we found that it is present in 100% (18/18) of Photorhabdus genomes in our dataset (Fisher exact test, odds ratio = infinity, q value = 2.97e−28), 89% of sequenced Chitinophaga (odds ratio = 276, q value = 1.69e−35), 86% of sequenced Dickeya (odds ratio = 211, q value = 3.78e−18), and 69% of sequenced Algoriphagus (odds ratio = 73, q value = 1.99e−24). These genera are known as environmental microbes; Photorhabdus is a commensal of entomopathogenic nematodes20, Chitinophaga is a soil microbe and a fungal endosymbiont21, Dickeya is a plant and pea aphid pathogen22,23, and Algoriphagus is an aquatic or terrestrial microbe24,25,26,27,28. In contrast, eCIS is strongly depleted from the most cultured and sequenced genera of Gram-positive and negative human pathogens, including Staphylococcus, Escherichia, Salmonella, Streptococcus, Acinetobacter, and Klebsiella. Strikingly, within these genera, for which our repository had 18,355 genomes, eCIS was totally absent (odds ratio = 0, q value ≤ 3.86E-16 for each one of these genera), suggesting a very potent purifying selection acting against eCIS integration into these microbial genomes, despite the eCIS operons’ tendency for extensive lateral transfer and its presence in other host-associated systems. Interestingly, 146 genomes, mostly from Photorhabdus, Dickeya, Actinokineospora, Streptomyces, Algoriphagus, Chitinophaga, Flavobacterium, and Calothrix genera, were found to contain more than one eCIS operon, ranging from 2 to 5 copies per genomes (Supplementary Data 7).eCIS presence is highly correlated with specific ecosystems, microbial lifestyles, and microbial hostsGiven the strong eCIS taxonomic bias we identified, we were curious to know if we could further associate eCIS with specific ecological features. To this end, we retrieved metadata available for all sequenced genomes in our repository (Methods). These traits include the microbial isolation site, ecosystem and habitat, microbial lifestyle and physiology, and the organisms hosting the microbes (Supplementary Data 8). We calculated the correlation of eCIS presence with certain microbial traits to identify significant enrichment and depletion patterns. This was done using a naïve enrichment test (Fisher exact test) together with a phylogeny-aware test, Scoary29, which is used to correct for the phylogenetic bias of the isolate genomes. Using this test we quantify to what extent the eCIS presence in a genome correlates with a certain trait, independently of the microbial phylogeny (Fig. 2, Supplementary Fig. 8). Notably, eCIS is positively correlated with terrestrial and aquatic environments, such as soil, sediments, lakes, and coasts, but is depleted from food production venues. In terms of microbial lifestyle and physiology, eCISs are enriched in environmental microbes, mostly symbiotic, and are depleted from pathogens (the vast majority of which were isolated from humans). eCISs are enriched in aerobic microbes that dwell in mild and cold temperatures. In general, the eCIS-encoding microbes tend to associate with terrestrial hosts including insects, nematodes, annelids, protists, fungi, and plants, and in aquatic hosts such as fish, sponges, and molluscs. Intriguingly, we detected a strong depletion from bacteria that were isolated from birds and mammals, including humans. We did find some eCIS isolated from bacteria associated with humans, but sparse and statistically depleted (Supplementary Fig. 8). Looking closer we also see that the operon is depleted from all tissues in which the human microbiome is abundant: oral and digestive systems, skin, and the urogenital tract. However, we detected a mild eCIS enrichment in the human gut commensal Bacteroides (Fig. 1b) and Parabacteroidetes genera. Bacteroides was recently reported by the Shikuma group as being eCIS-rich30.Fig. 2: eCIS-encoding microbes’ lifestyle and isolation.A Fisher exact test combined with a modified version of Scoary was used to perform a phylogeny-aware analysis of eCIS-encoding microbes’ metadata. The Odds Ratio represents the enrichment or depletion magnitude, with hotter colors representing enrichment, and colder colors representing depletion. The negative log10 of the q-values, shown in shades of gray, are corrected for multiple hypothesis testing. One q-value corresponds to the statistical significance of a two-sided Fisher exact test, and the other represents the same for the Scoary pairwise comparison test. Source Data are provided in Supplementary Data 8.Full size imageWe also see that eCIS is clearly associated with larger bacterial genomes in five bacterial phyla (Supplementary Fig. 9), although small genome endosymbionts are found to contain eCIS as well, for example, the Candidatus Regiella insecticola LSR1, which harbours an eCIS even though its genome size is ~2 Mbps and it contains 10 is defined “Core”, 4–10 is “Shell”, More