Acclimation by diverse phytoplankton species determines oceanic carbon to nitrogen ratios

The carbon to nitrogen (CN) ratio of phytoplankton connects the carbon and nitrogen cycles in the ocean. Any variation in this ratio under climate change will alter the amount of carbon fixed by photosynthesis, and ultimately the amount sequestered in the ocean. However, a consistent mechanistic explanation remains lacking for observed species‐specific variations in phytoplankton CN ratios. We show that acclimation to ambient environmental conditions explains the observed variation of phytoplankton CN ratios by incorporating phytoplankton acclimation theory based on a resource allocation trade‐off between carbon vs. nitrogen acquisition capacity into a three‐dimensional marine ecosystem model. Inter‐specific differences in CN ratio and its sensitivity are caused by inter‐specific differences in Droop's minimum nitrogen cell quota. Our model, constrained by observed phytoplankton parameters, shows that the global mean phytoplankton CN ratio is greater than the canonical Redfield ratio, as suggested previously based on regional in situ observations.

by observed phytoplankton parameters, shows that the global mean phytoplankton CN ratio is greater than the canonical Redfield ratio, as suggested previously based on regional in situ observations. The carbon to nitrogen (CN) ratio of oceanic phytoplankton, that is, the net ratio of carbon fixed by photosynthesis to nitrogen taken up, links the carbon and nitrogen cycles in the earth system (Gruber and Galloway 2008). Therefore, elucidating the biological basis for determining the phytoplankton CN ratio will enhance the ability to predict the absorption of anthropogenic CO 2 by the ocean. Typically, the phytoplankton CN ratio is expected to equal, on average, the Redfield ratio of 6.6 (106 mol C/16 mol N), and most oceanic biogeochemical models assume this constant ratio (Yamanaka et al. 2004;Kishi et al. 2007;Laufkötter et al. 2015). On the other hand, experimental and observational studies show that the phytoplankton CN ratio deviates substantially from the Redfield ratio (Falkowski 2000;Geider and La Roche 2002). In culture experiments, the phytoplankton CN ratio ranges from 3 to 20 (Geider and La Roche 2002), increasing with decreasing nutrient concentration (Geider and La Roche 2002) and with increasing light intensity (Dickman et al. 2006;Tanioka and Matsumoto 2020). Furthermore, different phytoplankton lineages have different CN ratios (Geider and La Roche 2002;Quigg et al. 2003); for example, Synechococcus exhibits only slight variation in its CN ratio (Mouginot et al. 2015;Garcia et al. 2016). Though in situ observations of phytoplankton CN ratios are scarce, observed CN ratios of particulate organic matter (Laws 1991;Schneider et al. 2003) range widely from 2.0 to 20.0 with a mean of 7.06 (Martiny et al. 2013;Martiny et al. 2014). Pahlow (2005) proposed the theory that acclimation to various environments determines the phytoplankton CN ratio. According to this theory, phytoplankton allocate nitrogenous intracellular resources among (1) carbon acquisition through photosynthesis, (2) nitrogen acquisition through nutrient uptake, and (3) constituting structural material. Phytoplankton are assumed to optimize their resource allocation in order to maximize their growth rate. In light-replete, nutrientdeficient environments, such as the subtropical surface, the phytoplankton CN ratio is relatively high (Fig. 1a) because carbon is easily acquired while nitrogen is difficult to acquire. Under such conditions, phytoplankton allocate fewer resources to carbon acquisition and more to nutrient uptake, resulting in lower intracellular chlorophyll content. Conversely, in light-deficient, nutrient-replete environments, the phytoplankton CN ratio is relatively low because nitrogen is more easily available than sunlight (hence, energy and carbon) (Fig. 1b), and intracellular chlorophyll content becomes high. Therefore, Pahlow's theory can naturally derive the relationship between the phytoplankton CN ratio and the intracellular chlorophyll content as observed in incubation experiments (Pahlow and Oschlies 2009;). Pahlow's theory also captures the increase in phytoplankton CN ratio with increasing light intensity (Pahlow and Oschlies 2009) and with nutrient depletion (Smith and Yamanaka 2007) in incubation experiments. Pahlow's theory later provided the first theoretical derivation (Pahlow and Oschlies 2013) of Droop's empirical model (Droop 1968(Droop , 1973(Droop , 1983Fig. 1c) for the dependence of phytoplankton growth rate on their nitrogen to carbon ratio (Q). In this framework, the minimum nitrogen to carbon ratio (Q 0 ), defines the theoretical upper limit of the phytoplankton CN ratio, equal to Q À1 0 . Q 0 varies from 0.038 to 0.13 depending on the phytoplankton species (Pahlow 2005; (Fig. S1).
Recently, Pahlow's theory has been applied in threedimensional (3D) ecosystem models Pahlow et al. 2020;Masuda et al. 2021), one of which advances our understanding of the global distribution of particulate CN ratios . Here, using a 3D ocean ecosystem model, we show that Pahlow's theory provides the physiological basis underlying the observed variation in phytoplankton CN ratios, which range widely from 3.0 to 20.0. To explain the inter-specific differences in CN ratios, we focused on the differences in Q 0 among species. We regard inter-specific differences in (physiological and behavioral) acclimation response as the result of evolutionary adaptation (Smith et al. 2011). Furthermore, we examine whether the global mean phytoplankton CN ratio calculated based on this theory is equal to the Redfield ratio.

Numerical model
We applied the lower-trophic level ocean ecosystem model described in Masuda et al. (2021). The ecosystem model is coupled with a global Ocean General Circulation model including a sea ice model (Meteorological Research Institute Community Ocean Model version 3, MRI.COM3) (Tsujino et al. 2011). The horizontal resolution of the model is 1 in longitude and 0.5 in latitude except north of 64 N, where tripolar coordinates are applied. The model has 51 vertical layers. The physical model is driven by realistic wind stress, surface heat and freshwater fluxes (Tsujino et al. 2011). The ecosystem model, the FlexPFT-3D model, is a 3D version of the 1D Flexible Phytoplankton Functional Type (FlexPFT) model (Smith et al. 2016). The FlexPFT-3D model represents nitrogen and iron cycles including iron limitation on phytoplankton growth rate. The FlexPFT-3D model represents one generic phytoplankton species, one generic zooplankton species, nitrate, ammonia, particulate organic nitrogen, dissolved organic nitrogen, particulate iron, and dissolved iron. Particulate organic carbon is not calculated due to a lack of sufficient observational data on the effect of zooplankton and Masuda et al. Phytoplankton carbon to nitrogen ratios decomposers on the CN ratio. The iron cycle includes iron input from dust and sediment, and a scavenging process. Light intensity is based on International Satellite Cloud Climatology Project data (Zhang et al. 2004). Initial nitrate concentration data are from World Ocean Database 1998 (Conkright et al. 1999). The model assumes instantaneous acclimation (Smith et al. 2016;Ward 2017;Anugerahanti et al. 2021;Kerimoglu et al. 2021), that is, the CN ratio in a phytoplankton cell is equal to the ratio of acquired carbon to acquired nitrogen. Therefore, once phytoplankton parameters are determined, phytoplankton CN ratio and intracellular chlorophyll content are uniquely determined responding to an environmental condition (Fig. S2). The FlexPFT-3D model can properly simulate the observed global distributions of chlorophyll including the subsurface chlorophyll maxima, nitrate, and primary production (Masuda et al. 2021).

Numerical experiments
For the standard experiment, a 10-yr model run (from 1995 to 2004) is performed after a spin-up period (from 1985 to 1994) (Fig. S3). We mainly analyzed results from the final year (2004) (Masuda et al. 2022). As Pahlow's model reduces to Droop's model (Fig. 1c) under constant light and temperature conditions, it responds in the same way: growth rate slows with increasing CN ratio, and phytoplankton cannot grow above a CN ratio of Q À1 0 . For Q 0 of 0.08 and 0.04, the theoretical maximum CN ratios are 12.5 and 25, respectively. Therefore, the sensitivity studies with different Q 0 (0.04-0.13 mol N mol C À1 ) are integrated 2-yr from 01 January 2003 to 31 December 2004, starting from the distributions of biological variables at the end of 2002 in the standard experiment ( Fig. S3). The 2-yr calculation period of the sensitivity studies is to minimize the differences in nutrient distribution from the standard experiment. Further information on the sensitivity studies is described in the Supporting Information.

Acclimation determines CN ratio
To show that acclimation response can explain the global distribution of phytoplankton CN ratio, as Pahlow theorized, we display the meridional distributions of the phytoplankton CN ratio (Fig. 2a), nitrate concentration (Fig. 2b), and resource allocation to nutrient uptake ( Fig. 2c) in the standard experiment. Values of the resource allocation to nutrient uptake near 0.5 (or 0) mean that resources are mainly allocated to nutrient uptake (or carbon acquisition), with minimal allocation to the competing use. In light-replete and nutrientdeficient environments, such as the subtropical surface, phytoplankton resource allocation is heavily skewed to nutrient  (Pahlow 2005). Resource allocation determines phytoplankton carbon to nitrogen (CN) ratio and intracellular chlorophyll content. (c) The dependence of phytoplankton growth rate on phytoplankton nitrogen to carbon ratio in Droop's model (Droop 1968(Droop , 1973(Droop , 1983. μ ∞ is the asymptotic growth rate at infinite cell quota. Q 0 is the minimum nitrogen cell quota. uptake. This means that the acquisition of nitrogen is more difficult than that of carbon, and therefore the phytoplankton CN ratio is higher. Since few resources are allocated to carbon acquisition through photosynthesis, intracellular chlorophyll content is lower (Fig. 2d). Conversely, in light-deficient and nutrient-replete environments, such as below 80 m in subpolar regions, resource allocation is heavily skewed to carbon acquisition through photosynthesis, resulting in lower phytoplankton CN ratio and higher intracellular chlorophyll content. In the subarctic surface layer north of 40 N, where both Meridional sections of phytoplankton carbon to nitrogen ratio and associated biogeochemical variables along 180 E. distributions of (a) phytoplankton CN ratio (mol C mol N À1 ), (b) nitrate concentration (μmol N L À1 ), (c) resource allocation to nutrient uptake (non-dim), and (d) intracellular chlorophyll content (g chl mol C À1 ), averaged in the simulated last year (2004) in the standard experiment of Q 0 = 0.08. In calculating the annual average, the values of variables except for nitrate concentration are weighted by primary production, and blank regions show that primary production does not exist.
light and nutrient are abundant, resource allocation is more evenly balanced between carbon acquisition and nutrient uptake, and the phytoplankton CN ratio is intermediate between the subtropical surface and deep layers. The simulated vertical change in phytoplankton CN ratio is consistent with experimental results that phytoplankton CN ratio increases with increasing light intensity (Dickman et al. 2006;Tanioka and Matsumoto 2020) and with depletion of inorganic nitrogen (Flynn et al. 1994). The interactive effects of light and nutrients embodied in our model formulation (Fig. S2) are also qualitatively consistent with experimental results (Dickman et al. 2006). Furthermore, the model used in this study properly simulates the observed vertical distribution of chlorophyll including the subsurface chlorophyll maxima (Cullen 2015) as previously shown (Masuda et al. 2021), thereby demonstrating the validity of this resource allocation theory.

Diversity of Droop's minimum nitrogen cell quota and CN ratios
To explain inter-specific differences in the phytoplankton CN ratio, we performed ten experiments with Q 0 varying from 0.04 to 0.13 in 0.01 intervals, based on the species-dependent variation in Q 0 ranging 0.038-0.13 estimated from laboratory experiments (Pahlow 2005; Oschlies 2013) (Fig. S1). The standard experiment uses a Q 0 of 0.08. As Q 0 increases in the sensitivity studies from 0.04 to 0.13, the global frequency distribution of the phytoplankton CN ratio with the minimum and maximum shifts toward lower CN ratios, and the width of the distribution narrows (Fig. 3). Therefore, the global mean phytoplankton CN ratio (inverted triangle) decreases with increasing Q 0 , which is in line with a previous numerical study ). The phytoplankton CN ratio is relatively lower in and around the Antarctic Ocean than in other regions, contributing to the formation of the lower of the two peaks of the distribution. For these 10 experiments, the maximum phytoplankton CN ratio is 25.0 at Q 0 = 0.4, and its minimum is 2.5 at Q 0 = 0.13, and therefore the simulated range of the phytoplankton CN ratio corresponds to the observed range (3.0-20.0) obtained in incubation experiments (Geider and La Roche 2002). Consequently, the observed variation in phytoplankton CN ratios can be explained by a combination of phytoplankton acclimation to oceanic environments based on Pahlow's theory and experiment-based variation in Q 0 by species. The simulation result that species with higher Q 0 have a narrower range of variation in the CN ratio is consistent with the experimental result that Synechococcus has higher Q 0 above 0.08 Garcia et al. 2016) than most of the other taxonomic groups and exhibits less variable CN ratios (Mouginot et al. 2015;Garcia et al. 2016). According to Pahlow's theory, species with higher Q 0 allocate more nitrogenous resources to structural material than other species and allocate fewer resources to nitrogen and carbon acquisition, resulting in lower flexibility. Though the CN ratios of a phytoplankton species also depend on other physiological parameters, Q 0 is the primary determinant of CN ratio (Pahlow 2005) (see also Fig. S2).

Estimation of the global mean phytoplankton CN ratio
The global mean phytoplankton CN ratio in the real ocean is determined by the acclimation response of a variety of differently adapted species, which can be captured by a distribution of Q 0 values. Here, for the sake of simplicity, we have estimated the global mean Q 0 , ignoring regional differences in species composition. This provides a good basis for a firstorder estimate of the global mean CN ratio, excluding the nonlinear averaging over the inter-specific distribution of acclimation response.
In incubation experiments, Synechococcus and Trichodesmium have Q 0 above 0.08 (Pahlow et   while diatoms and green algae have Q 0 in the range of 0.04-0.07 (Pahlow 2005; Oschlies 2013) (Fig. S1). Since the global net primary production by diatoms and green algae is greater than that by Synechococcus and Trichodesmium (Uitz et al. 2010), the global mean Q 0 is expected to be < 0.08. Even if Q 0 is not estimated in incubation experiments, phytoplankton species with an observed CN ratio > 12.5 have Q 0 < 0.08 since Q 0 strictly determines the maximum phytoplankton CN ratio, as Q À1 0 . Phytoplankton CN ratios in incubation experiments sometimes reach 12.5-20.0 (Goldman et al. 1979;Flynn et al. 1994;Geider and La Roche 2002), indicating many species of Q 0 < 0.08. Furthermore, our global net primary production calculation supports global mean Q 0 < 0.08. When Q 0 is 0.08, the simulated global net primary production of 29 Pg C yr À1 is smaller than satellite-estimated global net primary production of 50 Pg C yr À1 (Field et al. 1998;Carr et al. 2006). A decrease in Q 0 increases the simulated global net primary production due to the increased phytoplankton CN ratio.
The global mean phytoplankton CN ratio is close to the Redfield ratio of 6.6 when global mean Q 0 is 0.1 but our estimated global mean Q 0 < 0.08 implies global mean phytoplankton CN ratio > 8.4. Previous studies that have observed both in situ phytoplankton and particulate CN ratios have shown that phytoplankton CN ratios are significantly higher than particle CN ratios (Martiny et al. 2013;Talmy Fig. 4. Global distributions of simulated phytoplankton CN ratio and observed particulate CN ratio. (a) Vertically integrated phytoplankton CN ratio, which is the division of the vertically integrated carbon-based primary production by the vertically integrated nitrogen-based primary production, in the standard experiment of Q 0 = 0.08 in the simulated last year (2004), where essentially the same results are obtained in 1995-2004 (Fig. S4). (b) Particulate CN ratio averaged in 2 Â 2 , and 0-80 m. we used the archive of observed particulate CN ratios , https://doi.org/10.5061/ dryad.d702p), which are collected in the global ocean and obtained from 1971 to 2010. The number of observed data in each 2 Â 2 grid cell varies substantially (Fig. S5). et al. 2016). Therefore, our estimated global mean phytoplankton CN ratio > 8.4 is consistent with the observation-based global mean particulate CN ratio close to the Redfield ratio (Martiny et al. 2013). As described in previous studies (Talmy et al. 2016;Moreno and Martiny 2018), heterotrophs, which are thought to be carbon-limited (Tezuka 1990;Godwin and Cotner 2015) and therefore more nitrogen-rich, are inferred to assimilate relatively more nitrogen than carbon from their prey, thereby reducing the particulate CN ratio relative to the phytoplankton CN ratio.

Comparison with the distribution of particulate CN ratios
The global horizontal distribution of phytoplankton CN ratios in the standard experiment shows that phytoplankton CN ratios differ among oceanic regions due to acclimation responding to oceanic environments (Fig. 4a). Although the phytoplankton CN ratio differs from the particle CN ratio (Martiny et al. 2014 (Fig. 4b), similar patterns of variation are expected in spatial distributions. Consistent with the general regional pattern of particulate CN ratios (Martiny et al. 2013), simulated phytoplankton CN ratios are relatively high in the nutrient-poor subtropics, and relatively low in the nutrient-rich subarctic and Antarctic regions. Simulated phytoplankton CN ratios, however, overestimate observations in some equatorial and subtropical areas and underestimate them in some Antarctic areas. The limitation of Fig. 4a is the lack of regional differences in species composition and the effects of heterotrophs on the particulate CN ratio (Fig. S6). In future work, we need to represent, for example, that diatoms having lower Q 0 (0.04-0.05) (Fig. S7) are abundant in the Antarctic Ocean but rare in the subtropics. Furthermore, zooplankton is considered to have a more stable CN ratio than phytoplankton (Talmy et al. 2016), and therefore the total particulate CN ratio, including zooplankton, can be expected to exhibit less variability compared to the phytoplankton CN ratio. The global frequency distribution of vertical mean phytoplankton CN ratios is in line with that of observed particulate CN ratio (Martiny et al. 2014 if heterotrophs make the particulate CN ratio lower than the phytoplankton CN ratio and phytoplankton species have different Q 0 (Fig. S8).

Acclimation vs. adaptation
Acclimation and adaptation (i.e., inter-specific trait diversity) both determine ecological response and associated biogeochemical ratios (Smith et al. 2011;Moreno and Martiny 2018). For phytoplankton nitrogen to phosphorus ratio, the dominant contribution of adaptation is well accepted (Klausmeier et al. 2004;Sharoni and Halevy 2020). Differences in phytoplankton CN ratio among size or taxa are pointed out (Talmy et al. 2016;Matsumoto et al. 2020a). As shown in Fig. 5, the introduction of species composition modifies the dependence of the phytoplankton CN ratio on environmental conditions because different species or taxa have both different absolute values of CN ratio and different sensitivities to changing conditions. When species with low (high) Q 0 dominate, the average phytoplankton CN ratio will be high (low), and it will be more (less) sensitive to nutrient supply, particularly under low-nutrient conditions. Beyond this generic treatment for CN ratios in terms of the Droop model, future studies that better characterize inter-specific differences in acclimation response have the potential to further clarify the relative effects of adaptation and acclimation on CN ratios specifically and biogeochemistry more broadly.

Future outlook
Our model based on Pahlow's theory shows linkage among the observed variation in phytoplankton CN ratios, Droop's minimum cell quota, Q 0 , estimated from incubation experiments and observed variations in intracellular chlorophyll , light intensity and dissolved iron concentration are set to be 400 W m À2 and 0.3 nmol Fe L À1 , respectively. In this study, for each set of phytoplankton parameters (maximum carbon fixation rate, affinity, etc.), the phytoplankton CN ratio is uniquely determined as a function of environmental conditions. This is because we have assumed instantaneous acclimation (Smith et al. 2016), whereby phytoplankton acclimate to environmental change without time-lag. content. Among fundamental phytoplankton physiological traits, Q 0 , is the most important determinant of CN ratio. In general, other trait parameters being equal, phytoplankton species with lower Q 0 tend to grow faster than species with higher Q 0 (Fig. S9). However, species with low Q 0 , such as diatoms, do not necessarily dominate all oceanic regions, likely because of trade-offs with other physiological traits. In the future, observational data of various physiological traits including Q 0 will be obtained for many phytoplankton species to understand competition among species. Such observational data will make it possible to clarify how regional differences in species composition impact the global distribution of CN ratios, by representing multiple species with different Q 0 in our model. Our model does not include nitrogen fixers, for which CN ratio is relatively insensitive to environmental conditions, remaining near the Redfield ratio (Matsumoto et al. 2020b) based on a meta-analysis of experimental data (Tanioka and Matsumoto 2020). Introducing nitrogen fixers to the model would therefore bring the CN ratio of the phytoplankton community closer to the Redfield ratio, with variable contributions depending on their abundance relative to other phytoplankton.
Our present model does not include the phosphorus cycle. Since observational studies show that phosphorus deficiency affects the phytoplankton CN ratio (Garcia et al. 2016;Tanioka and Matsumoto 2020), introducing a phosphorus cycle is a future challenge.
Our model provides a theoretically sound basis for predicting changes of phytoplankton CN ratio in response to future climate change. Ocean stratification associated with climate change is expected to reduce nutrient supply and decrease in nutrient concentrations near the ocean surface (Hays et al. 2005;Capotondi et al. 2012). Previous studies that calculated dynamic CN ratios using different methods than ours have predicted no significant change in the global mean CN ratio of exported particulate organic matter under future climate (Kwiatkowski et al. 2018;Matsumoto et al. 2020a). Based on Pahlow's acclimation theory, the phytoplankton CN ratio increases in response to decreasing nutrient concentration (Fig. S2a), consistent with an empirical formula for eukaryotes based on incubation experiments (Matsumoto et al. 2020a). Therefore, if the global mean Q 0 does not change, the global mean phytoplankton CN ratio will be higher in the future, which will mitigate climate change. On the other hand, if species with lower Q 0 (e.g., diatoms) are replaced by species with higher Q 0 (e.g., Synechococcus) as near-surface nutrient concentrations decrease, the global mean phytoplankton CN ratio will decrease (Fig. 5a), resulting in less assimilation and sequestration of carbon, and potentially generating feedback to accelerate climate change. In our model, temperature affects not only nutrient supply through stratification but also resource allocation and the resultant phytoplankton CN ratio (Fig. 5b). Rising oceanic temperatures due to climate change enhances carbon acquisition through photosynthesis, more so than it increases the rate of nutrient uptake; hence, increasing temperatures increase the phytoplankton CN ratio. Since the dependence of the phytoplankton CN ratio on temperature is not necessarily clear in metaanalyses of culture experiments (Yvon-Durocher et al. 2015;Tanioka and Matsumoto 2020), further studies are needed to clarify temperature effects on the phytoplankton CN ratio.