Revisiting the growth rate hypothesis: Towards a holistic stoichiometric understanding of growth.

The growth rate hypothesis (GRH) posits that variation in organismal stoichiometry (C:P and N:P ratios) is driven by growth-dependent allocation of P to ribosomal RNA. The GRH has found broad but not uniform support in studies across diverse biota and habitats. We synthesise information on how and why the tripartite growth-RNA-P relationship predicted by the GRH may be uncoupled and outline paths for both theoretical and empirical work needed to broaden the working domain of the GRH. We found strong support for growth to RNA (r2  = 0.59) and RNA-P to P (r2  = 0.63) relationships across taxa, but growth to P relationships were relatively weaker (r2  = 0.09). Together, the GRH was supported in ~50% of studies. Mechanisms behind GRH uncoupling were diverse but could generally be attributed to physiological (P accumulation in non-RNA pools, inactive ribosomes, translation elongation rates and protein turnover rates), ecological (limitation by resources other than P), and evolutionary (adaptation to different nutrient supply regimes) causes. These factors should be accounted for in empirical tests of the GRH and formalised mathematically to facilitate a predictive understanding of growth.

Elevated CO2 affects kelp nutrient quality: A case study of Saccharina japonica from CO2 -enriched coastal mesocosm systems.

Kelps provide critical services for coastal food chains and ecosystem, and they are important food source for some segments of human population. Despite their ecological importance, little is known about long-term impacts of elevated CO2 (eCO2 ) on nutrient metabolites in kelps and the underlying regulation mechanisms. In this study, the kelp Saccharina japonica was cultured in CO2 -enriched coastal mesocosm systems for up to 3 months. We found that, although eCO2 significantly increased the growth rate, carbon concentrations, and C/N ratio of S. japonica, and it had no effect on total nitrogen and protein contents at the end of cultivation period. Meanwhile, it decreased the lipid, magnesium, sodium, and calcium content and changed the amino acid and fatty acid composition. Combining the genome-wide transcriptomic and metabolic evidence, we obtained a system-level understanding of metabolic response of S. japonica to eCO2 . The unique ornithine-urea cycle (OUC) and aspartate-argininosuccinate shunt (AAS), coupled with TCA cycle, balanced the carbon and nitrogen metabolism under eCO2 by providing carbon skeleton for amino acid synthesis and reduced power for nitrogen assimilation. This research provides a major advance in the understanding of kelp nutrient metabolic mechanism in the context of global climate change, and such CO2 -induced shifts in nutritional value may induce changes in the structure and stability of marine trophic webs and affect the quality of human nutrition resources.

Rising atmospheric CO2 is reducing the protein concentration of a floral pollen source essential for North American bees.

At present, there is substantive evidence that the nutritional content of agriculturally important food crops will decrease in response to rising levels of atmospheric carbon dioxide, Ca However, whether Ca-induced declines in nutritional quality are also occurring for pollinator food sources is unknown. Flowering late in the season, goldenrod (Solidago spp.) pollen is a widely available autumnal food source commonly acknowledged by apiarists to be essential to native bee (e.g. Bombus spp.) and honeybee (Apis mellifera) health and winter survival. Using floral collections obtained from the Smithsonian Natural History Museum, we quantified Ca-induced temporal changes in pollen protein concentration of Canada goldenrod (Solidago canadensis), the most wide spread Solidago taxon, from hundreds of samples collected throughout the USA and southern Canada over the period 1842-2014 (i.e. a Ca from approx. 280 to 398 ppm). In addition, we conducted a 2 year in situtrial of S. Canadensis populations grown along a continuous Ca gradient from approximately 280 to 500 ppm. The historical data indicated a strong significant correlation between recent increases in Ca and reductions in pollen protein concentration (r(2)= 0.81). Experimental data confirmed this decrease in pollen protein concentration, and indicated that it would be ongoing as Ca continues to rise in the near term, i.e. to 500 ppm (r(2)= 0.88). While additional data are needed to quantify the subsequent effects of reduced protein concentration for Canada goldenrod on bee health and population stability, these results are the first to indicate that increasing Ca can reduce protein content of a floral pollen source widely used by North American bees.

Down-regulation of tissue N:P ratios in terrestrial plants by elevated CO2.

Increasing atmospheric CO2 concentrations generally alter element stoichiometry in plants. However, a comprehensive evaluation of the elevated CO2 impact on plant nitrogen: phosphorus (N:P) ratios and the underlying mechanism has not been conducted. We synthesized the results from 112 previously published studies using meta-analysis to evaluate the effects of elevated CO2 on the N:P ratio of terrestrial plants and to explore the underlying mechanism based on plant growth and soil P dynamics. Our results show that terrestrial plants grown under elevated CO2 had lower N:P ratios in both above- and belowground biomass across different ecosystem types. The response ratio for plant N:P was negatively correlated with the response ratio for plant growth in croplands and grasslands, and showed a stronger relationship for P than for N. In addition, the CO2-induced down-regulation of plant N:P was accompanied by 19.3% and 4.2% increases in soil phosphatase activity and labile P, respectively, and a 10.1% decrease in total soil P. Our results show that down-regulation of plant N:P under elevated CO2 corresponds with accelerated soil P cycling. These findings should be useful for better understanding of terrestrial plant stoichiometry in response to elevated CO2 and of the underlying mechanisms affecting nutrient dynamics under climate change.

Subsurface fertilization boosts crop yields and lowers greenhouse gas emissions: A global meta-analysis.

The subsurface application (SA) of nitrogenous fertilizers is a potential solution to mitigate climate change and improve food security. However, the impacts of SA technology on greenhouse gas (GHG) emissions and agronomic yield are usually evaluated separately and their results are inconsistent. To address this gap, we conducted a meta-analysis synthesizing 40 peer-reviewed studies on the effects of SA technology on GHG and ammonia (NH3) emissions, nitrogen uptake (NU), crop yield, and soil residual NO3-N in rice paddies and upland cropping system. Compared to the surface application of N, SA technology significantly increased rice yields by 32 % and crop yield in upland systems by 62 %. The largest SA-induced increases in crop yield were found at low N input rates (<100 kg Nha-1) in rice paddies and medium N input rates (100-200 kg Nha-1) in upland systems, suggesting that soil moisture is a key factor determining the efficiency of SA technology. SA treatments increased yields by more at reduced fertilizer rates (~30 % less N), a shallow depth (<10 cm), and with urea in both cropping systems than at the full (recommended) N rate, a deeper depth (10-20 cm), and with ammonical fertilizer. SA treatments significantly increased NU in rice paddies (34 %) and upland systems (18 %), and NO3-N (40 %) in paddyland; however, NO3-N decreased (28 %) in upland conditions. Ammonia mitigation was greater in paddyland than in upland conditions. SA technology decreased the carbon footprint (CF) in paddyland by 29 % and upland systems by 36 %, and overall by 33 %. Compared with broadcasting, SA significantly reduced CH4 emissions by 16 %, N2O emissions by 30 %, and global warming potential (GWP) by 10 % in paddy cultivation. Given SA increased grain yield and NU while reducing NH3, CF, and GWP, this practice provides dual benefits - mitigating climate change and ensuring food security.

Eco-physiology and environmental impacts of newly developed rice genotypes for improved yield and nitrogen use efficiency coordinately.

Significant advancements have been made in understanding the genetic regulation of nitrogen use efficiency (NUE) and identifying crucial NUE genes in rice. However, the development of rice genotypes that simultaneously exhibit high yield and NUE has lagged behind these theoretical advancements. The grain yield, NUE, and greenhouse gas (GHG) emissions of newly-bred rice genotypes under reduced nitrogen application remain largely unknown. To address this knowledge gap, field experiments were conducted, involving 80 indica (14 to 19 rice genotypes each year in Wuxue, Hubei) and 12 japonica (8 to 12 rice genotypes each year in Yangzhou, Jiangsu). Yield, NUE, agronomy, and soil parameters were assessed, and climate data were recorded. The experiments aimed to assess genotypic variations in yield and NUE among these genotypes and to investigate the eco-physiological basis and environmental impacts of coordinating high yield and high NUE. The results showed significant variations in yield and NUE among the genotypes, with 47 genotypes classified as moderate-high yield with high NUE (MHY_HNUE). These genotypes demonstrated the higher yields and NUE levels, with 9.6 t ha-1, 54.4 kg kg-1, 108.1 kg kg-1, and 64 % for yield, NUE for grain and biomass production, and N harvest index, respectively. Nitrogen uptake and tissue concentration were key drivers of the relationship between yield and NUE, particularly N uptake at heading and N concentrations in both straw and grain at maturity. Increase in pre-anthesis temperature consistently lowered yield and NUE. Genotypes within the MHY_HNUE group exhibited higher methane emissions but lower nitrous oxide emissions compared to those in the low to middle yield and NUE group, resulting in a 12.8 % reduction in the yield-scaled greenhouse gas balance. In conclusion, prioritizing crop breeding efforts on yield and resource use efficiency, as well as developing genotypes resilient to high temperatures with lower GHGs, can mitigate planetary warming.

Dynamics and growth rate implications of ribosomes and mRNAs interaction in E. coli.

Understanding how cells grow and adapt under various nutrient conditions is pivotal in the study of biological stoichiometry. Recent studies provide empirical evidence that cells use multiple strategies to maintain an optimal protein production rate under different nutrient conditions. Mathematical models can provide a solid theoretical foundation that can explain experimental observations and generate testable hypotheses to further our understanding of the growth process. In this study, we generalize a modeling framework that centers on the translation process and study its asymptotic behaviors to validate algebraic manipulations involving the steady states. Using experimental results on the growth of E. coli under C-, N-, and P-limited environments, we simulate the expected quantitative measurements to show the feasibility of using the model to explain empirical evidence. Our results support the findings that cells employ multiple strategies to maintain a similar protein production rate across different nutrient limitations. Moreover, we find that the previous study underestimates the significance of certain biological rates, such as the binding rate of ribosomes to mRNA and the transition rate between different ribosomal stages. Furthermore, our simulation shows that the strategies used by cells under C- and P-limitations result in a faster overall growth dynamics than under N-limitation. In conclusion, the general modeling framework provides a valuable platform to study cell growth under different nutrient supply conditions, which also allows straightforward extensions to the coupling of transcription, translation, and energetics to deepen our understanding of the growth process.

Improving the accuracy of meta-analysis for datasets with missing measures of variance: Elevated [CO2] effect on plant growth as a case study.

Ongoing increases in atmospheric carbon dioxide (CO2) are expected to stimulate biomass and yield of plants possessing the C3 photosynthetic pathway; however, the extent of stimulation is likely to vary both intra- and inter-species specifically. Meta-analytic approaches can be applied to decrease variation and uncertainty by delineating and characterizing variation, allowing results to be used in modeling plant responses to elevated [CO2]. However, the use of meta-analysis in this effort could be limited by missing measures of variance, including standard deviations (SDs) of the compiled dataset. Here, we examined whether there were differences in effect sizes of elevated [CO2] on plant growth using various weighting and imputation approaches. Our results showed that the efficacy of different weighting functions and data interpolation methods on meta-analysis outcomes depended on the SDs provided by the studies. Comparing different methodologies for [CO2] fumigation as a case study, if the ratio of missing SD was low, the overall trend of effect values and 95% confidence interval (CI) were not changed. For datasets of greenhouse and growth chamber [CO2] methodologies, which had a high ratio of missing SDs, effect sizes and 95% confidence intervals using different weighing and imputation methods were influenced relative to that of the raw dataset, with reduced effect sizes and broader CI. Overall these results suggest that application of meta-analysis to discern general biological responses could be influenced by the number of missing SDs. As such, efforts should be made to check the proportion of missing SDs of the compiled dataset and if necessary, to apply various weighting functions and imputation methods to fully discern meta-analysis implications. Our findings could improve the assessment of methodological choices for future [CO2] experimentation and discerning long-term trends for agricultural productivity and food security.

The origins of the Redfield nitrogen-to-phosphorus ratio are in a homoeostatic protein-to-rRNA ratio.

One of the most intriguing patterns in the biosphere is the similarity of the atomic nitrogen-to-phosphorus ratio (N:P) = 16 found in waters throughout the deep ocean and in the plankton in the upper ocean. Although A.C. Redfield proposed in 1934 that the intracellular properties of plankton were central to this pattern, no theoretical significance for N:P = 16 in cells had been found. Here, we use theoretical modelling and a compilation of literature data for prokaryotic and eukaryotic microbes to show that the balance between two fundamental processes, protein and rRNA synthesis, results in a stable biochemical attractor that homoeostatically produces a given protein:rRNA ratio. Furthermore, when biochemical constants and reasonable kinetic parameters for protein synthesis and ribosome production under nutrient-replete conditions are applied in the model, it predicts a stable protein:rRNA ratio of 3 ± 0.7, which corresponds to N:P = 16 ± 3. The model also predicts that N-limitation, by constraining protein synthesis rates, will result in N:P ratios below the Redfield value while P-limitation, by constraining RNA production rates, will produce ratios above the Redfield value. Hence, one of most biogeochemically significant patterns on Earth is inherently rooted in the fundamental structure of life.

Climate Change, Crop Yields, and Grain Quality of C3 Cereals: A Meta-Analysis of [CO2], Temperature, and Drought Effects.

Cereal yield and grain quality may be impaired by environmental factors associated with climate change. Major factors, including elevated CO2 concentration ([CO2]), elevated temperature, and drought stress, have been identified as affecting C3 crop production and quality. A meta-analysis of existing literature was performed to study the impact of these three environmental factors on the yield and nutritional traits of C3 cereals. Elevated [CO2] stimulates grain production (through larger grain numbers) and starch accumulation but negatively affects nutritional traits such as protein and mineral content. In contrast to [CO2], increased temperature and drought cause significant grain yield loss, with stronger effects observed from the latter. Elevated temperature decreases grain yield by decreasing the thousand grain weight (TGW). Nutritional quality is also negatively influenced by the changing climate, which will impact human health. Similar to drought, heat stress decreases starch content but increases grain protein and mineral concentrations. Despite the positive effect of elevated [CO2], increases to grain yield seem to be counterbalanced by heat and drought stress. Regarding grain nutritional value and within the three environmental factors, the increase in [CO2] is possibly the more detrimental to face because it will affect cereal quality independently of the region.

Iterative chemostat: A modelling framework linking biosynthesis to nutrient cycling on ecological and evolutionary time scales.

In the classical chemostat, the output of the system has no effect on its input. This contrasts with many ecological systems, where the output at the end of a growing season affects nutrient inputs for subsequent seasons. Here, an iterative-continuous modelling framework is introduced that retains the structure of classical ecological models within each iteration but accounts for nutrient feedbacks between iterations. As an example, the framework is applied to the classical chemostat model, where nutrient outputs affect the supply ratio at each iteration. Furthermore, the biotic parameters in the model, including organismal demands for nitrogen (N) and phosphorus (P), are linked to core biogenic processes-protein and rRNA synthesis. This biosynthesis is further deconstructed into 11 biological constants and rates, most of which are deeply shared among all organisms. By linking the fundamental macromolecular machinery to the cycling of nutrients on the ecosystem scale, the framework enables to rigorously formulate qualitative and quantitative questions about the evolution of nutrient ratios and the existence of stoichiometric attractors, such as the puzzling persistence of the Redfield N:P ratio of 16 in the ocean. While the framework presented here is theoretical, it readily permits setting up empirical experiments for testing its predictions.

Rising Atmospheric CO2 Lowers Concentrations of Plant Carotenoids Essential to Human Health: A Meta-Analysis.

Plant and human tissues (e.g., leaves, retina) share the need for carotenoids to protect against light-induced and other oxidative stresses. While plants synthesize carotenoids de novo, humans must obtain them primarily through plant-based foods. In plants, elevated levels of atmospheric carbon dioxide (eCO2 ) decrease the concentrations of essential minerals, including magnesium and zinc (essential for brain and eye health), but the overall effect of globally rising CO2 levels on carotenoids is unknown. Here, investigation is sought on how eCO2 affects carotenoids in plants. A meta-analysis of 1026 experimental observations from 37 studies shows that eCO2 decreases plant carotenoid concentrations by 15% (95% CI: -26% to -6%). The meta-analysis of available gene expression data for Arabidopsis thaliana points to a potential CO2 -induced downregulation of carotenoid biosynthesis (Log2 fold-change -13%, 95% CI: -17% to -9%). Some other stoichiometric and biochemical mechanisms related to CO2 -induced changes in carotenoids are also highlighted. While overall eCO2 decreases carotenoid concentrations, individual CO2 studies report variable responses, including increases in carotenoid levels, especially in abiotically stressed plants. The initial assessment raises a novel question about the potential effects of rising CO2 on human health through its global effect on plant carotenoids.

Carbon dioxide (CO2) levels this century will alter the protein, micronutrients, and vitamin content of rice grains with potential health consequences for the poorest rice-dependent countries.

Declines of protein and minerals essential for humans, including iron and zinc, have been reported for crops in response to rising atmospheric carbon dioxide concentration, [CO2]. For the current century, estimates of the potential human health impact of these declines range from 138 million to 1.4 billion, depending on the nutrient. However, changes in plant-based vitamin content in response to [CO2] have not been elucidated. Inclusion of vitamin information would substantially improve estimates of health risks. Among crop species, rice is the primary food source for more than 2 billion people. We used multiyear, multilocation in situ FACE (free-air CO2 enrichment) experiments for 18 genetically diverse rice lines, including Japonica, Indica, and hybrids currently grown throughout Asia. We report for the first time the integrated nutritional impact of those changes (protein, micronutrients, and vitamins) for the 10 countries that consume the most rice as part of their daily caloric supply. Whereas our results confirm the declines in protein, iron, and zinc, we also find consistent declines in vitamins B1, B2, B5, and B9 and, conversely, an increase in vitamin E. A strong correlation between the impacts of elevated [CO2] on vitamin content based on the molecular fraction of nitrogen within the vitamin was observed. Finally, potential health risks associated with anticipated CO2-induced deficits of protein, minerals, and vitamins in rice were correlated to the lowest overall gross domestic product per capita for the highest rice-consuming countries, suggesting potential consequences for a global population of approximately 600 million.

Hidden shift of the ionome of plants exposed to elevated CO2depletes minerals at the base of human nutrition.

Mineral malnutrition stemming from undiversified plant-based diets is a top global challenge. In C3 plants (e.g., rice, wheat), elevated concentrations of atmospheric carbon dioxide (eCO2) reduce protein and nitrogen concentrations, and can increase the total non-structural carbohydrates (TNC; mainly starch, sugars). However, contradictory findings have obscured the effect of eCO2 on the ionome-the mineral and trace-element composition-of plants. Consequently, CO2-induced shifts in plant quality have been ignored in the estimation of the impact of global change on humans. This study shows that eCO2 reduces the overall mineral concentrations (-8%, 95% confidence interval: -9.1 to -6.9, p<0.00001) and increases TNC:minerals > carbon:minerals in C3 plants. The meta-analysis of 7761 observations, including 2264 observations at state of the art FACE centers, covers 130 species/cultivars. The attained statistical power reveals that the shift is systemic and global. Its potential to exacerbate the prevalence of 'hidden hunger' and obesity is discussed.DOI: http://dx.doi.org/10.7554/eLife.02245.001.

A stoichiometric producer-grazer model incorporating the effects of excess food-nutrient content on consumer dynamics.

There has been important progress in understanding ecological dynamics through the development of the theory of ecological stoichiometry. For example, modeling under this framework allows food quality to affect consumer dynamics. While the effects of nutrient deficiency on consumer growth are well understood, recent discoveries in ecological stoichiometry suggest that consumer dynamics are not only affected by insufficient food nutrient content (low phosphorus (P): carbon (C) ratio) but also by excess food nutrient content (high P:C). This phenomenon is known as the stoichiometric knife edge, in which animal growth is reduced not only by food with low P content but also by food with high P content, and needs to be incorporated into mathematical models. Here we present a Lotka-Volterra type model to investigate the growth response of Daphnia to algae of varying P:C ratios capturing the mechanism of the stoichiometric knife edge.

Dynamics of a mechanistically derived stoichiometric producer-grazer model.

One of the simplest predator-prey models that tracks the quantity and the quality of prey is the one proposed by [I. Loladze, Y. Kuang, and J.J. Elser, Stoichiometry in producer-grazer systems: Linking energy flow with element cycling, Bull. Math. Biol. 62 (2000) pp. 1137-1162.] (LKE model). In it, the ratio of two essential chemical elements, carbon to phosphorus, C:P, represents prey quality. However, that model does not explicitly track P neither in the prey nor in the media that supports the prey. Here, we extend the LKE model by mechanistically deriving and accounting for P in both the prey and the media. Bifurcation diagrams and simulations show that our model behaves similarly to the LKE model. However, in the intermediate range of the carrying capacity, especially near the homoclinic bifurcation point for the carrying capacity, quantitative behaviour of our model is different. We analyze positive invariant region and stability of boundary steady states. We show that as the uptake rate of P by producer becomes infinite, LKE models become the limiting case of our model. Furthermore, our model can be readily extended to multiple producers and consumers.

Competitive coexistence in stoichiometric chaos.

Classical predator-prey models, such as Lotka-Volterra, track the abundance of prey, but ignore its quality. Yet, in the past decade, some new and occasionally counterintuitive effects of prey quality on food web dynamics emerged from both experiments and mathematical modeling. The underpinning of this work is the theory of ecological stoichiometry that is centered on the fact that each organism is a mixture of multiple chemical elements such as carbon (C), nitrogen (N), and phosphorus (P). The ratios of these elements can vary within and among species, providing simple ways to represent prey quality as its C:N or C:P ratios. When these ratios modeled to vary, as they frequently do in nature, seemingly paradoxical results can arise such as the extinction of a predator that has an abundant and accessible prey. Here, for the first time, we show analytically that the reduction in prey quality can give rise to chaotic oscillations. In particular, when competing predators differ in their sensitivity to prey quality then all species can coexist via chaotic fluctuations. The chaos generating mechanism is based on the existence of a junction-fold point on the nullcline surfaces of the species. Conditions on parameters are found for such a point, and the singular perturbation method and the kneading sequence analysis are used to demonstrate the existence of a period-doubling cascade to chaos as a result of the point.

The dynamics of a stoichiometric plant-herbivore model and its discrete analog.

Stoichiometry-based models brought into sharp focus the importance of the nutritional quality of plant for herbivore-plant dynamics. Plant quality can dramatically affect the growth rate of the herbivores and may even lead to its extinction. These results stem from models continuous in time, which raises the question of how robust they are to time discretization. Discrete time can be more appropriate for herbivores with non-overlapping generations, annual plants, and experimental data collected periodically. We analyze a continuous stoichiometric plant-herbivore model that is mechanistically formulated. We then introduce its discrete analog and compare the dynamics of the continuous and discrete models. This discrete model includes the discrete LKE model (Loladze, Kuang and Elser (2000)) as a limiting case.

Biodiversity, habitat area, resource growth rate and interference competition.

For the majority of species, per capita growth rate correlates negatively with population density. Although the popular logistic equation for the growth of a single species incorporates this intraspecific competition, multi-trophic models often ignore self-limitation of the consumers. Instead, these models often assume that the predator-prey interactions are purely exploitative, employing simple Lotka-Volterra forms in which consumer species lack intraspecific competition terms. Here we show that intraspecific interference competition can account for the stable coexistence of many consumer species on a single resource in a homogeneous environment. In addition, our work suggests a potential mechanism for field observations demonstrating that habitat area and resource productivity strongly positively correlate to biodiversity. In the special case of a modified Lotka-Volterra model describing multiple predators competing for a single resource, we present an ordering procedure that determines the deterministic fate of each specific consumer. Moreover, we find that the growth rate of a resource species is proportional to the maximum number of consumer species that resource can support. In the limiting case, when the resource growth rate is infinite, a model with intraspecific interference reduces to the conventional Lotka-Volterra competition model where there can be an unlimited number of coexisting consumers. This highlights the crucial role that resource growth rates may play in promoting coexistence of consumer species.