Biological Stoichiometry Research Articles

Knowledge‐Based Deep Learning to Predict Vegetation Carbon, Nitrogen and Phosphorus Densities in China’s Shrublands

AbstractAccurate estimations of carbon (C), nitrogen (N), and phosphorus (P) densities in shrublands are pivotal for assessing terrestrial ecosystem carbon sequestration. Combining in‐situ investigations and machine learning facilitates large‐scale patterns mapping, however, which often overlooks underlying ecological regulations. Here we utilize data from 1,122 survey plots across China's shrublands and develop a novel knowledge‐based deep learning framework that integrates a structural equation model (SEM) to elucidate mechanisms and construct an artificial neural network (ANN) based on these causal relationships. Results show that biomass allocation to different organs follows allometric regulations and that N and P concentrations maintain a degree of stoichiometric homeostasis following biological stoichiometry theory. This insight guides the construction of our ANN, which outperforms both SEM and other prevalent machine learning methods. By leveraging ecological theories to inform model construction, our framework not only enhances prediction accuracy and explainability but also provides a methodological blueprint for ecological research.

Disentangling the Ecological Processes and Driving Forces Shaping the Seasonal Pattern of Halobacteriovorax Communities in a Subtropical Estuary.

Halobacteriovorax are predatory bacteria that have a significant ecological role in marine environments. However, understanding of dynamics of populations, driving forces, and community composition of Halobacteriovorax groups in natural marine environments is still limited. Here, we used high-throughput sequencing to study the underlying mechanisms governing the diversity and assembly of the Halobacteriovorax community at spatiotemporal scales in a subtropical estuary. Phylogenetic analysis showed that 10 of 15 known Halobacteriovorax clusters were found in the studied estuary. Halobacteriovorax α-diversity and β-diversity exhibited significant seasonal variation. Variation partitioning analysis showed that the effect of nutrients was greater than that of other measured water properties on Halobacteriovorax community distribution. The results of Spearman's and Mantel's tests indicated that the trophic pollutants dissolved inorganic phosphorus (DIP) and NH4+-N in the estuary were the key factors that significantly affected Halobacteriovorax species and community diversity. In addition, this work indicated that the biological stoichiometry (especially N/P) of nutrients exerted a significant influence on the Halobacteriovorax community. Furthermore, we found that both deterministic and stochastic processes contributed to the turnover of Halobacteriovorax communities, and environmental filtering dominated the assembly of estuarine Halobacteriovorax communities. Overall, we provide new insights into the mechanisms in the generation and maintenance of the Halobacteriovorax community in marine environments.

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.

Dynamics and Growth Rate Implications of Ribosomes and mRNAs Interaction in <i>E. coli</i>

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.

The Mid-Atlantic Bight Dissolved Inorganic Carbon System Observed in the March 1996 DOE Ocean Margins Program (OMP)—A Baseline Study

The United States Department of Energy (DOE)’s Ocean Margins Program (OMP) cruise EN279 in March 1996 provides an important baseline for assessing long-term changes in the carbon cycle and biogeochemistry in the Mid-Atlantic Bight (MAB) as climate and anthropogenic changes have been substantial in this region over the past two decades. The distributions of O2, nutrients, and marine inorganic carbon system parameters are influenced by coastal currents, temperature gradients, and biological production and respiration. On the cross-shelf direction, pH decreases seaward, but carbonate saturation state (ΩArag) does not exhibit a clear trend. In contrast, ΩArag increases from north to south, while pH has no clear spatial patterns in the along-shelf direction. In order to distinguish between the effects of physical mixing of various water masses and those of biological activities on the marine inorganic carbon system, we use the potential temperature-salinity diagram to identify water masses, and differences between observations and theoretical mixing concentrations to measure the non-conservative (primarily biological) effects. Our analysis clearly shows the degree to which ocean margin pH and ΩArag are regulated by biological activities in addition to water mass mixing, gas exchange, and temperature. The correlations among anomalies in dissolved inorganic carbon, phosphate, nitrate, and apparent oxygen utilization agree with known biological stoichiometry. Biological uptake is substantial in nearshore waters and in shelf-slope mixing areas. This work provides valuable baseline information to assess the more recent changes in the marine inorganic carbon system and the status of coastal ocean acidification.

Understanding the evolution of nutritive taste in animals: Insights from biological stoichiometry and nutritional geometry.

A major conceptual gap in taste biology is the lack of a general framework for understanding the evolution of different taste modalities among animal species. We turn to two complementary nutritional frameworks, biological stoichiometry theory and nutritional geometry, to develop hypotheses for the evolution of different taste modalities in animals. We describe how the attractive tastes of Na‐, Ca‐, P‐, N‐, and C‐containing compounds are consistent with principles of both frameworks based on their shared focus on nutritional imbalances and consumer homeostasis. Specifically, we suggest that the evolution of multiple nutritive taste modalities can be predicted by identifying individual elements that are typically more concentrated in the tissues of animals than plants. Additionally, we discuss how consumer homeostasis can inform our understanding of why some taste compounds (i.e., Na, Ca, and P salts) can be either attractive or aversive depending on concentration. We also discuss how these complementary frameworks can help to explain the evolutionary history of different taste modalities and improve our understanding of the mechanisms that lead to loss of taste capabilities in some animal lineages. The ideas presented here will stimulate research that bridges the fields of evolutionary biology, sensory biology, and ecology.

Biological Stoichiometric Analysis during Substrate Utilization and Secondary Metabolite Production by Non-Saccharomyces Yeasts Using Grape Pomace Extract as Fermentation Medium

The emerging interest in the search for alternatives to synthetic preservatives has led to various successful research studies exploring the use of yeasts as potential biological control agents and producers of biopreservatives. The findings that yeasts could be used as producers of biopreservatives lacked some engineering considerations regarding cost-effective process design for scale-up, although partial process optimization using renewable agro-waste has been achieved. This study investigated the biological stoichiometry and bioenergetic parameters during yeast growth and secondary metabolites production i.e., biopreservatives from non-Saccharomyces yeasts using grape pomace extract (GPE), a type of agro-waste, as a fermentation medium. This was achieved by reconfirming the optimum production conditions previously found for Candida pyralidae Y1117, Pichia kluyveri Y1125, and Pichia kluyveri Y1164 in GPE broth as a fermentation medium, conditions under which a high amount of yeast cells were obtained. High-density cell cultures were produced, from which the yeast cell pellets were harvested, dried, and combusted for the determination of elemental analysis, heat of combustion, biological stoichiometry, and bioenergetic parameters. This work generated biological stoichiometric models and bioenergetics information that could assist in the design of yeast biochemical conversion system when GPE is used as fermentation medium, thereby, addressing the biochemical engineering aspects that were lacking in a previous biopreservative production study using Candida pyralidae Y1117, Pichia kluyveri Y1125, and Pichia kluyveri Y1164.

Biological stoichiometry and growth dynamics of a diazotrophic cyanobacteria in nitrogen sufficient and deficient conditions

The role of nitrogen (N) fixation in determining the frequency, magnitude, and extent of harmful algal blooms (HABs) has not been well studied. Dolichospermum is a common HAB species that is diazotrophic (capable of N fixation) and thus growth is often considered never to be limited by low combined N sources. However, N fixation is energetically expensive and its cost during bloom formation has not been quantified. Additionally, it is unknown how acclimation to differing nutrient ratios affects growth and cellular carbon (C):N stoichiometry. Here, we test the hypotheses that diazotrophic cyanobacteria are homeostatic for N because of their ability to fix atmospheric N2 and that previous acclimation to low N environments will result in more fixed N and lower C:N stoichiometry. Briefly, cultures that varied in resource N:phosphorus (P) ranging from 0.01 to 100 (atom), were seeded with Dolichospermum which were previously acclimated to low and high N:P conditions and then sampled temporally for growth and C:N stoichiometry. We found that Dolichospermum was not homeostatic for N and displayed classic signs of N limitation and elevated C:N stoichiometry, highlighting the necessary growth trade-off within cells when expending energy to fix N. Acclimation to N limited conditions caused differences in both C:N and fixed N at various time points in the experiment. These results highlight the importance of environmentally available N to a diazotrophic bloom, as well as how previous growth conditions can influence population growth during blooms experiencing variable N:P.

Soil biological characteristic, nutrient contents and stoichiometry as affected by different types of remediation in a smelter-impacted soil

ABSTRACTIn order to evaluate the ecological risk reductions of copper (Cu) and cadmium (Cd) and the change of nutrient contents and stoichiometry in a smelter-impacted farmland in Guixi, Jiangxi Province, China, with ∼ 800 mg Cu kg−1 soil and 0.8 mg Cd kg−1 soil, an three years in situ experiment was conducted. The field trial consisted of 4 × 5 m plots in a completely randomised block design. Hydroxyapatite was added at 10 g kg−1 soil and Sedum plumbizincicola, Elsholtzia splendens, and Pennisetum sp. were planted. Post-treatment soil and plant samples were collected annually and analysed for Cu and Cd bioaccessibility, soil carbon: nitrogen: phosphorus (C:N:P), and the stoichiometries of soil β-glucosidase (BG), N-acetylglucosaminidase (NAG), and acid phosphatase (AP) activity levels. The results indicated that the hydroxyapatite treatments significantly reduced Cu and Cd bioaccessibility as well as the ratio of C:P and N:P. Moreover, BG, NAG, and AP activity levels all increased relative to those in untreated soil. Plants may also influence soil BG, NAG, and AP activity. This study demonstrated that in situ Cu and Cd stabilisation by hydroxyapatite and phytoextraction is ecologically safe and can alter soil mineral nutrient ecological stoichiometry and enzyme activity.

Efficient numerical method for a model arising in biological stoichiometry of tumour dynamics

In this paper, we extend a system of coupled first order non-linear system of delay differential equations (DDEs) arising in modeling of stoichiometry of tumour dynamics, to a system of diffusion-reaction system of partial delay differential equations (PDDEs). Since tumor cells are further modified by blood supply through the vascularization process, we determine the local uniform steady states of the homogeneous tumour growth model with respect to the vascularization process. We show that the steady states are globally stable, determine the existence of Hopf bifurcation of the homogeneous tumour growth model with respect to the vascularization process. We derive, analyse and implement a fitted operator finite difference method (FOFDM) to solve the extended model. This FOFDM is analyzed for convergence and we observe seen that it has second-order accuracy. Some numerical results confirming theoretical observations are also presented. These results are comparable with those obtained in the literature.

Stoichio-Metagenomics of Ocean Waters: A Molecular Evolution Approach to Trace the Dynamics of Nitrogen Conservation in Natural Communities.

Nitrogen is crucially limiting in ocean surface waters, and its availability varies substantially with coastal regions typically richer in nutrients than open oceans. In a biological stoichiometry framework, a parsimonious strategy of nitrogen allocation predicts nitrogen content of proteins to be lower in communities adapted to open ocean than to coastal regions. To test this hypothesis we have directly interrogated marine microbial communities, using a series of metagenomics datasets with a broad geographical distribution from the Global Ocean Sampling Expedition. Analyzing over 20 million proteins, we document a ubiquitous signal of nitrogen conservation in open ocean communities, both in membrane and non-membrane proteins. Efficient nitrogen allocation is expected to specifically target proteins that are expressed at high rate in response to nitrogen starvation. Furthermore, in order to preserve protein functional efficiency, economic nitrogen allocation is predicted to target primarily the least functionally constrained regions of proteins. Contrasting the NtcA-induced pathway, typically up-regulated in response to nitrogen starvation, with the arginine anabolic pathway, which is instead up-regulated in response to nitrogen abundance, we show how both these predictions are fulfilled. Using evolutionary rates as an informative proxy of functional constraints, we show that variation in nitrogen allocation between open ocean and coastal communities is primarily localized in the least functionally constrained regions of the genes triggered by NtcA. As expected, such a pattern is not detectable in the genes involved in the arginine anabolic pathway. These results directly link environmental nitrogen availability to different adaptive strategies of genome evolution, and emphasize the relevance of the material costs of evolutionary change in natural ecosystems.

Biological stoichiometry of oleaginous microalgal lipid synthesis: The role of N:P supply ratios and growth rate on microalgal elemental and biochemical composition

Biological Stoichiometry is an ecological framework connecting the balance of elements to the functioning of organisms. Here, we applied this framework to study the relationships between carbon:nitrogen:phosphorus (C:N:P) ratios and synthesis of industrial high value biochemicals in the highly oleaginous alga Tetradesmus bernardii. We expected an increase in protein content with increasing cellular N content and decreasing C:N stoichiometry, and an increase in lipid content with increasing C:N and C:P stoichiometry. We tested these hypotheses by exposing T. bernardii to N and P limitation at a range of N:P supply ratios in chemostats set at low and high dilution rates. Following expectations, the cellular protein content increased with the N content, and decreased with cellular C:N ratios across all treatments. Carbohydrates and lipids largely followed the relative availability of C and increased under both N and P limitation, with higher C:N and C:P ratios. Specifically, lipid content increased by 100–125% upon N and P limitation, with a shift towards more neutral lipids at the cost of glycolipids and phospholipids. Generally, we observed a re-allocation of cellular C from protein to carbohydrates upon modest N limitation, and towards lipids under P and severe N limitation. Our results demonstrate stoichiometrically predictable patterns of industrially valuable compounds in an oleaginous microalga.

Biodiversity of arbuscular mycorrhizal fungi and ecosystem function.

Contents Summary 1059 I. Introduction: pathways of influence and pervasiveness of effects 1060 II. AM fungal richness effects on ecosystem functions 1062 III. Other dimensions of biodiversity 1062 IV. Back to basics - primary axes of niche differentiation by AM fungi 1066 V. Functional diversity of AM fungi - a role for biological stoichiometry? 1067 VI. Past, novel and future ecosystems 1068 VII. Opportunities and the way forward 1071 Acknowledgements 1072 References 1072 SUMMARY: Arbuscular mycorrhizal (AM) fungi play important functional roles in ecosystems, including the uptake and transfer of nutrients, modification of the physical soil environment and alteration of plant interactions with other biota. Several studies have demonstrated the potential for variation in AM fungal diversity to also affect ecosystem functioning, mainly via effects on primary productivity. Diversity in these studies is usually characterized in terms of the number of species, unique evolutionary lineages or complementary mycorrhizal traits, as well as the ability of plants to discriminate among AM fungi in space and time. However, the emergent outcomes of these relationships are usually indirect, and thus context dependent, and difficult to predict with certainty. Here, we advocate a fungal-centric view of AM fungal biodiversity-ecosystem function relationships that focuses on the direct and specific links between AM fungal fitness and consequences for their roles in ecosystems, especially highlighting functional diversity in hyphal resource economics. We conclude by arguing that an understanding of AM fungal functional diversity is fundamental to determine whether AM fungi have a role in the exploitation of marginal/novel environments (whether past, present or future) and highlight avenues for future research.

An Operational Framework for the Advancement of a Molecule-to-Biosphere Stoichiometry Theory

Biological stoichiometry is an approach that focuses on the balance of elements in biological interactions. It is a theory that has the potential to causally link material processes at all biological levels – from molecules to the biosphere. But the lack of a coherent operational framework has so far restricted progress in this direction. Here, we provide a framework to help infer how a stoichiometric imbalance observed at one level impacts all other biological levels. Our framework enables us to high the areas of the theory in need of completion, development and integration at all biological levels. Our hope is that this framework will contribute to the building of a more predictive theory of elemental transfers within the biosphere, and thus, to a better understanding of human-induced perturbations to the global biogeochemical cycles.

Biological stoichiometry and bioenergetics of Fusarium oxysporum EKT01/02 proliferation using different substrates in cyanidation wastewater

AbstractCyanidation wastewater contains heavy metals, including high concentrations of ammonia and free cyanide (CN‐). Aerobic growth of Fusarium oxysporum EKT01/02 in synthetic gold mine wastewater under different substrates was examined using biological stoichiometry and thermodynamic models in batch systems. The molecular weight of the dry biomass obtained was 23.03 g/C‐mol, 33.14 g C‐mol−1, and 27.06 g/C‐mol in glucose with ammonia (GA), Beta vulgaris with ammonia (BA), and B. vulgaris with cyanide (BCN) cultures, respectively. The microbial growth model showed the highest biomass yield of 0.69 g dry cell/g substrate in BA cultures. The heat of reaction () and Gibbs energy dissipation per mole of biomass formed () were −652.55/−432.11 kJ/C‐mol, −132.59/−471.19 kJ/C‐mol, and −370.34/−225.35 kJ/C‐mol‐ for GA, BA, and BCN cultures, respectively. The total Gibbs energy dissipated increased steadily over time and the metabolic rate of the F. oxysporum used was minimally adversely affected by the cyanidation wastewater as shown by the degree of reduction including the respiratory quotient quantified. The F. oxysporum proliferation was determined to be enthalpically driven in the cultures studied. This study revealed that the use of B. vulgaris agro‐waste for the bioremediation of cyanidation wastewater is feasible and could engender sustainability of gold mining wastewater treatment processes.

Do deposit-feeders compete? Isotopic niche analysis of an invasion in a species-poor system.

Successful establishment of invasive species is often related to the existence of vacant niches. Competition occurs when invaders use the same limiting resources as members of the recipient community, which will be reflected in some overlap of their trophic niches. The concept of isotopic niche has been used to study trophic niche partitioning among species. Here, we present a two-year field study comparing isotopic niches of the deposit-feeding community in a naturally species-poor system. The isotopic niche analyses showed no overlap between a recent polychaete invader and any of the native species suggesting that it has occupied a vacant niche. Its narrow isotopic niche suggests specialized feeding, however, the high δ15N values compared to natives are most likely due to isotope fractionation effects related to nitrogen recycling and a mismatch between biological stoichiometry of the polychaete and the sediment nitrogen content. Notably, highly overlapping isotopic niches were inferred for the native species, which is surprising in a food-limited system. Therefore, our results demonstrate that invaders may broaden the community trophic diversity and enhance resource utilization, but also raise questions about the congruence between trophic and isotopic niche concepts and call for careful examination of assumptions underlying isotopic niche interpretation.

Differential Nutrient Limitation of Soil Microbial Biomass and Metabolic Quotients (qCO2): Is There a Biological Stoichiometry of Soil Microbes?

BackgroundVariation in microbial metabolism poses one of the greatest current uncertainties in models of global carbon cycling, and is particularly poorly understood in soils. Biological Stoichiometry theory describes biochemical mechanisms linking metabolic rates with variation in the elemental composition of cells and organisms, and has been widely observed in animals, plants, and plankton. However, this theory has not been widely tested in microbes, which are considered to have fixed ratios of major elements in soils.Methodology/Principal FindingsTo determine whether Biological Stoichiometry underlies patterns of soil microbial metabolism, we compiled published data on microbial biomass carbon (C), nitrogen (N), and phosphorus (P) pools in soils spanning the global range of climate, vegetation, and land use types. We compared element ratios in microbial biomass pools to the metabolic quotient qCO2 (respiration per unit biomass), where soil C mineralization was simultaneously measured in controlled incubations. Although microbial C, N, and P stoichiometry appeared to follow somewhat constrained allometric relationships at the global scale, we found significant variation in the C∶N∶P ratios of soil microbes across land use and habitat types, and size-dependent scaling of microbial C∶N and C∶P (but not N∶P) ratios. Microbial stoichiometry and metabolic quotients were also weakly correlated as suggested by Biological Stoichiometry theory. Importantly, we found that while soil microbial biomass appeared constrained by soil N availability, microbial metabolic rates (qCO2) were most strongly associated with inorganic P availability.Conclusions/SignificanceOur findings appear consistent with the model of cellular metabolism described by Biological Stoichiometry theory, where biomass is limited by N needed to build proteins, but rates of protein synthesis are limited by the high P demands of ribosomes. Incorporation of these physiological processes may improve models of carbon cycling and understanding of the effects of nutrient availability on soil C turnover across terrestrial and wetland habitats.

Biological Stoichiometry in Tumor Micro-environments

Tumors can be viewed as evolving ecological systems, in which heterogeneous populations of cancer cells compete with each other and somatic cells for space and nutrients within the ecosystem of the human body. According to the growth rate hypothesis (GRH), increased phosphorus availability in an ecosystem, such as the tumor micro-environment, may promote selection within the tumor for a more proliferative and thus potentially more malignant phenotype. The applicability of the GRH to tumor growth is evaluated using a mathematical model, which suggests that limiting phosphorus availability might promote intercellular competition within a tumor, and thereby delay disease progression. It is also shown that a tumor can respond differently to changes in its micro-environment depending on the initial distribution of clones within the tumor, regardless of its initial size. This suggests that composition of the tumor as a whole needs to be evaluated in order to maximize the efficacy of therapy.

Modelling the role of highly unsaturated fatty acids in planktonic food web processes: Sensitivity analysis and examination of contemporary hypotheses

Aquatic food web models typically treat the constituent trophic levels as static elements interacting with one another and the environment. Dynamic biological stoichiometry has relaxed this assumption and considers evolutionary responses in said elements. The incorporation of organismal response in food web models holds promise for a more realistic portrayal of ecosystem dynamics. Recent advances in aquatic ecology pinpoint the importance of highly unsaturated fatty acids (HUFAs) on food web interactions and ecosystem resilience. In this study, we utilized a HUFA explicit submodel in conjunction with a limiting nutrient–phytoplankton–zooplankton–detritus (NPZD) mathematical system to incorporate elements of the physiology of individual animals into the context of plankton dynamics. Our HUFA-augmented plankton model provided a realistic platform to examine functional properties and physiological strategies that modulate resource procurement in different trophic environments and to effectively link variability at the organismal level with ecosystem-scale patterns. First, we were able to illustrate the implications of the filling-cup hypothesis, in which species’ fitness stems from dynamic HUFA turnover rates in response to bottom-up stresses. We then examined an evolutionary hypothesis of consumer fitness dependence on HUFA quota management strategies, whereby adaptive individuals with low HUFA minimum and optimum requirements gain competitive advantage. Several studies have reported higher HUFA concentrations in consumers than producers, and our results suggest that this pattern could be driven by a combination of conservative turnover and elevated bioconversion rates. Oligotrophic settings showed strong reliance upon exogenous phosphorus subsidies and frequently yielded inverted food web biomass distributions. With the prevalence of eutrophic conditions, consumer growth is primarily controlled by HUFA availability, and the associated biochemical limitation can ultimately result in patterns of algal accumulation. Finally, our study discusses directions to improve the representation of the producer–grazer interactions and thus advance our understanding of the factors that determine the flow of nutrients and energy to the higher trophic levels.

Lotka re-loaded: Modeling trophic interactions under stoichiometric constraints

Nearly a century ago A.J. Lotka provided fundamental formulations for population modeling; less appreciated are his explorations of the underlying material (elemental) basis of life and its implications for ecology and evolution. This paper describes recent developments in ecological and biological stoichiometry that unify these aspects of Lotka's work. Stoichiometrically explicit versions of the Lotka–Volterra equations capture key missing aspects of food web interactions, such as the effects of food quality and nutrient recycling feedbacks, and encompass a richer, and potentially more realistic, set of dynamics than non-stoichiometric models. These stoichiometric models are now being further extended to include the recently discovered effects of excess dietary nutrient content on consumer performance. The multi-dimensional capacity of stoichiometric models is likely to be of particular value given the pressing need to anticipate the ecological effects of globally dynamic perturbations of multiple chemical elements (e.g. C, N, and P) due to human actions.