Lotka re-loaded: Modeling trophic interactions under stoichiometric constraints

Theory of Stoichiometric Intraguild Predation: Algae, Ciliate, and Daphnia

Consumers respond differently to external nutrient changes than producers, resulting in a mismatch in elemental composition between them and potentially having a significant impact on their interactions. To explore the responses of herbivores and omnivores to changes in elemental composition in producers, we develop a novel stoichiometric model with an intraguild predation structure. The model is validated using experimental data, and the results show that our model can well capture the growth dynamics of these three species. Theoretical and numerical analyses reveal that the model exhibits complex dynamics, including chaotic-like oscillations and multiple types of bifurcations, and undergoes long transients and regime shifts. Under moderate light intensity and phosphate concentration, these three species can coexist. However, when the light intensity is high or the phosphate concentration is low, the energy enrichment paradox occurs, leading to the extinction of ciliate and Daphnia. Furthermore, if phosphate is sufficient, the competitive effect of ciliate and Daphnia on algae will be dominant, leading to competitive exclusion. Notably, when the phosphorus-to-carbon ratio of ciliate is in a suitable range, the energy enrichment paradox can be avoided, thus promoting the coexistence of species. These findings contribute to a deeper understanding of species coexistence and biodiversity.

Ecosystem-level effects of re-oligotrophication and N:P imbalances in rivers and estuaries on a global scale

Trends and ecological consequences of phosphorus (P) decline and increasing nitrogen (N) to phosphorus (N:P) ratios in rivers and estuaries are reviewed and discussed. Results suggest that re-oligotrophication is a dominant trend in rivers and estuaries of high-income countries in the last two-three decades, while in low-income countries widespread eutrophication occurs. The decline in P is well documented in hundreds of rivers of United States and the European Union, but the biotic response of rivers and estuaries besides phytoplankton decline such as trends in phytoplankton composition, changes in primary production, ecosystem shifts, cascading effects, changes in ecosystem metabolism, etc., have not been sufficiently monitored and investigated, neither the effects of N:P imbalance. N:P imbalance has significant ecological effects that need to be further investigated. There is a growing number of cases in which phytoplankton biomass have been shown to decrease due to re-oligotrophication, but the potential regime shift from phytoplankton to macrophyte dominance described in shallow lakes has been documented only in a few rivers and estuaries yet. The main reasons why regime shifts are rarely described in rivers and estuaries are, from one hand the scarcity of data on macrophyte cover trends, and from the other hand physical factors such as peak flows or high turbidity that could prevent a general spread of submerged macrophytes as observed in shallow lakes. Moreover, re-oligotrophication effects on rivers may be different compared to lakes (e.g., lower dominance of macrophytes) or estuaries (e.g., limitation of primary production by N instead of P) or may be dependent on river/estuary type. We conclude that river and estuary re-oligotrophication effects are complex, diverse and still little known, and in some cases are equivalent to those described in shallow lakes, but the regime shift is more likely to occur in mid to high-order rivers and shallow estuaries.

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.

Stoichiometric constraints modulate temperature and nutrient effects on biomass distribution and community stability

Temperature and nutrients are two of the most important drivers of global change. Both can modify the elemental composition (i.e. stoichiometry) of primary producers and consumers. Yet their combined effect on the stoichiometry, dynamics and stability of ecological communities remains largely unexplored. To fill this gap, we extended the Rosenzweig-MacArthur consumer-resource model by including thermal dependencies, nutrient dynamics and stoichiometric constraints on both the primary producer and the consumer. We found that stoichiometric and nutrient conservation constraints dampen the paradox of enrichment and increased persistence at high nutrient levels. Nevertheless, stoichiometric constraints also reduced consumer persistence at extreme temperatures. Finally, we also found that stoichiometric constraints and nutrient dynamics can strongly influence biomass distribution across trophic levels by modulating consumer assimilation efficiency and resource growth rates along the environmental gradients. In the Rosenzweig-MacArthur model, consumer biomass exceeded resource biomass for most parameter values whereas, in the stoichiometric model, consumer biomass was strongly reduced and sometimes lower than resource biomass. Our findings highlight the importance of accounting for stoichiometric constraints as they can mediate the temperature and nutrient impact on the dynamics and functioning of ecological communities.

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.

Stoichiometric Ecotoxicology for a Multisubstance World

Nutritional and contaminant stressors influence organismal physiology, trophic interactions, community structure, and ecosystem-level processes; however, the interactions between toxicity and elemental imbalance in food resources have been examined in only a few ecotoxicity studies. Integrating well-developed ecological theories that cross all levels of biological organization can enhance our understanding of ecotoxicology. In the present article, we underline the opportunity to couple concepts and approaches used in the theory of ecological stoichiometry (ES) to ask ecotoxicological questions and introduce stoichiometric ecotoxicology, a subfield in ecology that examines how contaminant stress, nutrient supply, and elemental constraints interact throughout all levels of biological organization. This conceptual framework unifying ecotoxicology with ES offers potential for both empirical and theoretical studies to deepen our mechanistic understanding of the adverse outcomes of chemicals across ecological scales and improve the predictive powers of ecotoxicology.

Coexistence and extinction in a data-based ratio-dependent model of an insect community

In theory, pure competition often leads to competitive exclusion of species. However, what we often see in nature is a large number of distinct predator or consumer species coexist in a community consisting a smaller number of prey or plant species. In an effort of dissecting how indirect competition and selective predation may have contributed to the coexistence of species in an insect community, according to the replicated cage experiments (two aphid species and a specialist parasitoid that attacks only one of the aphids) and proposed mathematical models, van Veen et. al. [5] conclude that the coexistence of the three species is due to a combination of density-mediated and trait-mediated indirect interactions. In this paper, we formulate an alternative model that observes the conventional law of mass conservation and provides a better fitting to their experimental data sets. Moreover, we present an initial attempt in studying the stabilities of the nonnegative steady states of this model.

The effects of excess food nutrient content on a tritrophic food chain model in the aquatic ecosystem

Ecological stoichiometry is an approach that focuses on the balance of energy and elements in environmental interactions, and it leads to new insights and a better understanding of ecological processes and outcomes. Modeling under this framework enables us to investigate the effects of nutrient content (i.e., food quality) on organisms, whether the imbalance involves insufficient or excess nutrient content. In this paper, we develop and analyze a tritrophic food chain model that captures the phenomenon known as the "stoichiometric knife-edge", where consumer growth is limited under conditions of excess nutrients. The model tracks two essential elements, carbon and phosphorus, in each species. The dynamics of the system such as boundedness and positivity of the solutions, existence and stability conditions of boundary and internal equilibria are analyzed. Through numerical simulations and bifurcation analyses, we observe the dynamics of the system switching between periodic oscillations and chaos. Our findings also show that nutrient-rich food consumption can cause adverse effects on species.

The fitness of chemotrophs increases when their catabolic by-products are consumed by other species

Chemotrophic microorganisms synthesise biomass by utilising energy obtained from a set of chemical reactions that convert resources to by-products, forming catabolic interactions. The amount of energy obtained per catabolic reaction decreases with the abundance of the by-product named as the 'abundant resource premium'. Consider two species, Species 1 and 2, Species 1 obtains energy from a reaction that converts resource A to by-product B. Species 2 then utilises B as its resource, extracting energy from a reaction that converts B to C. Thus, the presence of Species 2 reduces the abundance of B, which improves the fitness of Species 1 by increasing the energy acquisition per reaction of A to B. We discuss the population dynamic implication of this effect and its importance in expanding a realised niche, boosting material flow through the ecosystem and providing mutualistic interactions among species linked by the material flow. Introducing thermodynamics into population ecology could offer us fundamental ecological insights into understanding the ecology of chemotrophic microorganisms dominating the subsurface realm.

Elevated carbon dioxide increases soil nitrogen and phosphorus availability in a phosphorus-limited Eucalyptus woodland

Free-air CO2 enrichment (FACE) experiments have demonstrated increased plant productivity in response to elevated (e)CO2, with the magnitude of responses related to soil nutrient status. Whilst understanding nutrient constraints on productivity responses to eCO2 is crucial for predicting carbon uptake and storage, very little is known about how eCO2 affects nutrient cycling in phosphorus (P)-limited ecosystems. Our study investigates eCO2 effects on soil N and P dynamics at the EucFACE experiment in Western Sydney over an 18-month period. Three ambient and three eCO2 (+150 ppm) FACE rings were installed in a P-limited, mature Cumberland Plain Eucalyptus woodland. Levels of plant accessible nutrients, evaluated using ion exchange resins, were increased under eCO2, compared to ambient, for nitrate (+93%), ammonium (+12%) and phosphate (+54%). There was a strong seasonality to responses, particularly for phosphate, resulting in a relatively greater stimulation in available P, compared to N, under eCO2 in spring and summer. eCO2 was also associated with faster nutrient turnover rates in the first six months of the experiment, with higher N (+175%) and P (+211%) mineralization rates compared to ambient rings, although this difference did not persist. Seasonally dependant effects of eCO2 were seen for concentrations of dissolved organic carbon in soil solution (+31%), and there was also a reduction in bulk soil pH (-0.18 units) observed under eCO2. These results demonstrate that CO2 fertilization increases nutrient availability - particularly for phosphate - in P-limited soils, likely via increased plant belowground investment in labile carbon and associated enhancement of microbial turnover of organic matter and mobilization of chemically bound P. Early evidence suggests that there is the potential for the observed increases in P availability to support increased ecosystem C-accumulation under future predicted CO2 concentrations.