Elements of disease in a changing world: modelling feedbacks between infectious disease and ecosystems.

An overlooked effect of ecosystem eutrophication is the potential to alter disease dynamics in primary producers, inducing disease-mediated feedbacks that alter net primary productivity and elemental recycling. Models in disease ecology rarely track organisms past death, yet death from infection can alter important ecosystem processes including elemental recycling rates and nutrient supply to living hosts. In contrast, models in ecosystem ecology rarely track disease dynamics, yet elemental nutrient pools (e.g. nitrogen, phosphorus) can regulate important disease processes including pathogen reproduction and transmission. Thus, both disease and ecosystem ecology stand to grow as fields by exploring questions that arise at their intersection. However, we currently lack a framework explicitly linking these disciplines. We developed a stoichiometric model using elemental currencies to track primary producer biomass (carbon) in vegetation and soil pools, and to track prevalence and the basic reproduction number (R0 ) of a directly transmitted pathogen. This model, parameterised for a deciduous forest, demonstrates that anthropogenic nutrient supply can interact with disease to qualitatively alter both ecosystem and disease dynamics. Using this element-focused approach, we identify knowledge gaps and generate predictions about the impact of anthropogenic nutrient supply rates on infectious disease and feedbacks to ecosystem carbon and nutrient cycling.

Trophic-Level Interactive Effects of Phosphorus Availability on the Toxicities of Cadmium, Arsenic, and Their Binary Mixture in Media-Exposed Scenedesmus acutus and Media and Dietary-Exposed Daphnia pulex.

Various anthropogenic activities simultaneously alter essential mineral nutrients and contaminant content in the environment. Depending on essential nutrient conditions, the uptake and effects of contaminants in exposed organisms may be altered. The addressing of ecological risk assessment (ERA) of contaminant mixtures has proven difficult. Furthermore, most assessments involving single contaminant exposures do not consider the interaction of essential nutrients on toxicological end points. Hypotheses for toxicological effects of cadmium (Cd), arsenic (As), and their binary mixture (Cd/Asmix) include alteration under varying dietary and media phosphorus (P) conditions. However, interactive effects and effect size (η2) are largely unknown. Here, we investigated the toxicities of Cd-, As-, and Cd/Asmix-treated media and diets on Scenedesmus acutus (a primary producer) and Daphnia pulex (a primary consumer), under varied media and dietary P conditions [low (LP), median (MP), and optimum (COMBO)]. Our results showed significant (p < 0.05) interactive effects and concentration dependent growth inhibition of S. acutus. The toxicity (at day 7) of Cd against S. acutus was 2×, 11×, and 4× that of As in LP, MP, and COMBO conditions, respectively, while the joint toxicity effects of Cd/Asmix were partially additive in LP and COMBO, and synergistic in MP media. Furthermore, acute lethal toxicity (96 h) of Cd in D. pulex was ∼60× that of As, while Cd/Asmix joint toxicity was synergistic. Chronic toxicity (14 d) in D. pulex showed significant (p < 0.05) interaction of As and P-availability on survival, reproduction, and behavior (distance moved, velocity, acceleration and mobility), while Cd and P availability showed significant interactive effect on rotational behavior. Dose response effects of Cd, As, and Cd/Asmix in S. acutus and D. pulex were either monophasic or biphasic under varying nutrient conditions. This study provides empirical evidence of the interactive effects of media/dietary P and toxic metals (Cd, As, and Cd/Asmix) at environmentally relevant concentrations, emphasizing the need for consideration of such interactions during ERA.

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.

Mechanistically derived Toxicant-mediated predator-prey model under Stoichiometric constraints.

Studies in ecological stoichiometry highlight that grazer dynamics are affected by insufficient food nutrient content (low phosphorus (P)/carbon (C) ratio) as well as excess food nutrient content (high P:C). Contaminant stressors affect all levels of the biological hierarchy, from cells to organs to organisms to populations to entire ecosystems. Eco-toxicological modeling under the framework of ecological stoichiometry predicts the risk of bio-accumulation of a toxicant under stoichiometric constraints. In this paper, we developed and analyzed a Lotka-Volterra type predator- prey model which explicitly tracks the environmental toxicant as well as the toxicant in the populations under stoichiometric constraints. Analytic, numerical, slow-fast steady state and bifurcation theory are employed to predict the risk of toxicant bio-accumulation under varying food conditions. In some cases, our model predicts different population dynamics, including wide amplitude limit cycles where producer densities exhibit very low values and may be in danger of stochastic extinction.

Seasonal Variation of Nutrient Loading in a Stoichiometric Producer-Consumer System.

Recent discoveries in ecological stoichiometry have indicated that food quality in terms of the phosphorus/carbon (P/C) ratio affects consumers whether the imbalance involves insufficient or excess nutrients. This phenomenon is called the "stoichiometric P/C knife-edge." In this study, we develop and analyze a producer-consumer model which captures this phenomenon. It assesses the effects of (external) nutrient (P) loading on consumer dynamics in an aquatic environment by mechanistically deriving and accounting for seasonal variation in nutrient loading. In the absence of seasonal effects, previous models suggest that the dynamics are Hopf bifurcation, saddle-node bifurcations, and limit cycles. However, seasonal effects can have major implications on the predicted solutions and enrich population dynamics. Bifurcation analyses demonstrate that seasonal forcing can cause both periodic and quasi-periodic solutions.

Dynamics of a Producer-Grazer Model Incorporating the Effects of Phosphorus Loading on Grazer's Growth.

Phosphorus is an essential element for all life forms, and it is also a limiting nutrient in many aquatic ecosystems. To keep track of the mismatch between the grazer's phosphorus requirement and producer phosphorus content, stoichiometric models have been developed to explicitly incorporate food quality and food quantity. Most stoichiometric models have suggested that the grazer dynamics heavily depends on the producer phosphorus content when the producer has insufficient nutrient content [low phosphorus (P):carbon (C) ratio]. However, recent laboratory experiments have shown that the grazer dynamics are also affected by excess producer nutrient content (extremely high P:C ratio). This phenomenon is known as the "stoichiometric knife edge." While the Peace et al. (Bull Math Biol 76(9):2175-2197, 2014) model has captured this phenomenon, it does not explicitly track P loading of the aquatic environment. Here, we extend the Peace et al. (2014) model by mechanistically deriving and tracking P loading in order to investigate the growth response of the grazer to the producer of varying P:C ratios. We analyze the dynamics of the system such as boundedness and positivity of the solutions, existence and stability conditions of boundary equilibria. Bifurcation diagram and simulations show that our model behaves qualitatively similar to the Peace et al. (2014) model. The model shows that the fate of the grazer population can be very sensitive to P loading. Furthermore, the structure of our model can easily be extended to incorporate seasonal P loading.

Stoichiometric food chain model on discrete time scale.

Stoichiometry-based models can yield many new insights into producer - grazer systems. Many interesting results can be obtained from models continuous in time. There raises the question of how robust the model predictions are to time discretization. A discrete stoichiometric food-chain model is analyzed and compared with a corresponding continuous model. Theoretical and numerical results show that the discrete and continuous models have many properties in common but differences also exist. Stoichiometric impacts of producer nutritional quality also persist in the discrete system. Both types of models can exhibit qualitatively different behaviors with the same parameter sets. Discretization enlarges the parameter ranges for the existence of chaotic dynamics. Our results suggest that the stoichiometric mechanisms are robust to time discretization and the nutritional quality of the producer can have dramatic and counterintuitive impacts on population dynamics, which agrees with the existing analysis of pelagic systems.

Effect of excess food nutrient on producer-grazer model under stoichiometric and toxicological constraints.

Accurately assessing the risks of contaminants requires more than an understanding of the effects of contaminants on individual organism, but requires further understanding of complex ecological interactions, elemental cycling, and the interactive effects of natural stressors, such as resource limitations, and contaminant stressors. There is increasing evidence that organisms experience interactive effects of contaminant stressors and food conditions, such as resource stoichiometry, availability and excess of nutrient. Here, we develop and analyze the first producer-grazer population model that incorporates the effects of excess nutrients, as well as nutrient limitations on grazer exposed to toxicants. We use analytical, numerical and bifurcation analysis to reduce and exploremodel parameterized for an aquatic system of algae and zooplankton exposed to methylmercury under varying phosphorus conditions. Under certain environmental conditions, our models predict higher toxicity than previous models that neglect the consequences excess nutrient conditions can have on grazer populations.

Mechanistically derived spatially heterogeneous producer-grazer model subject to stoichiometric constraints.

Known stoichiometric models of a two species producer-grazer ecosystem have either neglected spatial dynamics or failed to track free phosphorus in the media. In this paper we present a spatially heterogeneous model that tracks phosphorus content in the producer and free phosphorus in the media. We simulate our model numerically under various environmental conditions. Multiple equilibria, with bistability and deterministic extinction of the grazer, are possible here. In conditions that had been previously studied without tracking free phosphorus we find cases where qualitatively different behavior is observed. In particular under certain environmental conditions previous models predict stable equilibria where our model predicts stable limit cycles near the surface. Oscillatory dynamics can have consequences on the population densities, which may spend some time at low values throughout the cycles where they are in danger of stochastic extinction.

Dynamics of a producer-grazer model incorporating the effects of excess food nutrient content on grazer's growth.

Modeling under the framework of ecological stoichiometric allows the investigation of the effects of food quality on food web population dynamics. Recent discoveries in ecological stoichiometry suggest that grazer dynamics are affected by insufficient food nutrient content (low phosphorus (P)/carbon (C) ratio) as well as excess food nutrient content (high P:C). This phenomenon is known as the "stoichiometric knife edge." While previous models have captured this phenomenon, they do not explicitly track P in the producer or in the media that supports the producer, which brings questions to the validity of their predictions. Here, we extend a Lotka-Volterra-type stoichiometric model by mechanistically deriving and tracking P in the producer and free P in the environment in order to investigate the growth response of Daphnia to algae of varying P:C ratios. Bifurcation analysis and numerical simulations of the full model, that explicitly tracks phosphorus, lead to quantitative different predictions than previous models that neglect to track free nutrients. The full model shows that the fate of the grazer population can be very sensitive to excess nutrient concentrations. Dynamical free nutrient pool seems to induce extreme grazer population density changes when total nutrient is in an intermediate range.

Atmospheric nitrogen deposition is associated with elevated phosphorus limitation of lake zooplankton.

Here, we present data that for the first time suggests that the effects of atmospheric nitrogen (N) deposition on nutrient limitation extend into the food web. We used a novel and sensitive assay for an enzyme that is over-expressed in animals growing under dietary phosphorus (P) deficiency (alkaline phosphatase activity, APA) to assess the nutritional status of major crustacean zooplankton taxa in lakes across a gradient of atmospheric N deposition in Norway. Lakes receiving high N deposition had suspended organic matter (seston) with significantly elevated carbon:P and N:P ratios, indicative of amplified phytoplankton P limitation. This P limitation appeared to be transferred up the food chain, as the cosmopolitan seston-feeding zooplankton taxa Daphnia and Holopedium had significantly increased APA. These results indicate that N deposition can impair the efficiency of trophic interactions by accentuating stoichiometric food quality constraints in lake food webs.