Dynamics of a Producer–Grazer Model Incorporating the Effects of Phosphorus Loading on Grazer’s Growth

Mycoloop: Modeling phytoplankton-chytrid-zooplankton interactions in aquatic food webs

A dynamic model is proposed to describe a mycoloop in aquatic food webs. The model consists of phytoplankton, chytrids and zooplankton. It characterizes that zooplankton consume both phytoplankton and free-living chytrid spores, and that chytrids infect phytoplankton. The dynamics of the model are investigated containing the dissipativity, existence and stability of equilibria, and persistence. The ecological reproductive indexes for phytoplankton or zooplankton invasion and basic reproduction numbers for chytrid transmission are derived. The parameter values of the model are estimated based on experimental data. Numerical simulations explore the effects of the mycoloop on phytoplankton blooms and chytrid transmission. This research reveals that the mycoloop structure increases or reduces phytoplankton blooms, and controls the spread of chytrids among phytoplankton.

Asymmetrical resource competition in aquatic producers: Constant cell quota versus variable cell quota

In a shallow aquatic environment, a mathematical model with variable cell quota is proposed to characterize asymmetric resource competition for light and nutrients among aquatic producers. We investigate the dynamics of asymmetric competition models with constant and variable cell quotas and obtain the basic ecological reproductive indexes for aquatic producer invasions. The similarities and differences between the two types of cell quotas for dynamical properties and influences on asymmetric resource competition are explored through theoretical and numerical analysis. These results contribute to further revealing the role of constant and variable cell quotas in aquatic ecosystems.

Contrasting stoichiometric dynamics in terrestrial and aquatic grazer-producer systems

The turnover rate of producer biomass in aquatic ecosystems is generally faster than in terrestrial. That is, aquatic producer biomass grows, is consumed, and is replaced considerably faster than terrestrial. The WKL model describes the flow of phosphorus and carbon through a grazer-producer system, hence varying the model parameters allows for analysis of different ecosystems of this type. Here we explore the impacts of the intrinsic growth rate of the producer and the maximal ingestion rate of the grazer on these dynamics because these parameters determine turnover rate. Simulations show that for low intrinsic growth rate and maximal ingestion rate, the grazer goes extinct; for higher values of these parameters, coexistence occurs in oscillations. Sensitivity analysis reveals the relative importance of all parameters on asymptotic dynamics. Lastly, the impacts of changing these two parameters in the LKE model appears to be quantitatively similar to the impacts in the WKL 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.

Environmental seasonality on predator-prey systems under nutrient and toxicant constraints

Bioaccumulation of toxicants in aquatic food webs can pose risks to ecosystem function and human health. Toxicant models of aquatic ecosystems can be improved by incorporating realistic environmental impacts such as nutrient availability and seasonality. It is well known that the carrying capacity of predator-prey systems can vary seasonally due to environmental cycles resulting from natural and human activities. As such, incorporating seasonal variation in the carrying capacity of a predator-prey system provides a better understanding of the underlying population dynamics bioaccumulation of toxicants. Here, we develop a seasonally varied predator-prey model subject to concurrent nutrient and toxicant stressors. We investigate the effects of seasonality on population dynamics to increase understanding of the complex governing processes of the trophic transfer of nutrients, energy, and toxicants. We observe that the strength of seasonality can shift solutions from periodic to quasi-periodic and models that neglect environmental seasonality may be under-predicting adverse effects of toxicity.

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.