A. Priyadarshi

Plant‐mycorrhizal interactions mediate plant community coexistence by altering resource demand

As the diversity of plants increases in an ecosystem, so does resource competition for soil nutrients, a process that mycorrhizal fungi can mediate. The influence of mycorrhizal fungi on plant biodiversity likely depends on the strength of the symbiosis between the plant and fungi, the differential plant growth responses to mycorrhizal inoculation, and the transfer rate of nutrients from the fungus to plant. However, our current understanding of how nutrient-plant-mycorrhizal interactions influence plant coexistence is conceptual and thus lacks a unified quantitative framework. To quantify the conditions of plant coexistence mediated by mycorrhizal fungi, we developed a mechanistic resource competition model that explicitly included plant-mycorrhizal symbioses. We found that plant-mycorrhizal interactions shape plant coexistence patterns by creating a tradeoff in resource competition. Especially, a tradeoff in resource competition was caused by differential payback in the carbon resources that plants invested in the fungal symbiosis and/or by the stoichiometric constraints on plants that required additional, less-beneficial, resources to sustain growth. Our results suggested that resource availability and the variation in plant-mycorrhizal interactions act in concert to drive plant coexistence patterns. Applying our framework, future empirical studies should investigate plant-mycorrhizal interactions under multiple levels of resource availability.

L-shaped prey isocline in the Gause predator-prey experiments with a prey refuge.

Predator and prey isoclines are estimated from data on yeast-protist population dynamics (Gause et al., 1936). Regression analysis shows that the prey isocline is best fitted by an L-shaped function that has a vertical and a horizontal part. The predator isocline is vertical. This shape of isoclines corresponds with the Lotka-Volterra and the Rosenzweig-MacArthur predator-prey models that assume a prey refuge. These results further support the idea that a prey refuge changes the prey isocline of predator-prey models from a horizontal to an L-shaped curve. Such a shape of the prey isocline effectively bounds amplitude of predator-prey oscillations, thus promotes species coexistence.

ROLE OF PROTECTION IN A TRI-TROPHIC FOOD CHAIN DYNAMICS

In this paper, the role of protection in stabilizing the tri-trophic food chain dynamics has been explored. The density-dependent protection is provided to bottom prey or middle predator or both. It favors the oscillations damping and has the potential to control the chaotic fluctuations of population density. The bifurcation diagrams have been drawn with respect to protection parameter. They exhibit coexistence of all three species in the form of periodic solutions. The coexistence in the form of stable equilibrium is possible for higher values of protection parameters. Further increase in protection parameters may lead to extinction of one or two species. A two-parameter bifurcation diagram has also been drawn. The Poincare Maps further confirm the role of protection in controlling the chaos.

Micro-scale variability enhances trophic transfer and potentially sustains biodiversity in plankton ecosystems

We develop moment closure approximations to represent micro-scale spatial variability in the concentrations of nutrients (N), phytoplankton (P) and zooplankton (Z) in an NPZ model, which we apply to examine the impact of different levels of micro-scale variability on both ecosystem dynamics and trophic transfer. Accounting explicitly for both the mean-field and fluctuating components of each prognostic variable in the NPZ model yields different dynamics for the mean-field concentrations, as well as lower phytoplankton biomass and greater zooplankton biomass, compared to the conventional NPZ model without micro-scale variability. The biomass of zooplankton consistently increases with increasing total micro-scale variability, and a minimum threshold of such variability is required for the existence of stable steady state solutions in the NPZ closure model. Compared to the conventional NPZ model, the domain of parameter space over which stable solutions exist is larger than for the NPZ closure model, and this stable domain widens with increasing total variability. The latter result suggests that natural systems with greater micro-scale variability may have the potential to sustain greater biodiversity. We find that with the NPZ closure model: (1) the stability domains increases with micro-scale variability, (2) increase of the level of total micro-scale variability enhances trophic transfer, i.e. increases the biomass of zooplankton, and (3) the coefficient of variation (CVP) of phytoplankton increases with micro-scale variability.

Complex behaviour in four species food-web model

A four-dimensional food-web system consisting of a bottom prey, two middle predators and a generalist predator has been developed with modified functional response. The system is well posed and dissipative. Some results on uniform persistence have been developed. The dynamics of the system is found to be chaotic for certain choice of parameters. The coexistence of all four species is possible in the form of periodic orbits/strange attractors for suitably chosen set of parameters.

Modeling the Combined Effects of Physiological Flexibility and Micro-Scale Variability for Plankton Ecosystem Dynamics

Plankton are microscopic organisms that constitute the sustaining base of food chains in the ocean. Various models have been developed using equations to study their important roles in marine ecology and chemistry. Such models typically assume that plankton respond to changing environmental conditions according to simplistic response equations, and that they experience uniform local conditions. However, experiments and observations have revealed both of those assumptions to be false. We describe recent approaches for modeling the observed flexible physiological response and micro-scale heterogeneity of plankton and introduce preliminary findings concerning their combined effects on plankton ecosystem dynamics.

Dynamics of Density-Dependent Closure Term in a Simple Plankton Model

A three-component aquatic model, which consists of nutrient, phytoplankton and zooplankton has been investigated. To incorporate the effects of higher predation, the mortality of zooplankton is assumed to be density-dependent (sigmoidal form). The system has uniformly bounded and dissipative solutions in the non-negative octant. Some conditions on persistence of all three-species have been established. The parameter estimation technique ”Marquardt-Levenberg (M-L) algorithm” has been used to estimate the values of some parameters, specially for density-dependent mortality. The bifurcation analysis reveals that model has periodic solutions for some parameter range. The amplitude of short term oscillations is varying with nutrient input present in the system. It is consistent with the field observational results. The nutrient input in the system may be one of the reason for short-term oscillations observed in the sea water.