Micro-Scale Variability Impacts the Outcome of Competition Between Different Modeled Size Classes of Phytoplankton

Previous modeling studies have shown that observed micro-scale (mm) variability of nutrients and phytoplankton biomass can strongly impact the large-scale mean growth response of phytoplankton in ways that cannot be represented by typical models based on the mean field approximation. Also, models accounting for the flexible eco-physiology of phytoplankton predict quite different responses to changing environmental conditions compared to most current (inflexible) models. Combining these two ideas for nutrient-phytoplankton systems we have developed a new “Flexible NP closure model” to represent competition among the three typically observed phytoplankton size classes: pico-, nano-, and micro-phytoplankton. Both micro-scale variability and flexible eco-physiology are expected to impact the competition among these size classes. With this work we begin to address how both these factors determine the size structure and size diversity of phytoplankton in the ocean. Under eutrophic conditions, variability does not impact the modeled growth rate of any size class. On the other hand, under oligotrophic conditions, variability preferentially enhances the biomass of the largest typically observed micro-size class, and reduces the biomass of the smallest nano- and intermediate pico-size classes

Bigger perturbations enhance higher trophic levels biomass, increase transfer efficiency and may sustain for bigger plankton biodiversity

Highly intermittent phytoplankton is ubiquitously observed when measurements are performed at micro-scale (< 1mm). The conventional way of plankton modelling is based on the mean-field approach in which only the first central-moment approximations is retained and ignored higher central moments). The conventional modeling approach may be suitable for mesoor bigger scale (km) but it is inappropriate for micro-scale (< 1mm) where observed overlap in the intermittent spatial distributions of predators and prey become more important for determining the flow of nutrients and energy up the food chain. A new modelling approach called closure modelling is developed to account intermittent phytoplankton using Reynold’s decomposition from turbulence theory and retaining higher central moment approximations in Taylor series. In this study, we developed a NPZD compartmental model to describe the interactions of nutrient (N), phytoplankton (P), zooplankton (Z) and detritus (D) using closure modelling which accounts mean and fluctuating parts of these plankton variables. The results obtained in NPZD compartmental model confirm that perturbation / heterogeneity supports higher trophic levels involved in the model. This reassured the earlier results observed in case of NP and NPZ models in which perturbations enhances P-biomass and Z-biomass respectively. It is observed that perturbation / heterogeneity and a statistical quantity called coefficient of variations of phytoplankton (CVp) (ratio of standard deviation and mean) are positively associated in plankton ecosystems. The perturbations / heterogeneity leads to higher transfer efficiency (Z-biomass/P-biomass) in plankton ecosystems. These results are robust i.e. independent of parameters choices. Perturbation / heterogeneity effects on community structure, species richness and may quantify the energy transfer along trophic levels through biological process from primary production to higher trophic levels. Based on our study, we hypothesize that the locations with high (CVp) are highly heterogeneous and have high transfer efficiency, while low (CVp) locations are less heterogeneous around Tokyo Bay

Fish harvesting strategies with allee effect

Fish harvesting is important for nutritious food availability in human diet. In this manuscript, a simple fish harvesting model is developed using logistic growth along with allee effect. We study the basic mathematical properties of the model as equilibrium analysis and stability. For better understanding of the model performance, we perform the simulation of the system with different constant harvesting rate and periodic harvesting rate. The results shows that periodic harvesting is economically beneficial than the constant harvesting in fish stock

Impact of external applied currents in BVP model

The understanding of the activity of neurons in the brain has been modeled as nonlinear systems using mathematical modeling for decades. Nonlinearity in brain dynamics is complex structure to do mathematically but computational techniques make this area of research quite interesting and easy to study the dynamics. With advancement of new technology, mathematical and computational studies are more preferable to understand the behavior of neurons in a single cell to global cognitive process. In the present study, the impacts of different externally applied currents on the behavior of neurons in a simple BVP model (Bonhoeffer-Vander Pol Model) are analyzed thoroughly. The results of BVP model are similar to the characteristics of neurons shown by the Hodgkin-Huxley Model. In the BPV model, when system is stable, neurons are in resting-state. Unlike Hodgkin-Huxley model which follows all-or-none law, the BVP model does not follow this all-or-none rule. In the BVP model, there is an intermediate phase where no spike forms, but when sufficiently large input applied then spikes emerge. On applying constant current in BVP model, system is stable while it exhibits oscillatory behavior when current is applied externally above threshold value of it. If sinusoidal, continuous wavelet, and har wavelet form of external applied currents are injected then continuous firing emerges which have several interesting dynamics. Numerical simulations have been performed to understand the bifurcation analysis of the BVP model. Oneparameter and two-parameter bifurcation diagrams have been drawn in which threshold current values are discussed