ITM Web Conf.
Volume 34, 2020International Conference on Applied Mathematics and Numerical Methods – third edition (ICAMNM 2020)
|Number of page(s)
|Applied Mathematics and Numerical Methods
|03 December 2020
Bigger perturbations enhance higher trophic levels biomass, increase transfer efﬁciency and may sustain for bigger plankton biodiversity
Department of Mathematics, Banaras Hindu University, Varanasi- 221005 India
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.
© The Authors, published by EDP Sciences, 2020
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