Mathematical modelling of the seasonal variability of plankton and forage fish in the Gulf of Kachchh

Seasonal variability of plankton and small fish in the coastal water of west coast of India is studied with a non-linear mathematical model (NPZF model) having four compartments viz., nutrient, phytoplankton, zooplankton and forage fish. The inclusion of an additional compartment of forage fish increases the complexity of the earlier proposed NPZ model as it introduces additional seven unknown parameters, which need to be specified for performing numerical simulations. The key problem is therefore to estimate the range of values of these parameters in the dynamical system. With the help of local stability analysis, sensitivity analysis and numerical simulations, these parameters have been estimated. As a case study for the evaluation of the model, simulations are performed to explain the aquatic ecology of Gulf of Kachchh (22°20′ N-23°40′ N, 68°20′ E-70°40′ E), an inlet on west coast of India in the Arabian Sea. An important conclusion of this study is that by using the prescribed parameters as estimated from the sensitivity analysis, the NPZF model reproduces some salient features of the Gulf of Kachchh, especially the bimodal oscillations observed in the plankton and forage fish. The 4-compartment model could therefore serve as an ecological model of the Gulf of Kuchchh.