Implications of Agricultural Practices on Vegetation and Terrestrial Invertebrates in Riparian Zone: A Nonlinear Modelling Study

Uncontrolled land-use owing to agricultural practices has not only resulted in depletion of vegetation, but has also worsened the habitat of terrestrial invertebrates living in riparian zones. With these dynamic interactions in mind, a nonlinear model is developed using a set of differential equations, including riparian vegetation, terrestrial invertebrates, and agricultural production as system variables. The model is based on the notion that terrestrial invertebrates totally depend on riparian vegetation for their survival and utilization of riparian zones for agricultural purposes not only cause the loss of riparian vegetation, but of terrestrial invertebrates as well. The generated differential-equation system is examined for equilibrium solutions, their existences and stabilities. The mathematical analysis demonstrates the conditions under which agricultural production, riparian vegetation, and terrestrial invertebrates can coexist and create a stable system. These intuitive conclusions are supported by quantitative results using numerical simulation and differential sensitivity analysis. The qualitative as well as quantitative findings suggest that excessive utilization of forested riparian land for agricultural practices may cause destabilization of the system and therefore, they should be put under check in riparian zones.