Computational Simulation of the Lotka–Volterra Predator–Prey Model

Abstract

Ecological theory has long held that predator-prey dynamics drive oscillations between resource and consumer populations (hereafter, the predator-prey relationship). A classical Lotka–Volterra model was modified to represent the impacts of an oscillatory environment with sufficient seasonal forcing to maintain stability and homeostasis at the scale of the system, and to provide a dynamic home for examination of oscillatory dynamics and system stability. The study allows for the explicit display of trajectories of populations by using advanced numerical methods to accurately solve a constellation of nonlinear differential equations. The temporal evolution of simulation data shows a constant cycle of oscillation where the predator population rises from a phase lag relative to the background response in combination with a surge in prey density. In fact, as highlighted at the end of the citation we just provided, the fact that computer modeling is an important part of identifying regulatory mechanisms behind population cycles does not mean that it will not be an important part of the process going forward. In addition, the generality of this framework permits  its deployment with a full simulation environment for various real-world scenarios — from wildlife conservation and agricultural pest control, to more abstract activities models of research intervention, such as epidemic and treatment strategies.