Abstract:
This body of work makes use of the dynamics of Plant-Herbivore interaction based on Lotka-Voltera’s prey-predator model to study the relationship between traditional livestock production and vegetative conditions.This research focuses on developing advanced techniques to improve the accuracy and eciency of parameter estimation in these models, as well as integrating neural networks for enhanced forecasting capabilities. An extension of the Plant- Herbivore models is derived in order to incorporate the existing information of Botswana’s climate and livestock factors. Adequate approaches are taken to investigate
novel optimization algorithms for parameter estimation, evaluate their e↵ectiveness in dynamic plant-livestock models, and develop an integrated forecasting framework using neural networks. The utilization of the specialized Runge-Kutta method as an integrator is justified because of the inclusion of time series data for soil moisture in the model. The Runge-Kutta method paired with multi-start and local solver fmincon in MATLAB enabled ecient exploration of parameter spaces, to improve the accuracy of parameter estimation, with objective functions achieving set thresholds. The combination of these optimized parameter estimation techniques with the normalized nonlinear least squares, presented very robust results. Estimate weighting and time conversion are incorporated to reduce the error brought about by the assumption of homogeneity within the data. Systematic approaches were taken to estimate the extended Plant-Herbivore models parameters accurately and provide reliable predictions for system behavior despite the low observation points. The incorporation of nonlinear least squares is explored to further enhance the optimization process, allowing for the identification of parameters that best fit the observed livestock data, even in the presence of non-linearity. Neural Network Auto-Regressive (NNAR) forecasting, with its ability to learn complex patterns and relationships from historical data of livestock counts, was found to be a powerful tool for predicting soil moisture values which were then used for livestock count prediction. Based on numerous accuracy measures, ME, RMSE, MAE, and MPE, it was found out that NNAR models generally perform better for smaller numbers of predictions than ETS models. NNAR forecasts were found to have narrower confidence intervals than Exponential Smoothing
(ETS ) models ETS for soil moisture forecasts. NNAR models were used to obtain soil moisture, death and harvest rates forecasts, which were then integrated within the extended Plant-Herbivore model to estimate future trajectories of the model estimates and draw relevant interpretations.
