Comparative analysis of Euler and Runge-Kutta Fehlberg Methods in solving the Lotka-Volterra competitive model/ Nur Hidayah Abd Rahaman ... [et al.]

This study addresses the problem of determining equilibrium and stability in ecosystems where species compete for the same resources, as outlined by the principle of competitive exclusion. It is often challenging to ascertain the rate at which exclusion happens and whether species can coexist in competitive environments. To discover these issues, the study investigates the competitive interactions between lions (Panthera Leo) and leopards (Panthera pardus) in the Sabi Sand Game Reserve, South Africa, focusing on whether the dominant competitor, lions, limit the population and distribution of leopards. Using the Lotka-Volterra Competitive model, the research compares numerical solutions obtained through Euler and Runge-Kutta Fehlberg (RKF) methods. It also examines how carrying capacity and initial conditions influence equilibrium and stability in this competition. Data on dietary overlaps between lions and leopards were used to test their competitive dynamics, with lions targeting larger prey and leopards focusing on smaller prey. The findings indicate that the RKF method provides more accurate approximations than Euler's method, with leopards showing a higher carrying capacity and greater resilience in the face of competition from lions. This indicates that leopard populations are less affected by lion presence. The study emphasizes the role of carrying capacity in species survival during competition and highlights the utility of numerical methods for predicting competition outcomes without extended experimentation. These findings contribute to wildlife management strategies, particularly in efforts to restore large carnivores in ecosystems, and improve understanding of competitive exclusion in ecological systems.