Predicting Earth's Carrying Capacity of Human Population as the Predator and the Natural Resources as the Prey in the Modified Lotka-Volterra Equations with Time-dependent Parameters

Abstract: We modified the Lotka-Volterra Equations with the assumption that two of the original four constant parameters in the traditional equations are time-dependent. In the first place, we assumed that the human population (borrowed from the T-Function) plays the role as the prey while all lethal factors that jeopardize the existence of the human race as the predator. Although we could still calculate the time-dependent lethal function, the idea of treating the lethal factors as the prey was too general to recognize the meaning of them. Hence, in the second part of the modified Lotka-Volterra Equations, we exchanged the roles between the prey and the predator. This time, we treated the prey as the natural resources while the predator as the human population (still borrowed from the T-Function). After carefully choosing appropriate parameters to match the maximum carrying capacity with the saturated number of the human population predicted by the T-Function, we successfully calculated the natural resources as a function of time. Contrary to our intuition, the carrying capacity is constant over time rather than a time-varying function, with the constant value of 10.2 billion people.