Population Dynamics

Abstract

Within the context of population dynamics, a variety of models has been proposed with the purpose of describing the mechanisms of competition between biological populations. Among these models the most known is the Lotka-Volterra, used in describing the time behavior of populations of two biological species that coexist in a certain region. One of them is prey and the other is predator. The prey feed on plants, considered abundant. The predators live at the expense of prey. Suppose that at certain moment the number of predators is large. This implies that the prey are annihilated quickly, not even having the chance to reproduce. The decline in prey population, in turn, causes the decrease in the number of predators. Having no food, many do not reproduce and disappear. When this occurs, conditions are created for the prey reproduction, increasing, thus, the prey population. As a consequence, the predator population increases again. And so on. With the passage of time, these situations repeat periodically in time. Under these conditions, the system predator-prey presents auto-organization. The predator and prey populations oscillate in time with a period determined by parameters inherent to the predator-prey interactions. In other terms, we face an auto-organization in the sense of Prigogine, which is expressed here by means of time oscillations in the prey and predator populations.