Competition between species: Theoretical models and experimental tests

Abstract

Experimental determinations of Drosophila population dynamics cannot be explained by the Lotka-Volterra model of interspecific competition. This paper presents other possible mathematical models of competition between species, and gives the results of experiments designed to test the validity of such models. Eight of the ten new models presented contain the Lotka-Volterra model as a special case. The experiments made to test the models are of two kinds. Type 1 experiments are continuous one- or two-species populations, which permit the estimation of the carrying capacity of each species and the numbers of the two species at the point of stable equilibrium. Type 2 experiments measure the change in numbers over a short time interval in populations started with many different initial densities of the two species. Type 2 experiments give information on the dynamics of the two-species system in the phase plane whose coordinates are the number of individuals of each species. The models accounting best for the results are models five and seven (Table II). Each of these two models contains one parameter more than the Lotka-Volterra model. Model five adds a nonlinear term of self-interaction (−βiN2i). Model seven has the form, dNi/dt = riN/Kθii(Kθii − Nθi i − αijNj1−θi i). The exponential parameter θ removes the restriction of the logistic theory of population growth, that each individual added to the population decrease the rate of growth of the population by a constant amount. With model seven the rate of growth of a population of a single species need not have its maximum at K2, that is when the number of individuals is half the carrying capacity of the environment.