Growth with regulation in fluctuating environments. I. Alternative logistic-like diffusion models
The authors consider a third order logistic-like growth model. In order to account for environmental fluctuations, the idea of growth in a random environment is introduced, by substituting the intrinsic fertility parameter of the population with a normal stationary delta-correlated random process whose mean is identified with the population's fertility. Stochastic differential equations are thus obtained whose solutions X(t) are stationary diffusion processes. By means of a monotone transformation, such processes become Wiener processes Y(t). The different features of the processes X(t) and Y(t) are discussed and compared with the Gompertz growth process and the logistic model. Finally the first passage time T through a state is introduced for the processes X(t) and Y(t) and the Laplace transform of its p.d.f. is calculated. This is useful to acquire further information; e.g. it allows the evaluation of moments of the time necessary for a population to attain an assigned size for the first time.
normal stationary delta-correlated random process
scientific article; zbMATH DE number 3882255