On the relationship between the encounter rate and population density: Are classical models of population dynamics justified?

The problem of an adequate choice of functions describing the action of self-regulatory mechanisms in classical models of population dynamics is addressed. A stochastic model of migrations on a lattice with discrete time and with different methods of calculating the encounter rate between individuals is considered. For each variant of interactions between individuals, the average values were computed over space and time for different population sizes. The obtained samples were compared to the corresponding functions of classic models of isolated population dynamics: the Verhulst model, the Gompertz model, the Svirezhev model, and the theta-logistic model. It was shown that the data obtained for different variants of interactions can be approximated well with these classic models. However, in most cases, the conventional requirements for “good” models were not fulfilled: normality hypotheses for the deviation samples were rejected and strong serial correlations were observed. The only exceptions were the Verhulst and theta-logistic models when used for the fitting of the dataset, in which each individual interacted with all other individuals at every node. It is concluded that either the choice of a function describing self-regulatory effects should be argued for in a different way or different functions should be employed.