Approximation of time series of Paramecia caudatum dynamics by the Verhulst and Gompertz models: A non-traditional approach

Abstract

The Verhulst and Gompertz models were used for approximation of some well-known time series of Paramecia caudatum population dynamics (G.F. Gause, “The Struggle for Existence,” 1934). The parameters were estimated for each of the models in two different ways: with the least-squares method (global fitting) and a non-traditional approach (the method of extreme points). The results were compared with those presented by Gause. Deviations of theoretical (model) trajectories from experimental time series were tested using various non-parametric statistical tests. It was shown that the estimates by the least-squares method lead to results that do not always meet the requirements that are imposed on a “fine” model. However, in some cases a small modification of the least-squares-method estimates is possible that allows satisfactory representations of an experimental data set for approximation.