[Analysis of G.F. Gause experimental time-series by means of continuous-time models]

Four population dynamics models, namely Verhulst, Gompertz, Rosenzweig, and Svirezhev ones, have been used to approximate two well-known time-series of Paramecia aurelia and P. caudatum population size (Gause, 1934). The parameters are estimated for each of the models by the least-square method (with global fitting) in two different ways: with and without an additional upper bound for a parameter value. In the latter (traditional) case, when the deviations of theoretical (model) trajectories from experimental time-series have been tested for normality (Kolmogorov-Smirnov test, Shapiro-Wilk test) with zero average, and for the presence/absence of serial correlations (Durbin-Watson criteria), the best results are obtained for the Gompertz and Verhulst models. In the former, more realistic, case (when we impose an additional constraint that the parameter meaning the carrying capacity of the environment has to be greater than any element in the sample), the best results are observed for the Gompertz model. Under this constraint, the canonical technique for deviation analysis can be applied in a restricted version only.