Paramecium aurelia dynamics: Non-traditional approach to estimation of model parameters (on an example of Verhulst and Gompertz models)

Abstract

For fitting of well-known experimental time series on Paramecium aurelia population dynamics (Gause, 1934; Figures 24 and 25) Verhulst and Gompertz models were used. For every model for both considering time series values of parameters were estimated in two different ways: with least squared method (LSM) and with non-traditional method which does not require using of any loss-functions. Properties of deviations between theoretical (model) trajectories and experimental datasets were checked with certain number of non-parametric statistical tests. It was obtained that in some cases properties of deviations corresponding to LSM-estimations, do not satisfy requirements which are producible to “good models”. In some cases small modifications of LSM-estimations can lead to obtaining satisfactory results in approximation of experimental results. It was also obtained that in some cases Gompertz model demonstrates better fitting of time series than Verhulst model.