Computational Ecology and Software, 2011, 1(1): 25-36
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Analysis of some experimental time series by Gause: application of simple mathematical models

Lev V. Nedorezov
The Research Center for Interdisciplinary Environmental Cooperation (INENCO) of Russian Academy of Sciences, Kutuzova nab. 14, 191187 Saint-Petersburg, Russia

Received 21 February 2011; Accepted 15 March 2011; Published online 1 April 2011

For the approximation of some of well-known time series of Paramecia aurelia and Paramecia caudatum (under the separated cultivation of both species) population size changing in time, some well-known models were used. For all considering models values of parameters were estimated with least square method (with global fitting) in two different ways: with and without additional limits for parameter¡¯s values. In the case without additional limits for model¡¯s parameters deviations between theoretical (model) trajectories and experimental time series were tested for Normality (Kolmogorov¨CSmirnov test, and Shapiro¨CWilk test) with zero average, and for existence/absence of serial correlation (Durbin¨CWatson criteria). The best results were observed for Gompertz¡¯ and Verhulst¡¯ models. Under the assumption that parameter K (maximum value of population size) is greater than all elements of initial sample the best results were observed for Gompertz¡¯ model. In the last case the canonical technique for analysis of set of deviations can be applied in restricted form and needs in further development. In such a situation we cannot test the set of deviations on Normality with zero average (for big samples) because after a certain time moment all experimental points will be at one side of theoretical curve; at this situation we have to have a serial correlation in the sequence of deviations, etc.

Keywords Gause; time series; continuous time; model; approximation; test.

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