Generalized logistic functions in modelling emergence of Brassica napus L

Abstract

The objective of this study was to determine whether generalized logistic functions (Richards model with time shift) may be used to predict emergence of winter rapeseed (Brassica napus L.) after its seed treatment with plant extracts from Taraxacum officinale roots under controlled environment conditions. Emergence analyses were conducted for winter rape whose seeds were treated with a plant extract and for the non-treated seeds sown to the soil at the site of earlier point application of the extract. Curves were plotted for experimental data by minimizing the square sum of differences between the experimental data and the mathematical model. To evaluate model fit, the mean squared error was divided into four factors. Computing modelling efficiency coefficients were also introduced to enable complete analysis. Results of simulation research demonstrate that the determined parameters of curves (e.g. values of growth parameters, time shift or the upper limit of population) describing the number of seedlings in the function of time stayed compliant to the interpretation with regard to the biology of the analyzed processes. The proposed mathematical description based on generalized logistic functions showed extraordinary fit (r = 0.999) to the experimental data, which makes it highly useful in predictive control of rapeseed emergence. In addition, the study enabled concluding that plant extracts application to the soil allowed achieving a higher maximal emergence rate compared to the control sample. The application of the plant extracts increased the final population of rapeseed and significantly accelerated the occurrence of the maximal emergence rate.

Fig 1. Time relations of emergence of rapeseed seedlings for non-treated seeds (control) and for two methods of application of plant extracts (to soil and on seeds)—Generalized logistic curves.

Fig 2. Correlation between the experimentally determined emergence percentage and respective predicted values emergence of winter rape for control (a) and two methods of application of plant extracts to soil (b) and seeds (c).

Fig 3. Time dependence of a) first and b) second derivative and c) phase portrait of the generalized logistic curves (Fig 1).

Fig 4. Time dependence of B(t) used in scenario 1.

Fig 5. Time dependence of C(t) used in scenario 2.

Fig 6. Time dependence of K(t) used in scenario 3.

Fig 7. Time dependence of emergence of rapeseed seedlings for the application of plant extracts to soil (laboratory experiment) and for virtual scenarios 1–3.