Evaluation of the Gompertz function to model survival of bacteria introduced into soils

Survival dynamics of several bacterial strains introduced into soils under different inoculum conditions were estimated by the Gompertz model. The model is determined by a pair of parameters A and M. A is an estimation of the kinetic behavior of the strain in the soil (growth or die-off). M represents the stable amount of microorganisms reached in time. To evaluate the applicability of the model, the following five criteria were used: coefficient of determination R2 between experimental and estimated data; analysis of the residuals; biological meaning of the parameters; confidence intervals of the estimated parameters; and the simulating power of the model. In 21 cases out of 28 cases, the Gompertz model had a coefficient of determination > 0.8 but, in approximately half of the cases, the model failed to pass all criteria. The results indicate that factors such as soil, strain type and inoculum level influence the Gompertz parameters A and M. For sterile soils, the A value is in the range 1.5–2.5, whereas for non-sterile soils it was generally < 0.2. Characteristic A and M values for a specific strain, independent of its growth conditions, were not encountered; the latter mathematically confirms the importance of the ecological conditions upon introduction of bacteria.