Statistical Approach to the Gompertz Growth Model and the Underlying Timescales

The Gompertz growth model is one of the most established paradigms in biology. It is widely used to describe the growth of bacteria and tumour cell populations, as well as plants and animals. Here, a statistical approach is used to model biological growth. This approach involves the probabilistic estimation of population–environment interactions. By applying this theory, we derive stochastic equations, of which the Gompertz growth model is a limiting case. This is confirmed by numerical simulations. We examine the dynamic modes in dependence on the timescale relation. By altering the invariant measure, we suggest modified forms of the stochastic Gompertz growth model.