Non-linearity and heterogeneity in modeling of population dynamics

In this paper the power equation is considered within the frameworks of inhomogeneous population models; it is proven that any power equation describes the total population size of a frequency-dependent model with Gamma-distributed Malthusian parameter. Additionally, any super-exponential equation describes the dynamics of inhomogeneous Malthusian density-dependent population model. All statistical characteristics of the underlying inhomogeneous models are computed explicitly. The results of this analysis show that population heterogeneity can be a reasonable explanation for power law accurately describing total population growth.