Integration of logistic and kinetics equations of population growth

The procedure proposed by Sakanoue [Sakanoue, S., 2007. Extended logistic model for growth of single-species populations. Ecological Modelling 205, 159–168] is used to derive the kinetics equations of population growth. It is based on three assumptions: resource availability changes with population size; resource supply to population and population demand for resources are defined as functions of resource availability and population size; and resource availability and population size shift in the supply function attracted to the demand function. These assumptions are organized into an abstract equation, which can be transformed into the Verhulst logistic equation under certain supply and demand functions. On the other hand, by setting “per capita resource availability” as an independent variable, the abstract equation can also be transformed into some existing kinetics equations and new kinetics ones involving intraspecific interactions such as facilitation and interference. The procedure provides a unified means of deriving and relating the two types of population growth equation.