On the logistic modeling and forecasting of evolutionary processes: Application to human population dynamics

Abstract

We develop a novel analytic procedure and show how it can be used to explore the consequences of introducing a reproductive fitness or fertility factor (the “Allee's effect”) into the Verhulst logistic model of population dynamics. It consisted in splitting the logistic equation into a product of depensatory and compensatory components, as part of a new approach to deal with generic evolutionary growth processes, regarding both their time evolution and forecasting applications. A number of existing functional representations for the Allee effect are commented up and two are selected for deeper consideration. We use as testing grounds for our procedure the study of the evolution of two large groups of consolidated human populations: the whole world and a group of 16 Asian countries. The populations per capita growth rate are analytically construed from optimized parameters obtained by least squares fits to the available data. Our modified Verhulst logistic models, besides affording a very good description of the experimental population data, also proved well suited for population forecasting, with results that are in quite acceptable agreement with current official forecasts from the US Census Bureau and the United Nations Population Prospect for short and medium ranges.