Verhulst Equation and the Universal Pattern for the Global Population Growth

TL;DR

This paper analyzes global population growth using the Verhulst equation, identifying universal linear domains in growth rate data, and proposes a new data filtering method to improve modeling accuracy.

Contribution

It introduces a universal pattern in population growth rates and a novel data preparation approach for better modeling with the Verhulst equation.

Findings

Two linear domains in growth rate data identified

Universal scaling relations for P(t) changes established

New data filtering method enhances analysis accuracy

Abstract

The global population growth from 10,000 BC to 2023 is discussed within the Verhulst scaling equation and its extensions framework. The analysis focuses on per the capita global population rate coefficient Gp(P)=[dP(t)/P(t)]/dt=dlnP(t)/d, which reveals two linear domains: from 700CE till 1966 and from 1966 till 2023. Such a pattern can be considered a universal reference for reliable scaling relations describing P(t) changes. It is also the distortions-sensitive test indicating domains of their applicability and yielding optimal values of parameters. For models recalling the Verhulst equation, a single pair of growth rate and system capacity coefficients (r,s) should describe global population rise in the mentioned periods. However, the Verhulst equation with such effective parameters does not describe P(t) changes. Notable is the new way of data preparation, based on collecting data from various sources and their numerical filtering to obtain a smooth set of optimal values enabling the derivative-based analysis. The analysis reveals links between P(t) changes and some historical and pre-historical references influencing the global scale.