Role of specific growth rate in the development of different growth processes

TL;DR

This paper presents a unified analytical framework highlighting the role of specific growth rate in various sigmoidal and non-sigmoidal growth processes, deriving different growth equations from a common rate function.

Contribution

It introduces a unified approach to model diverse growth processes by deriving all from a single functional form of the specific growth rate.

Findings

Different growth equations can be derived from the same rate function.

The framework explains theta logistic growth.

Competitive environments can increase saturation levels.

Abstract

Effort has been given for the development of an analytical approach that helps to address several sigmoidal and non-sigmoidal growth processes found in literature. In the proposed approach, the role of specific growth rate in different growth processes has been considered in an unified manner. It is found that the different growth equations can be derived from the same functional form of rate equation of specific growth rate. A common functional form of growth and growth velocity have been derived analytically and it has been shown that different values of the parameters involved in the description lead to different growth function. The theta logistic growth can be explained in this proposed framework. It is found that the competitive environment may increase the saturation level of population size.