A biological growth curve is a sum of two distinct S-curves

Abstract

A growing population consists of successive generations of individuals interacting with each other and their environment. At every instant, these interactions can lead to either promotion or restriction of the population growth. Thus, within a growing population, differences arise over time due to both extrinsic and intrinsic factors such as resource utilization, competition, age distribution etc. These differences can lead to divergence within the population growth. The sum of these differences is manifested as the net population growth. In this work, we propose that these differences that arise over time within a growing population can be represented as two distinct S-curves. The sum of these two S-curves results in the growth curve of a population. These differences also arise in the growth curves of a populations attributes such as height or weight. We demonstrate this by applying the a- m biological growth model on (i) the population growth curves of Drosophila and yeast and (ii) the growth curves of the mean height of a population of sunflower plants and the mean body weight of male white rats. Finally, we also discuss the results using a coordinate system with the two distinct S-curves as the axes.