Importance of scaling exponents and other parameters in growth mechanism: an analytical approach

Abstract

The growth process of a living organism is studied with the help of a mathematical model where a part of the surplus power is assumed to be used for growth. In the present study, the basic mathematical framework of the growth process is based on a pioneering theory proposed by von Bertalanffy and his work is the main intellectual driving force behind the present analysis. Considering the existence of an optimum size for which the surplus power becomes maximum, it has been found that the scaling exponent for the intake rate must be smaller than the exponent for the metabolic cost. A relationship among the empirical constants in allometric scaling has also been established on the basis of the fact that an organism never ceases to generate surplus energy. The growth process is found to continue forever, although with a decreasing rate. Beyond the optimum point the percentage of shortfall in energy has been calculated and its dependence on scaling exponents has been determined. The dependence of optimum mass on the empirical constants has been shown graphically. The functional dependence of mass variation on time has been obtained by solving a differential equation based on the concept of surplus energy. The dependence of the growth process on scaling exponent and empirical constants has been shown graphically.

Mass and volume growth of larval insect tracheal system within a single instar

“…In most large animals, physiological supply networks distribute oxygen for metabolism throughout the body, while energy from metabolism is used to fuel key processes such as maintenance, development and growth. Whole-organism growth during the juvenile period in particular is energetically demanding in part because it is expensive to grow new tissues, and metabolic demand increases with total body mass (Glazier, 2005;da Silva et al, 2006;Biswas et al, 2008). As an organism grows, its respiratory capacity must also increase so that new tissues can be supplied with oxygen.…”

A theoretical analysis of the growth process of an organism and its dependence on various allometric relations

“…It has been found through some research [5][6][7] that, at the initial stage of growth the surplus power   S E increases with mass and then it decreases after reaching its peak value at a mass which is known as the optimum mass [7]. Based on this fact, we have shown in our earlier studies that 2 1    [24,25]. Thus, the scaling exponent for metabolic cost is found to be greater than the exponent for energy intake.…”

“…In the present study, we have taken 2 1   , under the consideration that metabolic cost is proportional to the body volume (which is directly proportional to mass), in accordance with some studies [3,7,24,27]. Using this value, Eq.1 is expressed as…”

“…Thus, the growth process must stop before reaching the point where According to some studies [24,25], an organism has a natural tendency to attain the optimum mass (…”