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

A new mathematical model regarding the growth process of an organism is proposed, based on the role of surplus power (i.e. power intake minus metabolic cost) and having an allometric dependence on mass. Considering its use in growth, a differential equation has been formed, similar to the von Bertalanffy growth function (VBGF). The time dependence of mass and growth rate, obtained from this equation, has been shown graphically to illustrate the roles played by scaling exponents and other parameters. Concepts of optimum mass, saturation mass and the mass corresponding to the highest growth rate have been discussed under the proposed theoretical framework. Information regarding the dependence of effective growth duration on various parameters has been found graphically. The time of occurrence of the highest growth rate and its dependence on various parameters have been explored graphically. A new parameter (ρ) has been defined, which determines the availability of surplus power at different stages of the growth process of an organism. Depending on its value, there can be three distinctly different modes of growth phenomenon, reflected in the change of surplus power with time. The variations of growth and reproduction efficiencies with time and mass have been shown for different values of the scaling exponent. The limitation regarding the practical measurement of growth rate has been discussed using the present model. Some aspects of length-biomass allometry have been explored theoretically and the results have been depicted graphically.