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

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.

[1]  J. Weiner,et al.  Interspecific Allometries Are by-Products of Body Size Optimization , 1997, The American Naturalist.

[2]  Jaap van der Meer,et al.  Metabolic theories in ecology , 2006 .

[3]  L. Bertalanffy,et al.  A quantitative theory of organic growth , 1938 .

[4]  Bai-lian Li,et al.  Ontogenetic growth: models and theory , 2004 .

[5]  C. Duarte,et al.  Allometric laws and prediction in estuarine and coastal ecology , 2006 .

[6]  K. Sebens.  Energetic Constraints, Size Gradients, and Size Limits in Benthic Marine Invertebrates1 , 2002, Integrative and comparative biology.

[7]  H. Lasker,et al.  Allometry of resource capture in colonial cnidarians and constraints on modular growth , 1998 .

[8]  J. Kozłowski.  Optimal allocation of resources to growth and reproduction: Implications for age and size at maturity. , 1992, Trends in ecology & evolution.

[9]  James H. Brown,et al.  Growth models based on first principles or phenomenology , 2004 .

[10]  James H Brown,et al.  Allometric scaling of metabolic rate from molecules and mitochondria to cells and mammals , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[11]  K. Sebens.  THE LIMITS TO INDETERMINATE GROWTH: AN OPTIMAL SIZE MODEL APPLIED TO PASSIVE SUSPENSION FEEDERS' , 1982 .

[12]  James H. Brown,et al.  A General Model for the Origin of Allometric Scaling Laws in Biology , 1997, Science.

[13]  L. Hedin.  Physiology: Plants on a different scale , 2006, Nature.

[14]  A. C. Economos,et al.  On the origin of biological similarity , 1982 .

[15]  R. Freckleton,et al.  Phenotypic plasticity in the scaling of avian basal metabolic rate , 2006, Proceedings of the Royal Society B: Biological Sciences.

[16]  L. Bertalanffy.  Quantitative Laws in Metabolism and Growth , 1957 .

[17]  Lloyd Demetrius,et al.  The origin of allometric scaling laws in biology. , 2006, Journal of theoretical biology.