Mathematical descriptions of indeterminate growth

Abstract

Two models were derived in an effort to better describe the indeterminate nature of growth exhibited by ectotherms. The models are characterized by their non-sigmoidal shape and are based on three assumptions: quantity of growth machinery works at a rate dependent on feed intake; the relationship between growth rate and intake level follows the law of diminishing returns; and growth is irreversible. The Michaelis-Menten and Mitscherlich equations are used in their formulation. To investigate their potential, the models were fitted to six datasets, representing repeated measures of live body weights of two species: rainbow trout (Oncorhynchus mykiss) and Nile tilapia (Oreochromis niloticus). The models were evaluated on the basis of fitting behaviour, examination of residuals, along with measures of goodness-of-fit. Agreement between predicted and observed body weights, and flexibility to mimic growth patterns given varying species and culture conditions, affirm the ability of both models to describe indeterminate growth in fish.

Keywords: Analytical solution; Differential equation; Ectotherm; Growth function; Indeterminate growth.