A mathematical model for growth in weight of silver catfish (Rhamdia quelen) (Heptapteridae, Siluriformes, Teleostei)

Abstract

The use of a mathematical model applied to biological science helps to predict the specific data. Based on biological data (weight and age) of silver catfish, Rhamdia quelen, a mathematical model was elaborated based on a nonlinear difference equation to demonstrate the relationship between age and growth in weight. Silver catfish growth was described following the Beverton-Holt model Pt+1 = (r Pt) / (1+α P t), where r > 0 is the maximum growth rate and α > 0 is a constant of growth inhibition. The solution of this equation is Pt= 1 /{[1/P0 - α / (r-1)] 1/rt + α/ (r-1)}, were P0 is the initial weight of the fish. Through this model it was observed that the female reaches the theoretical maximum weight approximately at the age of 18 years and the male at the age of 12 years in a natural environment.