A Mathematical Model of Some Aspects of Fish Growth, Respiration, and Mortality

Abstract

A simple metabolic model describing growth as the difference between what enters the body and what leaves it, is elaborated assuming that synthetic processes (the building-up, the anabolism) are consuming energy supplied by processes of decomposition (the break-down, the catabolism). This leads to partitioning total catabolism into two components, one being a function of the rate of synthesis, another keeping the body functioning independently of synthesis. The rate of synthesis is described as a function of food taken, of the efficiencies of digestion and energy conversion, and of the absorbing surface of the intestine. Catabolic processes are supposed to be functions of the oxygen concentration in the water, the absorbing surface of the gills, and the rate of oxygen transport. Both kinds of processes are made functions of temperature in the way enzymatic processes usually are. Assuming that molecular interactions accidentally go wrong makes natural mortality, like growth, a function of the rates of anabolic and catabolic processes and body size.Application of the model to data of length-at-age, food and oxygen consumption, weight loss, gill area, and natural mortality indicates that at least some of the main hypotheses cannot be rejected on available evidence.