Using Fish-Market-Fishes to Demonstrate the Methodological Approach to Establish Mathematical Relations Between Body Size and Body Weight

Body mass index (BMI) is widely used to evaluate if a person has a normal body weight. This index may appear strange to a student because he could expect a cubic relation between body volume and any linear body dimension. The aim of the present experiment was to show the experimental approach to establish a mathematical relation between linear body dimensions and body weight by using a simple animal model. To this end, twelve sea bass and thirteen sea breams were obtained from a local fish-market. For each fish it was measured the body weight, the linear body dimensions, the body volume, the body surface area, and the visceral fat weight. The mathematical relations between all the experimental variables were evaluated pairwise, by plotting them on X-Y graphs and calculating the best fitting power-model. The results demonstrated that in fishes body weight fitted with any of the linear body dimensions raised to a power smaller than 2. The strongest of such correlations was between body weight and body length raised to a power of 1.5. Moreover, BMI did not correlate with visceral fat content. These results demonstrated that in fishes: 1) a non-linear correlation exists between body weight and linear body dimensions; 2) growth is allometric; 3) BMI is a fictitious index and does not describe a physiological phenomenon; 4) BMI is not predictive of visceral fat content; 5) other variables should be taken into account to obtain a more affordable mathematical model to describe the relation between body weight and linear body dimensions.