Equations describing changes of shape along the flatfish body length and their importance for sustainable and responsible fisheries

Background. The purpose of this study was to identify mathematical equations describing changes in a flatfish body shape along its longitudinal axis. The initial function for the description of a cross-section contour is the ellipse equation including a factor deforming the symmetry with respect to one of axes. Such equations may find their use in fisheries engineering and food-fish processing. Materials and methods. The morphometric examination of the fish raw material was carried out in order to check whether the proposed function meets expectations and draws a curve. The model fish species used was flounder, Platichthys flesus (L.). Results. The mathematical equation describing changes in a cross-section contour of flatfish body shape along its longitudinal axis. The high value of correlation coefficients (r > 0.99) showed that a hypothetical curve matches experiment results quite well. The equation describing the shape of a flatfish body cross-section contour can be defined by means of the ellipse equation including a factor deforming the symmetry with regard to one of its axes. The function represented by equation (8) draws a curve that follows the contour of the fish cross-section. Conclusion. The shape of flounder, defined in the presently reported study may have importance for sustainable and responsible fisheries, helping to design more selective fishing gear. It can also be used in food-fish engineering for designing more effective fish-processing machinery.