A pigmentation model for farmed Atlantic salmon: Nonlinear regression analysis of published experimental data

The most prominent quality characteristic of post-smolt Atlantic salmon is the red/pink flesh colour. The primary source of this colouration is caused by deposition of relatively large amounts of colour pigments, such as astaxanthin and canthaxanthin, obtained from their diet. The accumulation of astaxanthin in the muscle is also dependent on fish size. The fish farmer must therefore optimise the dietary composition supplied to salmon that results in the desired flesh colour required by the customers. This study modelled the relationships between chemical muscle astaxanthin concentration and visual colour perception (SalmoFan score), and the explanatory variables dietary astaxanthin concentration and fish size. Parameter estimates were analyzed by nonlinear regression analysis (Levenberg–Marquardt algorithm). The results showed that the two dependent variables gave excellent fit to the observed data (R2 = 0.968; N = 43). The mathematical model developed in this study can therefore be used to explore the relationship flesh colour in salmon and its relationship to fish size and dietary composition on an integrated way.