When parameters in dynamic models become phenotypes: a case study on flesh pigmentation in the chinook salmon (Oncorhynchus tshawytscha).

The Pacific chinook salmon occurs as both white- and red-fleshed populations, with the flesh color type (red or white) seemingly under strong genetic influence. Previously published data on crosses between red- and white-fleshed individuals cannot be reconciled with a simple Mendelian two-locus, two-allele model, pointing to either a more complex inheritance pattern or the existence of gene interactions. Here we show that a standard single-locus, three-allele model can fully explain these data. Moreover, by implementing the single-locus model at the parameter level of a previously developed mathematical model describing carotenoid dynamics in salmon, we show that variation at a single gene involved in the muscle uptake of carotenoids is able to explain the available data. This illustrates how such a combined approach can generate biological understanding that would not be possible in a classical population genetic explanatory structure. An additional asset of this approach is that by allowing parameters to become phenotypes obeying a given genetic model, biological interpretations of mechanisms involved at a resolution level far beyond what is built into the original dynamic model are made possible. These insights can in turn be exploited in experimental studies as well as in construction of more detailed models.