http://www.bioflux.com.ro/docs/2014.207-216.pdf
There's not always a direct relationship, at least not with natural nutrients. Another way to put it is the same nutrient may be used by different species to produce different colors. Because a food or specific nutrient is a certain color, it doesn't necessarily equal the same color in an animal. Spirulina, which some people think enhances blue, has a blue pigmented nutrient, but also red/orange/yellow pigmented nutrients. Astaxanthin is a good example, an orange-red pigmented carotenoid that can produce red in some species but blue or purple in others, as in blue lobsters, where orange/red astaxanthin looks blue due to protein binding.
https://www.sciencedirect.com/science/article/pii/B9780080262246500206
The most striking and intriguing are the carotenoproteins, from marine invertebrate animals, in which binding to protein causes a large shift in the carotenoid light absorption spectrum so that the complexes are purple, blue or green in colour.
I see this in my kapampa gibberosa, krill based NLS, and Omega One shrimp pellets and Omega One Color pellets (which had salmon, including skin, as a natural color enhancer), were all good for their blue color-- I quit using Omega One when they cheapened their formula, replacing some seafood ingredients with more wheat, etc. I've recently been using some NLS Ultra Red with some (not all) of my kapampa, so far they're still blue, not turning red.
So it depends how an animal processes the nutrient. Red pigmented nutrients can enhance red in animals that are supposed to be red. Overall, though, whatever color fish, good nutrition, health, and clean water is the best formula for color ime.