Just rewatching this Carrot breeding video again and wanted to link to it.
Lots to learn about which colors are easy to get into a population (white and yellow) and which are more difficult (orange and red). And how you can maintain them long-term. Interestingly, the genes coding for purple are independent from those carotenoids, which is why you can get purple roots with either white, yellow, orange, red backgrounds.
I also learned that two traits are very difficult to select against once they are in your population: green shoulders and yellow core. But that you can cross your population with a type that doesn’t have the trait and then select against it.