Most bettas you see, like angels, are far removed from their wild ancestors. F0 is rarely used, the term wild is more often used, as in "wild caught angels" Wild fish are generally more difficult to breed, as they are more demanding in regards to water and diet. This makes anyone involved with breeding a certain species very interested in F1 wilds, as they have completely new bloodlines, in a fish that has been bred domestically. These are generally less demanding than wild caught fish.
F2, F3 etc. is generally used by a breeder to keep track of a certain line. Each successive number is an inbreeding of fish, and as mentioned, once you get beyond F5 with many species you may see a reduction in some other aspect of the fish. This is why breeders trying to fix a certain trait will get multiple lines breeding, and cross lines to reduce or eliminate inbreeding.
The F system is designed for one line of fish, and does not take into account outcrossing. There are many systems used, and most are probably individually created. Here's one explanation of how to keep track; http/www.angelsplus.com/ArticleLinebreeding.htm
F2, F3 etc. is generally used by a breeder to keep track of a certain line. Each successive number is an inbreeding of fish, and as mentioned, once you get beyond F5 with many species you may see a reduction in some other aspect of the fish. This is why breeders trying to fix a certain trait will get multiple lines breeding, and cross lines to reduce or eliminate inbreeding.
The F system is designed for one line of fish, and does not take into account outcrossing. There are many systems used, and most are probably individually created. Here's one explanation of how to keep track; http/www.angelsplus.com/ArticleLinebreeding.htm