I breed many species of fish. The bloodline subject isn't a big thing that I worry about. I do, from time to time, move fish (male or the female harem, from tank to tank to help prevent heavy inbreeding. A prime example of the bad effects of heavy inbreeding is the
Neon Tetra. The practice of heavy inbreeding can result in faded colors and other genetic abnormalities.
We cannot be sure when we buy a "colony" of fish to start a breeding setup from our lfs's, that these fish are not related in some way. Most, and I say most, breeders are not worried about gene purity, but species purity, unless they are trying to create a viable hybrid. Examples of this are guppies, mollies,
Discus, and some of the other new "mutts" currently showing up in the trade.