Selective breeding of small livestock is important to the survivalist because you will not be able to get replacement livestock from other sources if things get truly bad. You will have to maintain your own breeding population to replace those animal you consume, are killed by predators, die of disease, or even old age.
The first principle is that you will keep only a few male animals and a preponderance of female animals. The females of course gestate. The more females you have the more offspring can be produced. You will need some males. You certainly would want to have a “herd sire” and a spare. But you probably would not keep more than two because one male can service many females, and your space and feed will probably be limited. That having been said, your rooster, ram, buck goat, etc. should be the very best you can get. The old saying is that the male is 50% of the herd. He will provide his genetic material to ALL the offspring.
Once your animals are producing offspring, you will want to select the very best to raise up as replacements. First, they ought to be the daughters out of your very best females. Which are your best females? These would be the females that are healthy and have never been prone to any illness. Select chicks from your hens that started laying eggs the earliest, laid the most eggs, and kept laying even into the winter when the other hens stopped laying. For rabbits, select offspring from the does that raised the most bunnies to butcher weight on her milk alone. Select ones from does that breed readily, have large litters, but also have plenty of milk to feed their babies. For sheep and goats, select the offspring from the mothers that had no problems during their births, are calm mothers with lots of milk, never suffered from hoof or teeth problems, with well-formed udders and teats (“easy milkers”), and have been free of udder infections. Also, only select from ewes and doe goats that have twins. Twinning is an inherited trait. (Make sure your ram was a twin as well, because he can pass this gene on to his daughters).
The offspring you ought to eat first are the offspring from the inferior females that don’t lay as many eggs, don’t have twins, are prone to illnesses, are nervous mothers, or are less productive in some way. Your next step ids then to start raising up replacement young females. At the point when the yearlings come into production themselves you will want to cull your senior females that were not as healthy and productive as the others in the herd or flock. Your will also need to raise up a few young males to be eventual replacements. If you decide you have space to raise two young males you would be wise select males from two different mothers so as to maintain some genetic diversity.
In conclusion, I believe that your goal should be increased productivity and vigor in your herds and flocks. Obviously your goals will not be the same as someone who is breeding for “show”that is breeding for a certain look.