Populatiopn Genetics III
Effects of non-random breeding: inbreeding
Domestic animals are usually inbred to some extent, with breeders tending to mate animals that are very closely (inbreeding) or more distantly (linebreeding) related to each other. True outcrossing is relatively rare, and basically occurs only when an animal is brought in from a completely different gene pool. (In some cases, breeding to an imported animal plays this role.) If any inbreeding is going on, it will have the effect of increasing the number of matings in which both parents are of the same type.
As an extreme case of inbreeding, consider the case in which we start with a random-bred population, but breed only normals to normals, carriers to carriers, and affecteds to affecteds. (This is actually the strongest form of inbreeding in plants, as would be obtained by selfing the plants for generation after generation. It is not possible to inbreed this strongly with animals, but the results are instructive in sugesting the direction in which inbreeding will push the ratio of affected to carrier to normal individuals.
Let f be the gene frequency in the starting, random-bred population, with a = f x f, c = 2 x f x (1-f) and n = (1-f) x (1-f). Future generations are bred only to their own type, but there is no other selection. The result? There is no change in f (no selection) but the fraction of carriers is rapidly reduced (by a factor of 2 in each generation in the case given), with both the homozygous groups increasing. Eventually, the fraction of affecteds equals the gene frequency, the fraction of normals equals one minus the gene frequency, and there are no carriers.
This is one of the arguements for inbreeding - that it brings undesirable recessives to the surface, where they can be eliminated. Even a realistically inbred population will not follow the random-breeding figures of affected = f x f, carrier = 2 x f x (1-f), normal = (1-f) x (1-f), but will have more normals and affecteds, and fewer carriers.