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Many livestock and bird fancy breeders worry about inbreeding. They try to get as unrelated mates as possible. This is a pretty good viewpoint so long as it is feasible and the aim is to maintain type already established.
However, inbreeding is sometimes desirable to disclose or fix a new type. (Almost all the types [breeds] of cattle, horses, sheep, etc. were inbred in order to fix the type early in construction of the breed.) Sometimes an unrelated mate is not available. So some information about inbreeding should be useful. In lieu of a whole chapter from a genetics book on systems of mating and inbreeding, perhaps the following will suffice for those untrained in genetics.
Technically, inbreeding is the mating between individuals more closely related than a pair randomly chosen from the population. In humans cousin marriages, uncle-niece, even father-daughter, and brother-sister combinations are real examples. For example, there are 30% consanguineous ("blood relation") marriages among the Hindu of Bangalore in Southern India. 55% of marriages among Pakistanis are between first cousins. Many other examples in humans are not rare! Cleopatra is reputed to be the result of 9 generations of either uncle-niece or brother-sister marriages!
The only genetic consequence of inbreeding is to make an individual, the offspring, more homozygous than usual.
Homozygous means a gene [whether good, neutral, or bad] is present in double dose = is fixed. One such gene is from the father and one from the mother.
Inbreeding can fix good genes as well as bad ones. Selection along with inbreeding can eliminate most of the bad genes from a stock as happens in inbred corn (maize) which is a mainstay in American agriculture now [after it is crossed with other inbred stocks]. Many other examples occur, even in the poultry industry.
Inbreeding occurs in wild animals as well. Japanese quail and vervet monkeys have been shown to prefer a first cousin mate over siblings (brother/sister), but also over third cousins or unrelated individuals! Such studies result in a concept of optimal outbreeding in which there are selective benefits to choosing a mate which is not so closely related as to risk inimical genetic consequences, but not so distant that any specific genetic adaptations to local circumstances (niche) might be diluted and lost.
Undesirable results do occur when recessive bad genes get together in inbred offspring. This happens 1/4 of the time when both parents happen to carry the same bad gene which is, of course, more likely with relatives. It is slightly more frequent, however, since any one individual may carry several bad genes. Humans have been postulated by Muller, a Nobel prize winner, to have on the average 6 or 7 bad or detrimental genes each. More recent evidence increases this estimate. Cage birds likely carry fewer such bad genes since they have been periodically (sporadically) inbred in maintaining the stocks earlier on and by fanciers who cant (or dont) make great efforts to find unrelated mates.
Inbreeding depression is the term for reduced vigor and production in inbred agricultural stocks. Not all bad genes kill immediately. Various degrees of bad results may occur. Bad or detrimental genes may affect or effect almost any kind of character you can think of: fertility, disease resistance, environmental adaptation, the senses (e.g. blindness ), structure, and so on.
When an offspring has such a detrimental character, one can discard it, or if it is viable, breed it and study it. Such mutants are necessary to understand how normal genes act.
Generally, then, fanciers need not be afraid to inbreed. But they do need to be ready to accept infrequent, even rare, results that are bad and need to be selected out, or given to a geneticist.
Anyway it takes only one outcross to undo the effects of inbreeding!