The offspring resulting from inbreeding tend to have health problems and lower reproductive success. This is known as inbreeding depression. Inbreeding depression occurs because of a quirk of natural selection and genetics. As natural selection acts on a population, it weeds out genes that have disadvantageous effects, but it can only weed out these genes if they are actually expressed in an individual. For dominant gene versions, that's no problem. Individuals carrying dominant genes with a detrimental effect will be selected against, and eventually, these genes will be purged from the population. For recessive gene versions, however, the story is a bit different. Recessive genes are only expressed when an individual carries two copies of them. Once natural selection has removed most of the detrimental recessive genes from a population, these seldom wind up paired with an identical copy and are effectively hidden from the effects of natural selection. This means that most populations carry many deleterious recessive gene versions that are very rarely expressed — except in cases of inbreeding. Closely related individuals are likely to carry the same deleterious recessive gene versions and pass two copies of that gene on to their offspring.
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