You can ask yourself why is it risky to use a superior animal excessively? The answer is because of the increasing effect it has on the rate of inbreeding. The rate of inbreeding is an indication of the risk of increased frequency of genetic disorders. It has been estimated that every individual is carrier of at least 5 recessive disorders, most of them still unknown. Genetic contributions are directly related to the rate of inbreeding. Large contributions increase the risk of becoming homozygous for these genetic disorders in the future.
To get some insight in how genetic disorders spread through the population we will consider the ‘birth’ of a new disorder: the occurrence of a mutation with negative but recessive effect. It may take quite some time before this new mutation is noticed because at first it only occurs in a few offspring (approximately 50%) that became carrier. In the next generation usually it still will only occur as carrier because often brother-sister matings are prohibited. So it will take another generation for homozygous animals to occur, and only if matings between generations (parent-offspring or uncle-niece type of matings) are allowed. Even then the number of homozygous recessives will be small so, depending on the type of defect, it may still go unnoticed. Only in the fourth generation after the mutation occurred there will be animals that are homozygous because of mating between not very close relatives. It will depend on the severity of the disorder whether it will be recognized as such in the first generations of homozygosity of the disorder. Especially if the disorder does not lead to very severe problems it may go unrecognized for a very long time. By the time it is recognized the allele frequency in the population already may be quite substantial.
In the figure below you find a numerical example to create some feeling for the chance of timely detection of a mutation with negative effect. Underlying this table are a number of assumptions related to number of offspring (each animal will have 10 offspring) and avoiding close inbreeding (no brother-sister or parent-offspring mating). Given those assumptions, the table shows that a new mutation takes about 4 new generations before there is some chance of being noticed. It will only be noticed if the consequences of the mutation are very negative AND cannot be attributed to something else. For example, if the mutation has a negative effect on embryo survival, it will take much longer before it is realized that the seemingly lack of fertility is due to embryo mortality and not due to other reasons like poor sperm quality. To come back to the numerical example: At some point a negative recessive mutation occurs. The offspring of the animal will partly be carrier: half of the offspring inherited the mutated allele and half to wild type: In generation 1 5 animals are carrier and 5 are not. All other animals in the population are wild type, they are not in the table, but can be used for mating, as happened in generation 1 to create generation 2 (no mating between sibs was allowed). Again 10 offspring per animal, resulting in 25 carriers and 75 wild type. In the next generation again mating was only with wild type resulting in 125 carriers and 825 wild type. Then mating between carriers is allowed, but still not between sibs. So out of the 125 carriers only 100 are allowed to mate. IF ALL OF THESE ANIMALS MATE to each other (so only carrier mates to carrier), then the number of affected animals would be 25, out of 10,000! So given all assumptions, that are fairly realistic although the 10 offspring per animal may be a bit much, after 4 generations only a maximum of 0.25% of the animals are affected. If the effect of the genetic disorder is not very extreme or unusual, it will take many more generations before people realise that the number of affected animals is increasing and perhaps could it be heritable??
This was only a numerical example, but these things really happen! A famous (or rather infamous) example is that of the heritable disorders BLAD (bovine leucocyte adhesion deficiency) and CVM (complex vertebral malformation) in Holstein dairy cattle. A very large genetic contribution of a single bull resulted in two heritable disorders that were spread widely though the Holstein population.