An assumption from your question is that you have bull calves by the same sire as 13 heifer calves saved for replacements; thus, you are considering mating these bulls to their half-sisters. Mating half-sibs should not result in defective calves unless the parents are carriers of recessive genetic defects. Expression of recessive genetic defects requires that both parents carry a single copy of the defect gene. Animals with two copies of the recessive defect will express the trait. So, if the AI sire carried a single copy of the recessive defect, it is possible that mating half-sib progeny could produce affected calves. Inbreeding brings such defects to the surface faster.
Generally, inbreeding does depress fitness traits such as fertility and overall performance; however, at low levels, it may not have a noticeable effect. The inbreeding coefficient, or probability that an animal has two identical alleles or forms of a gene inherited from a common ancestor, of half-sib matings (assuming other ancestors are not inbred) is 12.5%. By comparison, most breeds of beef cattle in the United States are 8 to 10% inbred. Inbreeding is accumulated through the pedigree structure, so these animals could have inbreeding of 20 to 22.5% which is concerning for a commercial producer. The bottom line is that the half-sib matings you are considering will probably not present problems; however, further close matings might very well result in a depression of performance.
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beef cattle, inbreeding, half sibs