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A spreadsheet model was constructed to describe the change in allelic frequency over time for a lethal recessive mutation in an animal population. The model allowed relative fitness to differ between genotypes, between sexes, and over time. Whereas a lethal recessive allele is naturally eliminated very slowly from a population, a small selective disadvantage of the heterozygote results in a large increase in the rate of elimination. With selective advantage of the heterozygote through linkage with a production trait or pleiotropy, the allele is never naturally eliminated but tends toward a stable equilibrium frequency. The model was used to investigate various alternative control programs based on the detection of heterozygotes by genotyping and their exclusion from breeding. The programs (genotyping males only, genotyping males and 50% of females, and genotyping all breeding animals) were modeled for various initial heterozygote frequencies, and the results were described in terms of the number of generations, number of tests, and number of culls required to reduce the heterozygote frequency to a predefined level. The model can be used to compare the feasibility and cost of various control strategies and to illustrate clearly to breeders the expected outcomes, as well as the danger of prematurely terminating a control program when there is a selective advantage of the heterozygote.

Changes in disease gene frequency over time with differential genotypic fitness and various control strategies