An animal can be homozygous for a monogenic trait (it got the same allele from its sire and from its dam) or heterozygous (it got a different allele from its sire and from its dam).
The alleles determining the expression of monogenic traits may be dominant, intermediate or recessive. The heterozygous genotype has a value
...
equal to one of the homozygous genotypes (dominant), or higher (co-dominant) or equal to the average value of both homozygous genotypes (intermediate).
The Hardy and Weinberg equilibrium implies that in large populations with random mating among parents, and in the absence of selection, migration, mutation and random drift, the genotype and allele frequencies are constant (do not change from generation to generation) and the genotype frequencies can be calculated from the allele frequencies.
When the genotypes of the parents are known, you know what genotypes you may expect in the offspring. These expectations are based on the Mendelian laws, but due to random effects, the real world may deviate from the expectations.
In all species a lot of desired monogenic traits or traits with a large positive effect are known: e.g. colour genes and genes affecting the quality of animal’s products.
In all species a lot of undesired monogenic traits are known. They are often based on recessive alleles and cause genetic defects when homozygous present in an animal.
The allele for a genetic defect will be spread in the population when the carrier is used extensively for breeding and it will pop up when in later generations animals with an additive relationship with the carrier are mated.
Genetic markers for a recessive genetic defect are highly valuable in the selection against heterozygous carriers of the allele for the defect. A prerequisite is that the genetic marker is positioned close to the recessive allele, otherwise recombination may disrupt the linkage between the marker and the allele.
The best strategy to decrease the allele frequency for the recessive defect is to test the offspring of carriers with the genetic marker and to select for the subsequent generation only animals that do not carry the allele.