The frequencies of genotypes and of alleles have a relationship. When the allele frequencies are known, the genotype frequencies can be calculated. This relationship is known in population genetics as the law of Hardy and Weinberg. This law is valid in a population, stable (e.g. no migration) over generations. In such a stable population the Hardy and Weinberg equilibrium is at stake.
Definition
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
The Hardy and Weinberg equilibrium indicates the stability of a population over generations. The frequency of the genotype Z/Z = p*p = p2 , because they originate from a combination of sperm cells and oocytes carrying the Z allele each with a frequency of p. The frequency of the genotype z/z = q*q = q2 , because they originate from a combination of sperm cells and oocytes carrying the z allele each with a frequency of q. The genotype Z/z is created in two ways: by combination of a sperm cell with the Z allele (frequency p) and an oocyte with the z allele (frequency q) and by combination of a sperm cell with the z allele (frequency q) and an oocyte with the Z allele (frequency p). Therefore the frequency of the genotype Z/z = 2*p*q = 2pq.
Table 1: The frequencies of alleles and genotypes when animals are mated in a population in Hardy and Weinberg equilibrium
Oocyte Sperm cell | Allele Z | Frequency p | Allele z | Frequency q |
Allele Z | ZZ |
| Zz | |
Frequency P | P2 | pq | ||
Allele z | Zz | zz | ||
Frequency p | pq | q2 |
Allele and genotype frequencies in a population determine the proportion of animals with different phenotypes for monogenic traits. The effect of selection for desired monogenic traits or against undesired monogenic traits depends partly of the underlying allele frequencies. That is the reason to pay attention to allele and genotype frequencies here.
In populations of breeding animals mating of parents is often not ad random and parents are selected for breeding goal traits. Sometimes immigration of animals from other populations is at stake and in small populations random drift may cause shifts in allele frequencies. Therefore, in most breeding populations the presence of the Hardy and Weinberg equilibrium is doubtful. Nevertheless, it is of help to predict genotype frequencies from known allele frequencies for monogenic traits not under selection.