The Hardy-Weinberg Law states that under certain conditions, a population is able to maintain its relative allele frequencies, i.e., a stable ratio of dominant to recessive genes. This ratio is the Hardy-Weinberg Equilibrium. Consider a population whose gene pool contains the alleles A and a. Alleles are alternative forms of a gene at the same position on a chromosome. In a diploid individual, there are two possible alleles at each locus. If they are different, then the individual is said to be heterozygous and if they are the same, the individual is said to be homozygous. On the other hand, a population is able to have many different alleles at the same locus. The gene frequency of an allele within a population is the number of a specific type of allele divided by the total number of genes for that trait. Gene frequencies can be either low or high and do not depend upon how the gene is expressed. Changes in gene frequency result in evolutionary changes. In order for evolution to occur, the population must have enough genetic diversity, a reservoir of variability, so that at least some members of the population can respond to changing environmental conditions. If no mechanisms that can cause evolution are acting on a population, then evolution will not take place.
By convention, genetic nomenclature states A is dominant to a. English mathematician G. H. Hardy and German physician Wilhelm Weinberg, in 1908, assigned the letter p to the dominant allele A and the letter q for the recessive allele a. The sum of all the alleles must be equal to 100% so, p + q = 1. They then theorized that the frequency of AA types would be p2, the frequency of aa types would be q2, and the frequency of Aa individuals would be 2pq. (Refer to Punnett squares).For clarification, consider a hypothetical case where a population of mice in which 80 % of the gametes in the population carry the dominant allele A for gray coat, and 20% carry the recessive allele a for a white coat. In a random union of these gametes, 64% would be homozygous AA (0.8 x 0.8 = 0.64), 32% would be Aa (0.8 x 0.2 x 2= 0.32) and 4% would be homozygous aa (0.2 x 0.2 = 0.04). By adding 0.64 to 0.32, it is found that 0.96 % of the mice will have gray coats and only 4% will have white coats. Will the white coat eventually disappear? An explanation of why not follows. All the gametes formed by the AA mice will contain the A allele, and so will one-half of the heterozygous Aa mice (64 + 0.32/2 = 0.80%). All the gametes for the white aa individuals will contain the a allele, but so will one-half the heterozygous Aa mice (0.04 +.32/2 = 20 %). The relative ratio of alleles stays the same. This is true, however, only when certain criteria are met.
By definition, evolution occurs at the population level, so the first criteria needed to maintain Hardy-Weinberg equilibrium is a population large enough to minimize the random loss of alleles by genetic drift and to avoid inbreeding. The next condition is that there should be no mating preference, i.e., an AA female does not selectively prefer an aa male and that the entire population is involved in reproduction. Mutation probably plays a very minor role, but is also a factor. It is also necessary for no exchange of genes between populations (migration) to be present. The final criteria for maintaining Hardy-Weinberg equilibrium is that there be no natural selection. This means that there is no advantage (reproductive success) conferred on some individuals with a particular genotype, in their interactions with the environment.
In reality, these conditions are not met, as selection pressure is applied and gene frequencies within populations change over time. What then is the use of the Hardy-Weinberg equilibrium? It is very useful in determining gene frequencies in a population. The only time the genotype of an individual is known by looking at the phenotype, is when that individual is homozygous recessive. The previous example of the (aa) white mice is an illustration. (The gene frequency of the white trait was 4%.) Since A is dominant, the gray phenotype could be either the AA or Aa genotype. Remember (p + q = 1). So, (q = 1- p), and because q2 = 0.04, q =.2. Therefore, p = 0.8, since p2 + 2pq + q2 = 1, the frequency of the AA trait is 64%, and the frequency of the Aa trait is 32%.
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