How to solve Hardy-Weinberg problems

Godfrey Hardy and Wilhelm Weinberg went on to develop a simple equation that can be used to discover the probable genotype frequencies in a population and to track their changes from one generation to another. This has become known as the Hardy-Weinberg equilibrium equation. In this equation (p² 2pq q² = 1), p is defined as the frequency of the dominant allele and q as the frequency of the recessive allele for a trait controlled by a pair of alleles (A and a). In other words, p equals all of the alleles in individuals who are homozygous dominant (AA) and half of the alleles in people who are heterozygous (Aa) for this trait in a population. In mathematical terms, this is p = AA ½Aa Likewise, q equals all of the alleles in individuals who are homozygous recessive (aa) and the other half of the alleles in people who are heterozygous (Aa). q = aa ½Aa Because there are only two alleles in this case, the frequency of one plus the frequency of the other must equal 100%, which is to say p q = 1 Since this is logically true, then the following must also be correct: p = 1 - q There were only a few short steps from this knowledge for Hardy and Weinberg to realize that the chances of all possible combinations of alleles occurring randomly is (p q)² = 1 or more simply p² 2pq q² = 1 In this equation, p² is the predicted frequency of homozygous dominant (AA) people in a population, 2pq is the predicted frequency of heterozygous (Aa) people, and q² is the predicted frequency of homozygous recessive (aa) ones. From observations of phenotypes, it is usually only possible to know the frequency of homozygous recessive people, or q² in the equation, since they will not have the dominant trait. Those who express the trait in their phenotype could be either homozygous dominant (p²) or heterozygous (2pq). The Hardy-Weinberg equation allows us to predict which ones they are. Since p = 1 - q and q is known, it is possible to calculate p as well. Knowing p and q, it is a simple matter to plug these values into the Hardy-Weinberg equation (p² 2pq q² = 1). This then provides the predicted frequencies of all three genotypes for the selected trait within the population. #Genotype #Homozygous #Heterozygous #allele #HardyWeinbergEquilibrium #genetics #PopulationGenetics #Biology