Two more Hardy-Weinberg problems and solutions

The Hardy–Weinberg principle relates allele frequencies to genotype frequencies in a randomly mating population. Imagine that you have a population with two alleles (A and B) that segregate at a single locus. The frequency of allele A is denoted by p and the frequency of allele B is denoted by q. The Hardy–Weinberg principle states that after one generation of random mating genotype frequencies will be p2, 2pq, and q2. In the absence of other evolutionary forces (such as natural selection), genotype frequencies are expected to remain constant and the population is said to be at Hardy–Weinberg equilibrium. The Hardy–Weinberg principle relies on a number of assumptions: (1) random mating (i.e, population structure is absent and matings occur in proportion to genotype frequencies), (2) the absence of natural selection, (3) a very large population size (i.e., genetic drift is negligible), (4) no gene flow or migration, (5) no mutation, and (6) the locus is autosomal. When these assumptions are violated, departures from Hardy–Weinberg proportions can result. One useful way to think about the Hardy–Weinberg principle is to use the metaphor of a gene pool (Crow, 2001). Here, individuals contribute alleles to an infinitely large pool of gametes. In a randomly mating population without natural selection, offspring genotypes are found by randomly sampling two alleles from this gene pool (one from their mother and one from their father). Because the allele that an individual receives from their mother is independent of the allele they receive from their father, the probability of observing a particular genotype is found by multiplying maternal and paternal allele frequencies. Mathematically this involves the binomial expansion: (p q)2 = p2 2pq q2 (see the modified Punnett Square in Figure 1 for a graphical representation). Note that there are two ways that an individual can be an AB heterozygote: they can either inherit an A allele from their mother and a B allele from their father or they can inherit a B allele from their mother and an A allele from their father. #HardyWeinbergPrinciple #MathematicsFieldOfStudy #genetics #AlleleFrequency #HardyWeinbergLaw #population #alleleFrequencies #mutation #genotypes #HardyWeinbergEquilibrium #populationGenetics #hardyWeinbergAssumptions #hardyWeinberg #genotypeFrequencies #hardyWeinbergEquations #hardyWeinbergEquilibriumExplained #genotype #educational #biology #NikolaysGeneticsLessons #apBiology #hardyweinbergProblems #hardyWeinbergEquilibrium #genes