The Hardy-Weinberg Theorem practice problem

The Hardy-Weinberg Theorem deals with Mendelian genetics in the context of populations of diploid, sexually reproducing individuals. Given a set of assumptions (discussed below), this theorem states that: allele frequencies in a population will not change from generation to generation. if the allele frequencies in a population with two alleles at a locus are p and q, then the expected genotype frequencies are p2, 2pq, and q2. This frequency distribution will not change from generation to generation once a population is in Hardy-Weinberg equilibrium. For example, if the frequency of allele A in the population is p and the frequency of allele a in the population is q, then the frequency of genotype AA = p2, the frequency of genotype Aa = 2pq, and the frequency of genotype aa = q2. If there are only two alleles at a locus, then p q , by mathematical necessity, equals one. The Hardy-Weinberg genotype frequencies, p2 2pq q2, represent the binomial expansion of (p q)2, and also sum to one (as must the frequencies of all genotypes in any population, whether it is in Hardy-Weinberg equilibrium). It is possible to apply the Hardy-Weinberg Theorem to loci with more than two alleles, in which case the expected genotype frequencies are given by the multinomial expansion for all k alleles segregating in the population: (p1 p2 p3 . . . pk)2. The conclusions of the Hardy-Weinberg Theorem apply only when the population conforms to the following assumptions: Natural selection is not acting on the locus in question (i.e., there are no consistent differences in probabilities of survival or reproduction among genotypes). Neither mutation (the origin of new alleles) nor migration (the movement of individuals and their genes into or out of the population) is introducing new alleles into the population. Population size is infinite, which means that genetic drift is not causing random changes in allele frequencies due to sampling error from one generation to the next. Of course, all natural populations are finite and thus subject to drift, but we expect the effects of drift to be more pronounced in small than in large populations. Individuals in the population mate randomly with respect to the locus in question. Although nonrandom mating does not change allele frequencies from one generation to the next if the other assumptions hold, it can generate deviations from expected genotype frequencies, and it can set the stage for natural selection to cause evolutionary change. If the genotype frequencies in a population deviate from Hardy-Weinberg expectations, it takes only one generation of random mating to bring them into the equilibrium proportions, provided that the above assumptions hold, that allele frequencies are equal in males and females (or else that individuals are hermaphrodites), and that the locus is autosomal. If allele frequencies differ between the sexes, it takes two generations of random mating to attain Hardy-Weinberg equilibrium. Sex-linked loci require multiple generations to attain equilibrium because one sex has two copies of the gene and the other sex has only one. Given these conditions, it is easy to derive the expected Hardy-Weinberg genotype frequencies if we think about random mating in terms of the probability of producing each genotype via random union of gametes into zygotes (Table 1). If each allele occurs at the same frequencies in sperm and eggs, and gametes unite at random to produce zygotes, then the probability that any two alleles will combine to form a particular genotype equals the product of the allele frequencies. Since there are two ways of generating the heterozygous genotype (A egg and a sperm, or a egg and A sperm), we sum the probabilities of those two types of union to arrive at the expected Hardy-Weinberg frequency of the heterozygous genotype. It is important to recognize that the Hardy-Weinberg equilibrium is a neutral equilibrium, which means that a population perturbed from its Hardy-Weinberg genotype frequencies will indeed reach equilibrium after a single generation of random mating (if it conforms to the other assumptions of the theorem), but it will be a new equilibrium if allele frequencies have changed. This property distinguishes a neutral equilibrium from a stable equilibrium, in which a perturbed system returns to the same equilibrium state. It makes sense that the Hardy-Weinberg equilibrium is not stable, since a change from the equilibrium genotype frequencies will generally be associated with a change in allele frequencies (p and q), which will in turn lead to new values of p2, 2pq and q2. Problem: The people living in a small town were tested to determine the Rh factor. From the 899 samples tested with anti-Rh serum, 75.9 percent were positive and 24. 1 percent were negative. Assuming a single pair of alleles R and r , what proportion of the people would be expected to be RR, Rr, and rr? #Genetics #ABOBloodGroup #populationGenetics #alleleFr