HARDY- WEINBERG PRACTICE PROBLEMS PROBLEMS TO SOLVE: 1. The proportion of homozygous recessives of a certain population is 0.09. If we assume that the gene pool is large and at equilibrium and all genotypes are equally successful in reproduction, what proportion of the population would you expect to be heterozygous for this trait? 2. Approximately 36% of a certain population are unable to taste the compound phenylthiocarbamide (PTC). Everyone else finds it very bitter tasting. If we assume that the non-tasters are homozygous for the recessive gene, t, what is the frequency of: a) homozygous dominants, (TT) b) heterozygotes, (Tt) 3. In a certain population, approximately one child in 2500 is homozygous for the gene z. Assuming Hardy-Weinberg equilibrium, what is the proportion of carriers (heterozygotes) in the population? 4. The frequency of sickle-cell anemia (ss) among the children in one malarial region of Africa is 144 out of 10 000. Assuming H-W equilibrium, what is the approximate frequency of heterozygotes (Ss) in this population? 5. In a population with two alleles for a particular locus, B and b, the allele frequency of B is 0.7. What would be the frequency of heterozygotes if the population is in H-W equilibrium? 6. In a population that is in H-W equilibrium, 16% of the individuals show the recessive trait. What is the frequency of the dominant allele in the population? 7. If 9% of an African population is born with a severe form of sickle-cell anemia (ss), what percentage of the population will be more resistant to malaria because they are heterozygous (Ss) for the sicklecell gene? 8. After graduation, you and 19 friends build a raft, sail to a deserted island, and start a new population, totally isolated from the world. Two of your friends carry (that is, are heterozygous for) the recessive cf allele, which in homozygotes causes cystic fibrosis. A. Assuming that the frequency of this allele does not change as the population grows, what will be the instance of cystic fibrosis on your island? B. Cystic fibrous births on the island is how many times greater than the original mainland. The frequency of births on the mainland is.059%.
HARDY-WEINBERG PRINCIPLE Phenotype Black Black White Genotypes AA Aa (aa) Number of moths 320 160 20 (total = 500) Genotype frequencies Number of alleles In gene pool (total = 1000) x 2 x 2 Allele frequencies
For a gene with only two different alleles (A and a), the Hardy-Weinberg principle can be expressed using the equation below: If p = frequency of allele A and q = frequency of allele a, then: p + q = 1 (p + q) 2 = 1 2 p 2 + 2 p q + q 2 = 1 p 2 = frequency of AA genotype (homozygous dominant); 2pq = frequency of Aa genotype (heterozygous); q 2 = frequency of aa genotype (homozygous recessive)
Hardy-Weinberg Equilibrium I'm confused! How can O be the most common of the blood types if it is a recessive trait? If Huntington's disease is a dominant trait, shouldn't three-fourths of the population have Huntington's while one-fourth have the normal phenotype? These questions reflect the common misconception that the dominant allele of a trait will always have the highest frequency in a population and the recessive allele will always have the lowest frequency. On the contrary, as G. H. Hardy stated in 1908, "There is not the slightest foundation for the idea that a dominant trait should show a tendency to spread over a whole population, or that a recessive trait should die out." Gene frequencies can be high or low no matter how the allele is expressed, and can change, depending on the conditions that exist. It is the changes in gene frequencies over time that result in evolution. The Hardy-Weinberg Principle provides a baseline to determine whether of not gene frequencies have changed in a population and thus whether evolution has occurred. Evolution is equivalent to change. Microevolution - adaptation Macroevolution - appearance of new species Indirect Evidence of Change - can be suggested by the use of the Hardy-Weinberg Principle which takes into account: size of population random mating external influences BUT Hardy-Weinberg can be affected by: migration (immigration and emigration) genetic drift (random loss of alleles - sm. pop.) inbreeding (non-random mating) mutation natural selection There is a change in the gene frequency and it can be inferred that there is a change in the population resulting in some members of the population being more fit than others. H-W equilibrium states that proportions of alternate forms of a gene (alleles) in a large population will not change from generation to generation unless they are influenced by mutation, migration, genetic drift, nonrandom mating (which result in genetic variation) or selection (which drives evolution). If these conditions have no effect, and if mating is random then the proportions of genotypes in the population will also remain the same after one generation. H-W equilibrium defines the conditions under which evolution DOES NOT occur and population genetics. is basis of
EXAMPLE: In a population of 100 toads, there are 4 with phenotype horny-back (recessive) and 96 with normal phenotype (dominant). Find the number of heterozygotes in this population. We know that 4% or 0.04 are hh (homozygous recessive) Therefore q = 0.2 (square root of hh or frequency of h gamete) and p = 0.8 (frequency of H gamete is 0.8 by subtraction p + q = 1) - assume random mating and remember you are considering allele frequencies Consider if p = 0.8, q = 0.2 and p + q = 1, ( p + q ) 2 = 1 Homozygous dominant HH = p 2 = 0.8 2 = 0.64 = 64% Heterozygous Hh = 2pq = 2 (0.8)(0.2) = 0.32 = 32% Total of HH and Hh = 96% Homozygous recessive hh = q 2 = 0.2 2 = 0.04 = 4% OR Use the binomial expansion: 1. If p + q = 1, then (p + q) 2 = 1 2. q = 0.2 (square root of 0.04) 3. heterozygotes are 2 pq 4. 2 pq = 2(0.2)(0.8) = 0.32 = 32%
PROBLEMS TO SOLVE: NAME: I AM RIGHT HARDY- WEINBERG PRACTICE PROBLEMS 1. The proportion of homozygous recessives of a certain population is 0.09 (q 2 = 0.9). If we assume that the gene pool is large and at equilibrium and all genotypes are equally successful in reproduction, what proportion of the population would you expect to be heterozygous for this trait? Answer: 2pq = 0.42 2. Approximately 36% (q 2 = 0.36) of a certain population are unable to taste the compound phenylthiocarbamide (PTC). Everyone else finds it very bitter tasting. If we assume that the non-tasters are homozygous for the recessive gene, t, what is the frequency of: a) homozygous dominants, (TT) Answer: p 2 = 0.16 b) heterozygotes, (Tt) Answer: 2pq = 0.48 3. In a certain population, approximately one child in 2500 (q 2 = 1/2500) is homozygous for the gene z. Assuming Hardy-Weinberg equilibrium, what is the proportion of carriers (heterozygotes) in the population? Answer: 2pq = 0.0392 4. The frequency of sickle-cell anemia (ss) among the children in one malarial region of Africa is 144 out of 10 000 (q 2 = 144/10 000). Assuming H-W equilibrium, what is the approximate frequency of heterozygotes (Ss) in this population? Answer: 2pq = 0.2112 5. In a population with two alleles for a particular locus, B and b, the allele frequency of B is 0.7 (P = 0.7). What would be the frequency of heterozygotes if the population is in H-W equilibrium? Answer: 2pq = 0.42 6. In a population that is in H-W equilibrium, 16% (q 2 = 0.16) of the individuals show the recessive trait. What is the frequency of the dominant allele in the population? Answer: p = 0.6 7. If 9% (q 2 = 0.09) of an African population is born with a severe form of sickle-cell anemia (ss), what percentage of the population will be more resistant to malaria because they are heterozygous(ss) for the sickle-cell gene? Answer: 2pq = 0.42 8. After graduation, you and 19 friends build a raft, sail to a deserted island, and start a new population, totally isolated from the world. Two of your friends carry (that is, are heterozygous for) the recessive cf allele, which in homozygotes causes cystic fibrosis. A. Assuming that the frequency of this allele does not change as the population grows, what will be the instance of cystic fibrosis on your island? B. Cystic fibrous births on the island is how many times greater than the original mainland. The frequency of births on the mainland is.059%.
HARDY-WEINBERG PRINCIPLE Moth Example Phenotype Black Black White Genotypes AA Aa (aa) Number of moths 320 160 20 (total = 500) Genotype frequencies 320/500 = 0.64 AA 160/500 = 0.32 Aa 20/500 = 0.04 (aa) Number of alleles In gene pool (total = 1000) x 2 x 2 640 A 160 A 160 a 40 a Allele frequencies 800/1000 = 0.8 A p=frequency of A = 0.8 200/1000 = 0.2 a q = frequency of a = 0.2
For a gene with only two different alleles (A and a), the Hardy-Weinberg principle can be expressed using the equation below: If p = frequency of allele A and q = frequency of allele a, then: p + q = 1 (p + q) 2 = 1 2 p 2 + 2 p q + q 2 = 1 p 2 = frequency of AA genotype (homozygous dominant); 2pq = frequency of Aa genotype (heterozygous); q 2 = frequency of aa genotype (homozygous recessive)