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Addendum to Exercise 13 Population Genetics and the Hardy-Weinberg Equation All the members of a species living in one location make up a population. The occurrence of evolution within a population is established by determining that the genetic makeup of a population has changed. This is done by showing that the frequency of alleles in a population’s gene pool has changed over time. The Hardy-Weinberg law, which is a way to calculate gene pool frequencies, provides a baseline by which to judge whether or not evolution has occurred. It shows that the relative frequencies of alleles do not change in large populations from one generation to the next, unless there is an evolutionary agent, such as genetic drift, natural selection, nonrandom mating, mutation or gene flow. Remember that the dominant phenotype characteristic is displayed by both the homozygous dominant and the heterozygous genotypes. The homozygous recessive genotype automatically results in the recessive phenotype; therefore, the frequency of the recessive phenotype equals the frequency of the homozygous recessive genotype in a population. The frequency of the recessive and dominant allele and the other two genotypes (homozygous dominant and heterozygous) can be determined by using the Hardy Weinberg law. In 1908, G.H.Hardy and W. Weinberg independently suggested a scheme whereby evolution could be viewed as changes in frequency of alleles in a population of organisms. In this scheme, if A and a are alleles for a particular gene locus and each diploid individual has two such loci, then p can be designated as the frequency of the A allele and q as the frequency of the a allele. For example, in a population of 100 individuals (each with two loci) in which 40% of the alleles are A, p would be 0.40. The rest of the alleles would be (60%) would be a and q would be equal to 0.60. We can generalize that: p+q=1 These are referred to as allele frequencies. The frequency of the possible diploid combinations of these alleles ( AA, Aa, aa ) is expressed as: p2 +2pq +q2 = 1.0 Hardy and Weinberg also argued that if 5 conditions are met, the population's alleles and genotype frequencies will remain constant from generation to generation. These conditions are as follows: 1. 2. 3. 4. 5. The breeding population is large. (Reduces the problem of genetic drift.) Mating is random. (Individuals show no preference for a particular mating type.) There is no mutation of the alleles. No differential migration occurs. (No immigration or emigration.) There is no natural selection. (All genotypes have an equal chance of surviving and reproducing.) The Hardy-Weinberg equation describes an existing situation. If the five conditions are met, then no change will occur in either allele or genotype frequencies in the population. Of what value is such a rule? It provides a yardstick by which changes in allelic frequencies can be measured. If a population's allelic frequencies change it is undergoing evolution. Estimating Allele Frequencies for a Specific Trait within a Sample Population: Using the class as a sample population, the allele frequency of a gene controlling the ability to taste the chemical PTC (phenylthiocarbamide) could be estimated. A bitter-taste reaction to PTC is evidence of the presence of the dominant allele in either the homozygous condition (AA) or heterozygous condition (Aa). The inability to taste the chemical at all depends on the presence of the homozygous recessive alleles (aa). To estimate the frequency of the PTC -tasting allele in the population, one must find p. To find p, one must first determine q (the frequency of the non- tasting allele), because only the genotype of the homozygous recessive individuals in known for sure (i.e. those that show the dominant trait could be AA or Aa). Procedure 1. Obtain one piece each of PTC paper and untreated taste paper from your instructor. Place the untreated paper on your wet tongue to see how it tastes. Dispose of this piece of paper in the trash can. 2. Next, place the PTC paper on your wet tongue to see if you can taste the chemical. Discard the PTC paper in the trash can. Record yourself as either a “taster” or “nontaster” phenotype: My Phenotype: ____________________ 3. Based on your phenotype, determine your possible genotype(s). Since tasting PTC is governed by a dominant gene, if you are a taster then your possible genotypes are TT and Tt. You must include both in your answer, because without further testing or pedigree analysis (looking at the traits of your family members) you cannot tell if you are homozygous dominant or heterozygous for the trait, just that you do carry the dominant gene. If you are a nontaster, then your genotype is tt. Record you possible genotypes. My possible genotype(s): __________________________ 4. Once you have determined your phenotype and genotype(s), the instructor will tally the number of tasters and non-tasters in the class. Record the results below: Tasters: _________________ Non-tasters: _____________ Total: ______________ 5. A decimal number representing the frequency of tasters (p2+2pq) should be calculated by dividing the number of tasters in the class by the total number of students in the class. A decimal number representing the frequency of the non tasters (q2) can be obtained by dividing the number of non tasters by the total number of students. You should then record these numbers in Table 1. 6. Use the Hardy-Weinberg equation to determine the frequencies (p and q) of the two alleles. The frequency q can be calculated by taking the square root of q2. Once q has been determined, p can be determined because 1 - q = p. Record these values in Table 1 for the class and also calculate and record values of p and q for the North American population. Table 1: Phenotypic Proportions of Tasters and Nontasters and Frequencies of the Determining Alleles Allele Frequency Based on the H-W Equation Phenotypes Tasters (p2 + 2pq) Class Population # = _____ North American Population % = ____ 0.55 Non-tasters (q2) # = _____ p q % = ____ 0.45 Topics for Discussion What is the percentage of heterozygous tasters (2pq) in your class? ______________________ What percentage of the North American population is heterozygous for the taster trait? _________________________________ Hardy-Weinberg Problems 1. In Drosophila, the allele for normal length wings is dominant over the allele for vestigial wings. In a population of 1,000 individuals, 360 show the recessive phenotype. How many individuals would you expect to be homozygous dominant and heterozygous for this trait? 2. The allele for the ability to roll one's tongue is dominant over the allele for the lack of this ability. In a population of 500 individuals, 25% show the recessive phenotype. How many individuals would you expect to be homozygous dominant and heterozygous for this trait? 3. The allele for the hair pattern called "widow's peak" is dominant over the allele for no "widow's peak." In a population of 1,000 individuals, 510 show the dominant phenotype. How many individuals would you expect of each of the possible three genotypes for this trait? 4. In a certain population, the dominant phenotype of a certain trait occurs 91% of the time. What is the frequency of the dominant allele?