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Lab 1 Population Genetics: The Hardy-Weinberg Theorem Name_________________ Objectives After completing this lab, you should be able to: 1. Explain Hardy-Weinberg equilibrium. 2. Describe the conditions necessary to maintain Hardy-Weinberg equilibrium. 3. Estimate allele frequencies and use them to calculate genotype frequencies expected under Hardy-Weinberg equilibrium. 4. Compare observed and expected genotype frequencies. Introduction Charles Darwin’s unique contribution to biology was not that he “discovered evolution” but, rather, that he proposed a mechanism for evolutionary change – natural selection, the differential survival and reproduction of individuals in a population. In On the Origin of Species, published in 1859, Darwin described natural selection and provided abundant and convincing evidence in support of evolution, the change in populations over time. Evolution can be defined as “changes in the genetic constitution of populations over time.” A population is defined as a group of organisms of the same species that occur in the same area and interbreed or share a common gene pool, all the alleles at all gene loci of all individuals in the population. The population is considered the basic unit of evolution. Populations evolve, not individuals. In 1908, English mathematician G. H. Hardy and German physician W. Weinberg independently developed models of population genetics that showed that the process of heredity by itself did not affect the genetic structure (i.e., the allele and genotype frequencies) of a population. The Hardy-Weinberg theorem states that when certain conditions are met, the frequency of alleles in the population will remain the same from one generation to the next, regardless of the starting frequencies. Furthermore, the equilibrium genotypic frequencies will be established after one generation of random mating. The conditions under which this theorem is valid are: 1. The population is very large. 2. Matings are random. 3. There are no net changes in the gene pool due to mutation; that is, mutation from A to a must be equal to mutation from a to A. 4. There is no migration of individuals into and out of the population. 5. There is no selection; all genotypes are equal in reproductive success. Basically, the Hardy-Weinberg theorem provides a baseline model in which gene frequencies do not change and evolution does not occur. By comparing observed genotype frequencies to those predicted by the HardyWeinberg theorem, biologists can begin to study the extent to which mutation, migration, population size, nonrandom. mating, and natural selection cause evolutionary change in natural populations. For example, the Hardy-Weinberg theorem has been used to show that certain alleles in the human population provide a selective advantage in people infected with HIV, that is, these alleles provide resistance to onset of AIDS symptoms in people infected with the AIDS virus. The Hardy-Weinberg Theorem The Hardy-Weinberg theorem provides a mathematical formula for calculating allele and genotype frequencies in a nonevolving population. For a population with two alleles at a single gene locus—a dominant allele, A, and a recessive allele, a—assume that the frequency of the dominant allele is p and the frequency of the recessive allele is q. Since there are only two alleles, p + q = 1. If the frequency of one allele, p, is known for a population, the frequency of the other allele, q, can be determined by using the formula q = 1 – p. In a large population, during sexual reproduction the frequency of each type of gamete produced is equal to the frequency of the alleles in the population. If the gametes combine at random, then the probability of AA in the next generation is p2, and the probability of aa is q2. The heterozygote can be obtained in two ways, with either the sperm or the egg providing a dominant allele, so the probability would be 2pq. The Hardy-Weinberg theorem can then be written: p2 + 2pq + q2 = 1, where p2 is the frequency of AA, 2pq is the frequency of Aa, and q2 is the frequency of aa. In this lab, you will perform an experiment (using beans) that simulates the “no evolution” case (i.e., the conditions that result in the Hardy-Weinberg equation—see below) and an experiment (using beans) that illustrates how natural selection can drive populations away from Hardy-Weinberg equilibrium. With this material on the Hardy-Weinberg theorem in hand, we are now ready to begin Experiment 1. Experiment 1: Testing Hardy-Weinberg Equilibrium Using a Bead Model Materials paper bag containing 50 red and white beans Introduction Working in pairs, you will test Hardy-Weinberg equilibrium by simulating a population using colored beans. The bag of beans represents the gene pool for the population. Each bean should be regarded as a single gamete, the two colors representing different alleles of a single gene. Each bag should contain 100 beans of the two colors in the proportions specified by the instructor. Record in the space provided below the color of the beans and the initial frequencies for your gene pool. A =______________________ color_____________________allelic frequency a =_______________________color_____________________allelic frequency 1. How many diploid individuals are represented in this population? 2. What would be the color of the beans for a: homozygous dominant individual? homozygous recessive individual? heterozygous individual? Hypothesis State (in your own words) the Hardy-Weinberg theorem in the space provided. Your working hypothesis will be that the Hardy-Weinberg theorem holds for the population modeled by the beans. Procedure 1. Without looking, randomly remove one bean from the bag. Return that bean to the bag, shake the bag for several seconds, and then remove a second bean from the bag. These two beans represent two gametes (e.g., one sperm, one egg) that will fuse to form a diploid individual in the next generation. Record the diploid genotype of the individual formed from these two gametes. Diploid AA= Aa= aa= 2. Return the second bean to the bag and shake the bag to replenish the gene pool. By replacing the beans each time you sample one, the size of the gene pool remains constant and the probability of selecting any allele remains constant and equal to its frequency in the bag. This procedure is called sampling with replacement. 3. Repeat steps 1 and 2 (select one bean, shake the bag, select another bean, shake the bag, and record the genotype of the new individual) until you have recorded the genotypes for 50 individuals who will form the next generation. Diploids= Results 1. Before calculating the results of your experiment, determine the expected frequencies of genotypes and alleles for the population. To do this, use the original allelic frequencies for the population provided by the instructor; recall that the frequency of A = p, and the frequency of a = q. Calculate the expected genotypic frequencies using the Hardy- Weinberg equation. The number of individuals expected for each genotype can be calculated by multiplying 50 (total population size) by the expected frequencies. Record these results in Table 1.1. Table 1.1 Expected Genotypic and Allelic Frequencies for the Next Generation Produced by the Bead Model Parent population Allelic frequency A a New Populations Genotypic number and (frequency) AA Aa aa Allelic frequency A a 2. Next, using the results of your experiment, calculate the observed frequencies in the new population created as you removed beads from the bag. Record the number of diploid individuals for each genotype in Table 1.2, and calculate the observed frequencies for the three genotypes (AA, Aa, aa). In addition, calculate the observed frequencies for the A and a alleles. Genotypic frequencies and allelic frequencies should each sum to 1. Table 1.2 Observed Genotypic and Allelic Frequencies for the Next Generation Produced using the Bead Model Parent population Allelic frequency A a New Populations Genotypic number and (frequency) AA Aa aa Allelic frequency A a Natural Selection Work with a partner. Pick one background from those provided. Introduce the organisms provided into the environment. The organisms are blue, orange or white dots. Introduce 10 of each color into the environment. Then allow your partner to prey on the organisms for 3 seconds. Record your data in the table. Make sure you record the starting population and the allele frequency of each population after an eating frenzy. After each eating frenzy mating occurs and organisms are replaced to match the survivors. Base the replacement organisms on the allele frequency of each surviving population. Repeat 5 times and then use the Hardy- Weinberg equation to compare the starting population to what remains after 5 generations. Blue-AA White-Aa Orange-aa Parent population Allelic frequency A a XXXXXX XXXXXX XXXXXX XXXXXX XXXXXX XXXXXX XXXXXX XXXXXX New Populations Genotypic number and (frequency) AA Aa aa Allelic frequency A a Hardy Weinberg equation for the starting population p= q= p2= 2pq= q2= Hardy Weinberg for the remaining population p= q= p2= 2pq= q2= Are the numbers the same??? Why??? NO SELECTION Repeat with a black background. Parent population Allelic frequency A a New Populations Genotypic number and (frequency) AA Aa aa XXXXXX XXXXXX XXXXXX XXXXXX XXXXXX XXXXXX XXXXXX XXXXXX Hardy Weinberg equation for the starting population p= q= Allelic frequency A a p2= 2pq= q2= Hardy Weinberg for the remaining population p= q= p2= 2pq= q2= Are the numbers the same??? Why??? In what situations do the Hardy Weinberg numbers stay in equilibrium and what situations do they change?