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What is the Hardy-Weinberg Theorem? The principle states that allele and genotype frequencies in a population will remain constant from generation to generation in the absence of other evolutionary influences. 5 principles of theorem: 1. Population is large 2. Matings are random 3. There are no net changes in the gene pool due to mutation 4. No migration 5. No selection= equal reproductive success Important Terms • • • • • • Natural Selection Evolution Population Gene Pool Hardy Weinberg What are allele frequencies? • Because there are only two alleles in this case, the frequency of one plus the frequency of the other must equal 100%, which is to –p+q=1 • where p= A and q= a • Frequency of the diploid combinations – p2 + 2pq + q2 = 1 • p2 is AA • 2pq is Aa, and • q2 is aa The purpose of Hardy-Weinberg Theorem: • Scientists can investigate the roles of mutation, migration, population size, nonrandom mating, and natural selection effecting evolutionary change • Some populations maintain genetic equilibrium • The principle describes an ideal condition against which the effects of these influences can be analyzed. • Allele frequencies will remain unaltered indefinitely unless evolutionary mechanisms such as mutation and natural selection cause them to change Example Problem: 1.You calculate that you have 16% homozygous recessive bears (happy) or q2 = 20% or .20, by taking the square root q = .45 (2 out 10 bears were happy) 2. p + .45 = 1, so p = .55 • .45 + .55 = 1 or 40% + 60% = 100% 3. Solve for p2 by .55 x .55 = .30 4. Then solve for 2pq = 2 x .45 x .55= .50 5. So you data would show, AA=.30, Aa=.50, and aa=.20 Let’s practice: • Pull a random population of 10 teddy grahams from the den • How many homozygous recessive bears do you have? (happy) That would be q2 because % of population. – Make sure to convert to a decimal value to fill it in table • Take the Square root of q2 to give you q • You can then solve for p by using the formula p + q = 1 • Solve for p2 squaring p • Solve for 2pq by taking 2 x p x q = • Check out another example on you tube: https://www.youtube.com/watch?v=xPkOAnK20kw Complete your lab! • Fill in your data table • Your generations should increase 10, 14, 18, 22 • Answer the questions on looseleaf on the bottom of your lab. • For the question asking about eating sad bears- run 2 rounds to see what would happen to p? On your OWN! • 18% of the bear population is happy. Happy is the recessive trait in the bear population. 1. What is the percent of individuals in the population that are dominant? 2. What is the frequency of dominant and recessive alleles? 3. What is the percentage of the population that is heterozygous for the trait?