1. Copyright © 2005 Pearson Education, Inc. publishing as Benjamin Cummings D.4 High Level Only D.4 The Hardy-Weinberg Principle – D.4.1 Explain how the Hardy-Weinberg equation is derived – D.4.2 Calculate allele, genotype and phenotype frequencies for two alleles of a gene using the Hardy Weinberg Equation – D.4.3 State the Assumptions made when the Hardy-Weinberg Equation is used

2. Copyright © 2005 Pearson Education, Inc. publishing as Benjamin Cummings Hardy-Weinberg Equation Uses Useful in determining how fast a population is changing (allele frequency is changing) Predicting outcomes of mating crosses

3. Copyright © 2005 Pearson Education, Inc. publishing as Benjamin Cummings p = frequency of DOMNANT allele in a population q = frequency of RECESSIVE allele in a population Frequencies of the alleles on a chromosome must add up to 1 THUS p + q = 1 D.4.1 Explain how the Hardy-Weinberg equation is derived

4. Copyright © 2005 Pearson Education, Inc. publishing as Benjamin Cummings p = frequency of DOMNANT allele in a population – EXAMPLE: T frequency is 0.25 or 25% q = frequency of RECESSIVE allele in a population – Example: t frequency is 0.75 or 75% Frequencies of the alleles on a chromosome must add up to 1 or 100% p + q = 1.75 +.25 = 1 D.4.1 Explain how the Hardy-Weinberg equation is derived

5. Copyright © 2005 Pearson Education, Inc. publishing as Benjamin Cummings Apply p + q = 1 to a diploid situation Because we are all diploid ( p + q ) 2 =1 If you remember your mathematics about polynomials ( p + q ) 2 =1 can be changed to – p 2 + 2pq + q 2 = 1 Now you know how the Hardy-weinberg equation was derived D.4.1 Explain how the Hardy-Weinberg equation is derived

6. Copyright © 2005 Pearson Education, Inc. publishing as Benjamin Cummings If p and q represent the relative frequencies of the only two possible alleles in a population at a particular locus, then – p 2 + 2pq + q 2 = 1 – And p 2 and q 2 represent the frequencies of the homozygous genotypes. Examples: p2 = p x p = TT (homozygous dominant) and 2pq represents the frequency of the heterozygous genotype Hardy-Weinberg Equations---What it means..

7. Copyright © 2005 Pearson Education, Inc. publishing as Benjamin Cummings p 2 + 2pq + q 2 = 1 p 2 = p x p = TT (homozygous dominant) q 2 = q x q = tt ( homozygous recessive) 2 pq Heterozygote Hardy-Weinberg Equations---What it means.. Tt TTTTt t tt

8. Copyright © 2005 Pearson Education, Inc. publishing as Benjamin Cummings Hardy-Weinberg Equation Uses Useful in determining how fast a population is changing (allele frequency is changing) Predicting outcomes of mating crosses Allele Frequencies Recessive tq Dominant Tp Genotype Frequencies Homozygous Recessiveq2q2 Heterozygote2pq Homozygous Dominantp2p2

9. Copyright © 2005 Pearson Education, Inc. publishing as Benjamin Cummings Example Problems: p 2 + 2pq + q 2 = 1 One SquareTwo SquareOne square GenotypesTT2 Tttt Phenotypes ¼½¼ Frequency of TT = p 2 = ¼ Frequency of Tt = 2pq = ½ Frequency tt = q 2 = ¼ ¼ + ½ + ¼ = 1 0.25 + 0.50 + 0.25 = 1

10. Copyright © 2005 Pearson Education, Inc. publishing as Benjamin Cummings Problem 1 calculating allele frequency Recessive allele t is 10% of a given population. Calculate the percentage of the dominant allele q = 0.10 or 10% p + q =1 So…….p = 1 - 0.10 p= 0.90 or 90% Remember this is allele frequency NOT genotype frequency.

11. Copyright © 2005 Pearson Education, Inc. publishing as Benjamin Cummings Problem 2 calculating allele frequency In a study 989 members of the population from example 1, it was found that 11 people had showed the recessive phenotype (t). Calculate the frequency of of the recessive allele (t). 1 st calculate the percentage of people who have the recessive phenotype (tt) 11/ 989 = 0.011 ----thus 1.1 % of the population have this phenotype tt) Hence q 2 = 0.011 To calculate q (frequency of recessive allele) just take the square root of q 2 = 0.011 √ q 2 =√ 0.011 = 0.105 This means that the frequency of this recessive allele is 10.5 % of the population

12. Copyright © 2005 Pearson Education, Inc. publishing as Benjamin Cummings Problem 3 calculating genotype frequency Use the information from the previous problems to fill in the charter below: Allele Frequencies Recessive tq Dominant Tp Genotype Frequencies Homozygous Recessiveq2q2 Heterozygote2pq Homozygous Dominantp2p2

13. Copyright © 2005 Pearson Education, Inc. publishing as Benjamin Cummings Problem 3 calculating genotype frequency We know from problem 1, q= 0.10 so q 2 = 0.01 we know from problem 1, p = 0.9 so p 2 = 0.81 So 2pq = 2 x 0.10 x 0.9 = 0.18 Allele Frequencies Recessive tq Dominant Tp Genotype FrequenciesHomozygous Recessiveq2q2 Heterozygote2pq Homozygous Dominantp2p2 0.1 0.9 0.01 0.18 0.81

14. Copyright © 2005 Pearson Education, Inc. publishing as Benjamin Cummings Practice Problem In a randomly breeding population of mice, 640 had black fur and 360 brown fur. Black fur is dominant to brown fur. The Hardy-Weinberg Principle (p 2 + 2pq + q 2 =1) can be used to calculate allele and phenotype frequencies. (a)Calculate the frequency of the recessive allele (1 point). Solve for q Calculate q 2 frequency of homozygous recessive genotype q 2 = 360/640 = 0.5625 q = √q 2 = √0.5625 = 0.75 or 75%

15. Copyright © 2005 Pearson Education, Inc. publishing as Benjamin Cummings The Hardy-Weinberg Theorem The Hardy-Weinberg theorem describes a population that is not evolving It states that frequencies of alleles and genotypes in a population’s gene pool remain constant from generation to generation, provided that only Mendelian segregation and recombination of alleles are at work Mendelian inheritance p reserves genetic variation in a population

16. Copyright © 2005 Pearson Education, Inc. publishing as Benjamin Cummings Preservation of Allele Frequencies In a given population where gametes contribute to the next generation randomly, allele frequencies will not change

17. Copyright © 2005 Pearson Education, Inc. publishing as Benjamin Cummings Hardy-Weinberg Equilibrium Hardy-Weinberg equilibrium describes a population in which random mating occurs It describes a population where allele frequencies do not change

18. Copyright © 2005 Pearson Education, Inc. publishing as Benjamin Cummings Conditions for Hardy-Weinberg Equilibrium The Hardy-Weinberg theorem describes a hypothetical population In real populations, allele and genotype frequencies do change over time

19. Copyright © 2005 Pearson Education, Inc. publishing as Benjamin Cummings The five conditions for non-evolving populations are rarely met in nature: – Extremely large population size – No gene flow – No mutations – Random mating – No natural selection

20. Copyright © 2005 Pearson Education, Inc. publishing as Benjamin Cummings More Help check out this tutorial http://www.youtube.com/watch?v=xPkOAnK20kw