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Honors Biology

Honors Biology. Evidence for Evolution- Hardy-Weinberg equation. Getting Started 11-7-12. Which of Darwin’s 4 postulates are shown in this picture?. Today’s Topic. Evidence for Evolution Hardy-Weinberg Equation. What is Hardy-Weinberg?.

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Honors Biology

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  1. Honors Biology Evidence for Evolution- Hardy-Weinberg equation

  2. Getting Started 11-7-12 • Which of Darwin’s 4 postulates are shown in this picture?

  3. Today’s Topic • Evidence for Evolution Hardy-Weinberg Equation

  4. What is Hardy-Weinberg? • Mathematical method of telling if a population is changing… aka Evolving • If population frequencies are stable= not changing, then not evolving • You can use HW equation to make predictions about the relative frequencies (%) of different alleles and genotypes

  5. How to Solve Hardy-Weinberg problems Do Now: Copy the following problem solving steps into your notes: Find f(AA) or f(aa) from the problem Use f(AA) = P2 or f(aa) = Q2 to find P or Q. Use P + Q = 1 to find the other frequency. Find the genotype frequencies asked for in the question by using f(AA) = P2 f(Aa) = 2pq f(aa) = Q2

  6. What the terms mean • f(AA) = frequency (%) of homozygous dominant individuals • f(Aa) = frequency (%) of heterozygous individuals • f(aa) = frequency (%) of homozygous recessive individuals. • P = allele frequency (%) of dominant allele • Q = allele frequency (%)of recessive allele

  7. Example Problem • 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 sickle-cell gene?

  8. Step 1: Find f(ss) • We are told 9% of the population is ss, the homozygous recessive genotype. • Therefore, f(ss) = .09

  9. Step 2: Find P or Q • Since f(ss) = Q2 • .09 = Q2 • Q = .30

  10. Step 3: Find the Other Frequency • Since P + Q = 1 • P + .30 = 1 • P = .70

  11. Step 4: Find Unknown Phenotype or Genotype Frequency • The question asks you to find the % of heterozygotes. • Since f(Ss) = 2PQ • P = .70 • Q = .30 • f(Ss) = 2(.70)(.30) • f(Ss) = .41 • 41% of the population is heterozygous (Ss) for the trait.

  12. Practice. • Complete the 2 practice problems – I’m here to help. • We’ll go over them in a few minutes.

  13. Practice problem #- Pigeons • Pigeons have two basic colors to the feathers on their chests, blue which is dominant and red which is recessive. • Imagine there is a population of 50 pigeons in a local park. Two of the pigeons have red chest feathers while the rest have blue feathers. • How many of the blue feathered pigeons are Heterozygous?

  14. Practice Problem 1: Pigeons • Step 1: Find f(BB) or f(bb). • Since we know the red birds are recessive, we must solve for Q first (a blue bird may be BB or Bb) • f(bb) = 2/50 = .04

  15. Practice Problem 1: Pigeons • Step 2: Find P or Q • Since we know f(bb) = .04, we can solve for Q • f(bb) = Q2 • .04 = Q2 • Q = .20

  16. Practice Problem 1: Pigeons • Step 3: Find the other allele frequency • Since we know Q = .20, we can solve for P • P + Q = 1 • P + .20 = 1 • P = .80

  17. Practice Problem 1: Pigeons • Step 4: Find what the question asks • Since we know P = .80 and Q = .20, we can solve for f(Bb), the frequency of heterozygotes • f(Bb) = 2PQ • f(Bb) = 2(.80)(.20) • f(Bb) = .32 • 32% of the pigeon population is heterozygous.

  18. Practice Problem 2- Dogs • In a certain breed of dogs, black coloration is dominant over white coloration. 15% of a population of dogs is homozygous dominant for black coloration. What is the percentage of heterozygotes?

  19. Practice Problem 2: Dogs • Step 1: Find f(BB) or f(bb). • We are given this step in the problem • f(BB) = 15% = .15

  20. Practice Problem 2: Dogs • Step 2: Find P or Q • Since we know f(BB) = .15, we can solve for P • f(BB) = P2 • .15 = P2 • P = .39

  21. Practice Problem 2: Dogs • Step 3: Find the other allele frequency • Since we know P = .39, we can solve for Q • P + Q = 1 • .39 + Q = 1 • Q = .61

  22. Practice Problem 2: Dogs • Step 4: Find what the question asks • Since we know P = .39 and Q = .61, we can solve for f(bb), the frequency of white dogs • f(bb) = Q2 • f(bb) = .612 • f(bb) = .37 • 37% of the dogs are white (bb)

  23. Practice Problem 2: Dogs • Step 4: Find what the question asks • Since we know P = .39 and Q = .61, we can solve for f(Bb), the frequency of spotted dogs • f(Bb) = 2PQ • f(Bb) = 2(.39)(.61) • f(Bb) = .48 • 48% of the dogs are spotted (Bb)

  24. Check • If we add up the 3 percentages, we should get 100%: • 15% black + 37% white + 48% spotted = 100% • Sometimes, because of rounding to 2 decimal places, you may get a total of 99-101%

  25. Homework • Complete the first 2 problems of the Hardy-Weinberg problem set.

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