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Population Genetics Hardy Weinberg

Population Genetics Hardy Weinberg. Population Genetics. Mendelian genetics predicts the outcome of specific matings between individuals What about the genetics of an entire population? Population = all individuals of one species living in a given area

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Population Genetics Hardy Weinberg

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  1. Population GeneticsHardy Weinberg

  2. Population Genetics • Mendelian genetics predicts the outcome of specific matingsbetween individuals • What about the genetics of an entirepopulation? • Population = all individuals of one species living in a given area • Population genetics works with the entire gene pool • or all the alleles present in the whole population

  3. How will alleles change in the population? • Among a population of 2000 people: • 720 have blue eyes (recessive) • 1280 have brown eyes (dominant) • DNA testing reveals: • 320 are homozygous for Brown Eyes(BB) • 960 are heterozygous for Brown Eyes (Bb)

  4. Allele frequency • Allele frequency is the fraction: no. of a particular allele no. of all alleles in population • For these 2000 people, there are 4000 alleles in the gene pool: • 720 bb • 960 Bb • 320 BB how many B alleles? how many b alleles? f(B)= 960 + 320 + 320/ 4000 = 0.4 F(b) = 960 + 720 +720/4000 = 0.6

  5. What happens in the next generation? • In all the matings for this generation, what is the chance that an egg with the B allele will be fertilized by a sperm with the b allele and create a person with Bb genotype? Recall: • 40% of all eggs will carry B • 60% of all sperm will carry b Recall the Rule of Multiplication: (prob. of event a) (prob of event b)= probability of both events happening 0.4 x 0.6 = 0.24 24% of offspring Bb *Assuming no difference between sexes and no mating preferences!

  6. What happens in the next generation? • In all the matings for this generation: • 0.4 x 0.4 = 16% BB • 0.4 x 0.6 x 2 = 48% Bb • Bb and bB • (rule of addition) • 0.6 x 0.6 = 36% bb

  7. What happens in the next generation? • In all the matings for this generation: if 4000 offspring are born: • 0.4 x 0.4 = 16% BB 640 BB • 0.4 x 0.6 x 2 = 48% Bb 1920 Bb • 0.6 x 0.6 = 36% bb 1440 bb 2560 Brown 1440 Blue

  8. What happens in the next generation? • New allele frequencies: If 4000 offspring 640 BB 1920 Bb 1440 bb 3200 B allele/8000 = 0.4 4800 b allele/8000 = 0.6 After 5 generations: 64,000 offspring 10,240 BB 30,720 Bb 23,040 bb 51,200 brown alleles / 128,000 = 0.4 76,800 blue alleles / 128,000 = 0.6

  9. After 5 generations (or any number): • Allele frequencies do not change! • Recessive alleles are maintained in the population *If some specific assumptions are made

  10. Hardy-Weinberg equilibrium • Godfrey Hardy (mathematician) and Wilhelm Weinberg (physician) (early 1900s): • Given some assumptions, allele frequencies won’t change: • The population is large • Mating is random • No migration in or out • No mutation • No selection (no allele is advantageous) • How often in nature are ALL of these assumptions met? • Rarely, if ever. This is an “ideal” state.

  11. Does Hardy-Weinberg work? • In large populations, the Hardy-Weinberg equations predict results quite well for many traits • If a population is not in equilibrium: • Allele frequencies are changing • Evolution is occurring!

  12. Hardy-Weinberg equations • Allele frequency: • Let p = frequency of the dominant allele • Let q = frequency of the recessive allele • Then, p + q = 1 • Genotype frequency: • p2 = frequency of homozygous dominant genotype • q2 = frequency of homozygous recessive genotype • 2pq = frequency of heterozygous genotype • p2 + 2pq + q2 = 1

  13. 4 Steps to solving H-W Problems • set recessives = q2 • Take square root of q2 • 1-q = p • Plug into expanded equation Example: 16% of the cat population is white: • q2= 0.16 • square root = 0.4 • 1- 0.4 = p p = 0.6 • .16 + 2 (.6) (.4) + .36 = 1 so, 36% of population is TT 48% of population is Tt

  14. Another Example: • Fraggles are mythical, mouselike creatures that live beneath flower gardens. • Of the 100 fraggles in a population, 75 have green hair (FF or Ff) and 25 have grey hair (ff). • Assuming genetic equilibrium: • What are the gene frequencies of F and f? • What are the genotypic frequencies?

  15. Answer to Fraggle Problems: • Gene frequencies: • q2= .25, so: • q= .5 • p= .5 • Genotypic frequencies • FF = .25 • Ff = .5 • f f = .25

  16. Application of H-W principle • Sickle cell anemia • inherit a mutation in gene coding for hemoglobin • oxygen-carrying blood protein • recessive allele = s • normal allele = S • low oxygen levels causes RBC to sickle • breakdown of RBC • clogging small blood vessels • damage to organs • often lethal

  17. Sickle cell frequency • High frequency of heterozygotes • 1 in 5 in Central Africans = Ss • unusual for allele with severe detrimental effects in homozygotes • 1 in 100 =ss • usually die before reproductive age Why is the s allele maintained at such high levels in African populations? Suggests some selective advantage of being heterozygous…

  18. Malaria Single-celled eukaryote parasite (Plasmodium) spends part of its life cycle in red blood cells 1 2 3

  19. Heterozygote Advantage • In tropical Africa, where malaria is common: • homozygous dominant (normal) • die or reduced reproduction from malaria: SS • homozygous recessive • die or reduced reproduction from sickle cell anemia: ss • heterozygote carriers are relatively free of both: Ss • survive & reproduce more, more common in population Hypothesis: In malaria-infected cells, the O2 level is lowered enough to cause sickling which kills the cell & destroys the parasite. Frequency of sickle cell allele & distribution of malaria

  20. Sickle Cell Example: • 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? • f(ss)= .09 = q2 • q= .3 • P= .7 • 2pq= .42 • so 42% of the population is resistant to malaria.

  21. Using Hardy-Weinberg Cystic Fibrosis: 1 in 1700 US Caucasian newborns have cystic fibrosis. Use an F for the normal allele and f for recessive: What percent of the above population have cystic fibrosis? What percent are healthy, non carriers? What percent are carriers of cyctic fibrosis? In a population of 1700 people, how many would you expect to be homozygous normal? In a population of 1700 people, how many would you expect to be heterozygous? .00058 = q2 q= .024 p= .976 P2= .9524 2pq= .0468 1700 x .9524= 1619 1700 x .0468= 80

  22. Stem Cells • Nova

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