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Measuring Evolution of Populations 5 Agents of evolutionary change Mutation Gene Flow Genetic Drift Non-random mating Selection Populations & gene pools Concepts a population is a localized group of interbreeding individuals gene pool is collection of alleles in the population remember difference between alleles & genes! allele frequency is how common is that allele in the population how many A vs. a in whole population Evolution of populations Evolution = change in allele frequencies in a population hypothetical: what conditions would cause allele frequencies to not change? non-evolving population REMOVE all agents of evolutionary change 1. very large population size (no genetic drift) 2. no migration (no gene flow in or out) 3. no mutation (no genetic change) 4. random mating (no sexual selection) 5. no natural selection (everyone is equally fit) Hardy-Weinberg equilibrium Hypothetical, non-evolving population preserves allele frequencies Serves as a model (null hypothesis) natural populations rarely in H-W equilibrium useful model to measure if forces are acting on a population measuring evolutionary change G.H. Hardy mathematician W. Weinberg physician Hardy-Weinberg theorem Counting Alleles assume 2 alleles = B, b frequency of dominant allele (B) = p frequency of recessive allele (b) = q frequencies must add to 1 (100%), so: p+q=1 BB Bb bb Hardy-Weinberg theorem Counting Individuals frequency of homozygous dominant: p x p = p2 frequency of homozygous recessive: q x q = q2 frequency of heterozygotes: (p x q) + (q x p) = 2pq frequencies of all individuals must add to 1 (100%), so: p2 + 2pq + q2 = 1 BB Bb bb H-W formulas Alleles: p+q=1 B Individuals: p2 + 2pq + q2 = 1 BB BB b Bb Bb bb bb Using Hardy-Weinberg equation population: 100 cats 84 black, 16 white How many of each genotype? p2=.36 BB q2 (bb): 16/100 = .16 q (b): √.16 = 0.4 p (B): 1 - 0.4 = 0.6 2pq=.48 Bb q2=.16 bb What assume Must are the genotype population frequencies? is in H-W Using Hardy-Weinberg equation p2=.36 Assuming H-W equilibrium 2pq=.48 q2=.16 BB Bb bb p2=.20 =.74 BB 2pq=.64 2pq=.10 Bb q2=.16 bb Null hypothesis Sampled data How do you explain the data? Application of H-W principle Sickle cell anemia inherit a mutation in gene coding for hemoglobin oxygen-carrying blood protein recessive allele = HsHs normal allele = Hb low oxygen levels causes RBC to sickle breakdown of RBC clogging small blood vessels damage to organs often lethal Sickle cell frequency High frequency of heterozygotes 1 in 5 in Central Africans = HbHs unusual for allele with severe detrimental effects in homozygotes 1 in 100 = HsHs usually die before reproductive age Why is the Hs allele maintained at such high levels in African populations? Suggests some selective advantage of being heterozygous… Single-celled eukaryote parasite (Plasmodium) spends part of its life cycle in red blood cells Malaria 1 2 3 Heterozygote Advantage In tropical Africa, where malaria is common: homozygous dominant (normal) die or reduced reproduction from malaria: HbHb homozygous recessive die or reduced reproduction from sickle cell anemia: HsHs heterozygote carriers are relatively free of both: HbHs 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 Any Questions?? 2005- Practice Problem #1 In a population of foxes, 85% of the alleles for fur color are for red (R) and 15% are for brown (r). What percentage of the population of foxes is heterozygous if the population is in equilibrium? What do you know? 85% of the alleles are R 15% of the alleles are r p = .85 q = .15 What do you want to know? Percentage of the population that is heterozygous 2pq 2pq = 2(.85)(.15) = .255 Practice Problem #1 In a population of foxes, 85% of the alleles for fur color are for red (R) and 15% are for brown (r). What percentage of the population of foxes is heterozygous if the population is in equilibrium? 26% of the population of foxes is heterozygous. Practice Problem #2 In guppies, the allele for blue scales (B) is dominant over red scales (b). In a population of 1000 guppies, 960 blue and 40 are red. A. What are the frequencies of the two alleles in this population if the population is in Hardy-Weinberg equilibrium? B. How many homozygous dominant individuals are there in the population? What do you know? 960 out of 1000 fish are blue (.96) 40 out of 1000 fish are red (.04) q2 = .04 What do you want to know? Frequencies of the alleles in the population p+q=1 p and q q2 = .04 q = .2; p = .8 Practice Problem #2 In guppies, the allele for blue scales (B) is dominant over red scales (b). In a population of 1000 guppies, 960 blue and 40 are red. A. What are the frequencies of the two alleles in this population if the population is in Hardy-Weinberg 80% of the alleles are B, equilibrium? and 20% of the alleles are b. B. How many homozygous dominant individuals are there in the population? What do you know? 960 out of 1000 fish are blue (.96) 40 out of 1000 fish are red (.04) q2 = .04 What do you want to know? How many homozygous dominant individuals? p2 p2 = (.8)2 = .64 .64 x 1000 = 640 Practice Problem #2 In guppies, the allele for blue scales (B) is dominant over red scales (b). In a population of 1000 guppies, 960 blue and 40 are red. A. What are the frequencies of the two alleles in this population if the population is in Hardy-Weinberg 80% of the alleles are B, equilibrium? and 20% of the alleles are b. B. How many homozygous dominant individuals are there in the population? 640 fish are homozygous dominant. Practice Problem #3 Flower color in snapdragons shows incomplete dominance. When pure-breeding red flowering plants are cross with pure-breeding white flowering plants, all of the offspring have pink flowers. In a garden of 100 snapdragon plants, 30 plants have red flowers (RR), 20 plants have pink flowers (RW), and 50 plants have white flowers (WW). A.What are the frequencies of the R and W alleles? B.Is the population in Hardy-Weinberg equilibrium? Explain. What do you know? 30 out of 100 snapdragons are red/RR (.3) 20 out of 100 snapdragons are pink/RW (.2) 50 out of 100 snapdragons are white/WW (.5) p and q What do you want to know? Frequencies of the alleles in the population q = .2; p = .8