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Measuring Evolution of Populations AP Biology 5 Agents of evolutionary change Mutation Gene Flow Genetic Drift AP Biology 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 AP Biology 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) AP Biology 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 AP mathematician Biology 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 AP Biology 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 AP Biology Bb bb H-W formulas Alleles: p+q=1 B Individuals: p2 + 2pq + q2 = 1 BB BB AP Biology 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 MustWhat assume are the population genotype is frequencies? in H-W equilibrium! AP Biology 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? AP Biology 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 AP Biology 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… AP Biology Single-celled eukaryote parasite (Plasmodium) spends part of its life cycle in red blood cells Malaria 1 2 AP Biology 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. AP Biology Frequency of sickle cell allele & distribution of malaria Practice Question A population called the “founder generation”, consisting of 2000 AA individuals, 2000 Aa individuals, and 6000 aa individuals is established on a remote island. Mating within this population occurs at random, the three genotypes are selectively neutral, and mutations occur at a negligible rate. a) What are the frequencies of the alleles A and a in the founder generation? b) Is the founder generation at Hardy-Weinberg Equilibrium? c) What is the frequency of the A allele in the second generation (that is, the generation subsequent to the founder generation)? d) What are the frequencies of the AA, Aa, and aa genotypes in the second generation? AP Biology AP Biology For each of the following problems in population genetics use the Hardy-Weinberg equation. Show all of your work and label each frequency, probability, and allele. 1. Suppose that in a breeding experiment, 7,000 AA individuals and 3,000 aa individuals mate at random. In the first generation of offspring, what would be the frequencies of the three genotypes (AA, Aa, and aa)? What would be the frequencies of the two alleles? What would be the values in the second generation? AP Biology 2. Among African-Americans, the frequency of sickle-cell anemia (which, as you will recall is a homozygous recessive condition) is about 0.0025. What is the frequency of heterozygotes? When on African-American marries another, what is the probability that both will be heterozygotes? If both are heterozygotes, what is the probability that their first child will have sickle-cell anemia? AP Biology 3. If q = 0.3 and there are Hardy-Weinberg proportions, what is the most common genotype and what is its frequency? What is the least frequent genotype and its frequency? AP Biology 4. In a large, randomly mating population with no forces acting to change gene frequencies, the frequency of homozygous recessive individuals for the character extralong eyelashes is 90 per 1000, or 0.09. What percentage of the population carries this trait but displays the dominant phenotype, short eyelashes? Would the frequency of the extra-long-lash allele increase, decrease, or remain the same if long-lashed individuals preferentially mated with each other and no one else? AP Biology Any Questions?? AP Biology