OSU BI 445 - Population Genetics

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Slide 1Slide 2Slide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12Slide 13Slide 14Slide 15Slide 16Slide 17Slide 18Slide 19Slide 20Charles Darwin’s Theory of Evolution by Natural Selection • For selection to be the cause of evolution:1. variation in traits (phenotype) among individuals2. variation is in part heritable (genotype)3. There is differential reproductive success4. Differential is because of particular variants• successful variants contribute their alleles to the gene pool• their alleles therefore increase in frequencyPopulation Genetics• independent assortment and segregation of alleles: Mendel (rediscovered early 1900s)• mutation is the source of genetic variation (1920s and 1950s)Darwin did not know the source of new variation nor the mechanism of inheritanceAccounting of alleles was recognized as possible after MendelEvolution is a change in frequency of inherited traits over generationsEvolution is a change in the frequency of alleles over generationsGG and GT have dark colorTT have light color (G to T; cysteine replaced with phenylalanine)aAA aaAAAAaaaaMendelian GeneticsPre-meiosis S-phaseMeiosis IMeiosis IIHeterozygote = A a (Homozygote = A A or a a)gametesgametesAllele freq. (a) = 2/4 = 0.5Allele freq. (A) = 2/4 = 0.5This is for one individual’s potential contribution to the gene pool.The gene pool is the set of all copies of all alleles in a population that potentially couldbe passed on to the next generationAPopulation: a group of interbreeding individuals and offspringPopulation that does not evolve is in equilibriumPunnett SquareMating Simulation based on Punnett SquareFor 100 adultseach making 10 gametes: AA = 36 A a = 48 a a = 16A = 360 + 240 a = 160 + 240 1000 1000 Allele frequencies in the gene pool0.4 0.24 0.60.6 of eggspopulation of spermgene poolA aAa360A gametes240A and 240a gametes160a gametesHardy-Weinberg Equilibrium Principle1. Allele frequencies in a population will not change from generation to generation2. If allele frequencies in a population are given by p and q, the genotype frequencies will be given by p2, 2pq and q2Hardy-Weinberg Equation1. Allele frequenciesp = freq of allele A q = freq of allele a p + q = 1q pqpp qpqq2p2aaAAspermeggs2. Genotype frequenciesp2 + 2pq + q2 = 13. Calculate allele frequencies in the next generation: pn = p2 + pq qn = q2 + pqHardy-Weinberg Equilibrium Principle – a null modelAssumptions 1. No selection 2. No mutation 3. No chance events (genetic drift) 4. No migration 5. Mating is randomIn other words, these are the mechanisms that cause a population to evolveHardy-Weinberg provides a null hypothesis anda modifiable, mathematical model that makes predictionsCan then do experiments to test predictions• Predicts what allele and genotype frequencies do when evolution does not happen • The null model has 5 assumptionsSelection and Hardy-Weinberg equilibrium1. Assume differential mortality 25% for B1 B2 50% for B2 B24. Final allele frequencies Total gametes = 800 B1 = 540/800 = 0.675 B2 = 260/800 = 0.325 Violation of ‘no selection’ assumptionresults in allele change (evolution)Population is not in Hardy-Weinberg equilibrium2. Assume 10 gametes/individual3. Gametes with B1 and B2 alleles B1 B1 - 360 B1 gametes B1 B2 - 180 B1 and 180 B2 B2 B2 - 80 B2 gametesModifying Hardy-Weinberg to predict selection’s effect on evolutionFitness = genotype’s lifetime reproductive successFitness of genotypes = w (survival rate, assume equal # offspring) B1 B1 x w11 B1 B2 x w12 B2 B2 x w22 Mean fitness of the population: w = p2w11 + 2pqw12 + q2w22p = B1 allele frequencyp2 = B1 B1 genotype frequency2. New genotype frequencies among surviving adults p2w11/ w2pqw12/ w q2w22/ w 3. New allele frequencies p2w11 + pqw12 pqw12 + q2w22 wwpn = qn =1. Starting allele frequencies: p and qw12w22w111 0.99 0.98Change in allele frequencies under different degrees of selectionInitial frequencies: p (B1) = 0.01, q (B2) = 0.99Will the HIV epidemic increase the frequency of the CCR5- 32 allele?ΔNorthern Europe: CCR5- 32 frequency, 0.10 to 0.20Δ infection rates < 1%sub-Saharan Africa: CCR5- 32 frequency, 0.01Δ 25% infected and diePhenotype varies depending on the genotypegenotypes: homozygotes and heterozygotes (A A, a a) (A a)An allele can be dominant, recessive or have incomplete dominance selection for a dominant allele selection for a recessive alleleAlso overdominance that is selection for heterozygoteand underdominance that is selection against the heterozygoteChange in allele frequencies depends on the relationship ofthe paired alleles to the phenotype under selection.Selection against a recessive lethal alleleL locus: + and l alleles (l allele is lethal)1. Initial population is all heterozygotes + freq. = 0.5 l freq. = 0.52. Zygotes (assuming 100 individuals) ++ + l l l 25 50 253. Assume 10 gametes/individual ++ = 250 + gametes + l = 250 + and 250 l gametes l l = 0 gametes (selection against)4. Allele freq. + = 500/750 = 0.67 l = 250/750 = 0.33 Why does + allele only reach ~ 90%?Selection: Dominant orRecessive allelesRate of evolution is slow when a recessive allele is rareRecessive alleles are hidden by the heterozygoteSelection for heterozygote (overdominance)Blue line, 2nd experimentset initial V allele frequencyat 0.975.Even though LL is lethal,the allele increases in frequency!!!(survival rate: wVV, wVL and wLL)but survival rates favor the heterozygoteOverdominance maintains genetic variation in the populationFrequency for V allele atfixation expected to be .94,as with the beetle experimentalso called heterozygote superiorityStable and unstable equilibriaUnstable equilibria with underdominance (reduces genetic variation)Stable equilibria with overdominance (maintains genetic variation)Equilibrium is when Δp = 0 A1A1 A1A2 A2A2 1-s 1 1-t genotype fitnessRed linePopulation evolves towards maximum fitness,which includes both alleles Blue linePopulation evolves towards maximum fitness,which is mutually exclusive:either allele A1 rises to fixationor allele A2 rises to fixationp2 + 2pq + q2 = 1p2w11 + 2pqw12 + q2w22 = 1ww wHWE:modified HWE: Selection For: Recessive 1-s 1-s 1 Dominant 1

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OSU BI 445 - Population Genetics

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