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Population Genetics: Selection and mutation as mechanisms of evolution Population genetics: study of Mendelian genetics at the level of the whole population. Population genetics: study of Mendelian genetics at the level of the whole population.

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Hardy-Weinberg Equilibrium To understand conditions under which evolution can occur, it is necessary to understand the population genetic conditions under which it will not occur. To understand conditions under which evolution can occur, it is necessary to understand the population genetic conditions under which it will not occur.

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Hardy-Weinberg Equilibrium Hardy-Weinberg Equilibrium Principle allows us to predict allele and genotype frequencies from one generation to the next in the absence of evolution. Hardy-Weinberg Equilibrium Principle allows us to predict allele and genotype frequencies from one generation to the next in the absence of evolution.

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Hardy-Weinberg Equilibrium Assume two alleles A and a with known frequencies (e.g. A = 0.6, a = 0.4.) Assume two alleles A and a with known frequencies (e.g. A = 0.6, a = 0.4.) Only two genes in population so their allele frequencies add up to 1. Only two genes in population so their allele frequencies add up to 1.

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Hardy-Weinberg Equilibrium Can predict frequencies of genotypes in next generation using allele frequencies. Can predict frequencies of genotypes in next generation using allele frequencies. Possible genotypes: AA, Aa and aa Possible genotypes: AA, Aa and aa

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Hardy-Weinberg Equilibrium Assume alleles A and a enter eggs and sperm in proportion to their frequency in population (i.e. 0.6 and 0.4) Assume alleles A and a enter eggs and sperm in proportion to their frequency in population (i.e. 0.6 and 0.4) Assume sperm and eggs meet at random (one big gene pool). Assume sperm and eggs meet at random (one big gene pool).

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Hardy-Weinberg Equilibrium Then we can calculate genotype frequencies. Then we can calculate genotype frequencies. AA: To produce an AA individual, egg and sperm must each contain an A allele. AA: To produce an AA individual, egg and sperm must each contain an A allele. This probability is 0.6 x 0.6 or 0.36 (probability sperm contains A times probability egg contains A). This probability is 0.6 x 0.6 or 0.36 (probability sperm contains A times probability egg contains A).

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Hardy-Weinberg Equilibrium Similarly, we can calculate frequency of aa. Similarly, we can calculate frequency of aa. 0.4 x 0.4 = 0.16. 0.4 x 0.4 = 0.16.

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Hardy-Weinberg Equilibrium Probability of Aa is given by probability sperm contains A (0.6) times probability egg contains a (0.4). 0.6 x 0.4 = 0.24 Probability of Aa is given by probability sperm contains A (0.6) times probability egg contains a (0.4). 0.6 x 0.4 = 0.24

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Hardy-Weinberg Equilibrium But, theres a second way to produce an Aa individual (egg contains A and sperm contains a). Same probability as before: 0.6 x 0.4= 0.24. But, theres a second way to produce an Aa individual (egg contains A and sperm contains a). Same probability as before: 0.6 x 0.4= 0.24. Overall probability of Aa = 0.24 + 0.24 = 0.48. Overall probability of Aa = 0.24 + 0.24 = 0.48.

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Hardy-Weinberg Equilibrium Genotypes in next generation: Genotypes in next generation: AA = 0.36 AA = 0.36 Aa = 0.48 Aa = 0.48 Aa= 0.16 Aa= 0.16 Adds up to one. Adds up to one.

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General formula for Hardy-Weinberg Let p= frequency of dominant allele A and q = frequency of recessive allele a. Let p= frequency of dominant allele A and q = frequency of recessive allele a. So p + q = 1 So p + q = 1 Therefore, p 2 + 2pq + q 2 = 1 Therefore, p 2 + 2pq + q 2 = 1 Frequency of the homozygous dominant + frequency of the heterozygous + frequency of the homozygous recessive = 1 Frequency of the homozygous dominant + frequency of the heterozygous + frequency of the homozygous recessive = 1

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Conclusions from Hardy- Weinberg Equilibrium Allele frequencies in a population will not change from one generation to the next just as a result of assortment of alleles and zygote formation. Allele frequencies in a population will not change from one generation to the next just as a result of assortment of alleles and zygote formation. If the allele frequencies in a gene pool with two alleles are given by p and q, the genotype frequencies will be given by p 2, 2pq, and q 2. If the allele frequencies in a gene pool with two alleles are given by p and q, the genotype frequencies will be given by p 2, 2pq, and q 2.

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Assumptions of Hardy- Weinberg 1. No selection. 1. No selection. –When individuals with certain genotypes survive better than others, allele frequencies may change from one generation to the next.

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Assumptions of Hardy- Weinberg 2. No mutation 2. No mutation – If new alleles are produced by mutation or alleles mutate at different rates, allele frequencies may change from one generation to the next.

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Assumptions of Hardy- Weinberg 3. No migration 3. No migration –Movement of individuals in or out of a population will alter allele and genotype frequencies.

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Assumptions of Hardy- Weinberg 4. No chance events. 4. No chance events. –Luck plays no role. Eggs and sperm collide at same frequencies as the actual frequencies of p and q. –When assumption violated and by chance some individuals contribute more alleles than others to next generation allele frequencies may change. This mechanism of allele change called Genetic Drift.

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Assumptions of Hardy- Weinberg 5. Individuals select mates at random. 5. Individuals select mates at random. –If this assumption violated allele frequencies will not change, but genotype frequencies may.

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Hardy Weinberg equilibrium principle identifies the forces that can cause evolution. Hardy Weinberg equilibrium principle identifies the forces that can cause evolution. If a population is not in H-W equilibrium then one or more of the 5 assumptions is being violated. If a population is not in H-W equilibrium then one or more of the 5 assumptions is being violated.

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5.10

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Solving Hardy-Weinberg Problems What are we given? What are we given? What are we trying to find? What are we trying to find?

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Lets solve one: 84% of my students are tasters 84% of my students are tasters What is the frequency of the recessive allele in this population? What is the frequency of the recessive allele in this population?

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What are we given? The frequency of the TT and Tt The frequency of the TT and Tt p 2 and 2pq p 2 and 2pq

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What we are trying to find? The frequency of the recessive allele in the population The frequency of the recessive allele in the population q

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84% are TT and Tt 84% are TT and Tt 16% are tt, or q 2 16% are tt, or q 2 q 2 = 16% or 0.16 q 2 = 16% or 0.16 q = 0.4 q = 0.4 40% of the alleles are the recessive gene for non-taster 40% of the alleles are the recessive gene for non-taster

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Try this one on your own! Assume that there are only 6 people in this room with blue eyes. How many people are heterozygous for brown eyes? Assume that there are only 6 people in this room with blue eyes. How many people are heterozygous for brown eyes?

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About 1% of West Africans have sickle cell anemia. A single mutation that causes a valine amino acid to replace a glutamine in an alpha chain of the hemoglobin molecule. Mutation causes molecules to stick together.

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Why isnt mutant sickle cell gene eliminated by natural selection?

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Only individuals homozygous for sickle cell gene get sickle cell anemia. Individuals with one copy of sickle cell gene (heterozygotes) get sickle cell trait (mild form of disease). Individuals with sickle cell allele (one or two copies) dont get malaria. copies) dont get malaria.

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Heterozygotes have higher survival than either homozygote. Heterozygote advantage. Sickle cell homozygotes die of sickle cell anemia. Normal heterozygotes more likely to die of malaria. Stabilizing selection for sickle cell allele.

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Maintaining multiple alleles in gene pool Another way in which multiple alleles are maintained is frequency- dependent selection. Another way in which multiple alleles are maintained is frequency- dependent selection. Frequency-dependent selection occurs when rare alleles have a selective advantage. Frequency-dependent selection occurs when rare alleles have a selective advantage.

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Frequency-dependent selection Color polymorphism in Elderflower Orchid Color polymorphism in Elderflower Orchid Two flower colors: yellow and purple. Offer no food reward to bees. Bees alternate visits to colors. Two flower colors: yellow and purple. Offer no food reward to bees. Bees alternate visits to colors. How are two colors maintained in the population? How are two colors maintained in the population?

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Gigord et al. hypothesis: Bees tend to visit equal numbers of each flower color so rarer color will have advantage (will get more visits from pollinators). Gigord et al. hypothesis: Bees tend to visit equal numbers of each flower color so rarer color will have advantage (will get more visits from pollinators). Frequency-dependent selection

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Experiment: provided five arrays of potted orchids with different frequencies of yellow orchids in each. Experiment: provided five arrays of potted orchids with different frequencies of yellow orchids in each. Monitored orchids for fruit set and removal of pollinaria (pollen bearing structures) Monitored orchids for fruit set and removal of pollinaria (pollen bearing structures) Frequency-dependent selection

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As predicted, reproductive success of yellow varied with frequency. As predicted, reproductive success of yellow varied with frequency. Frequency-dependent selection

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