Population Genetics: Population Genetics: Selection and mutation Selection and mutation as mechanisms of as mechanisms of evolutionevolution

Population genetics: study of Population genetics: study of Mendelian genetics at the level of Mendelian genetics at the level of the whole population.the whole population.

Hardy-Weinberg Hardy-Weinberg EquilibriumEquilibrium To understand conditions under To understand conditions under

which evolution can occur, it is which evolution can occur, it is necessary to understand the necessary to understand the population genetic conditions population genetic conditions under which it will not occur.under which it will not occur.

Hardy-Weinberg Hardy-Weinberg EquilibriumEquilibrium Hardy-Weinberg Equilibrium Hardy-Weinberg Equilibrium

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

Hardy-Weinberg Hardy-Weinberg EquilibriumEquilibrium Assume two alleles A and a with Assume two alleles A and a with

known frequencies (e.g. A = 0.6, known frequencies (e.g. A = 0.6, a = 0.4.)a = 0.4.)

Only two genes in population so Only two genes in population so their allele frequencies add up to their allele frequencies add up to 1.1.

Hardy-Weinberg Hardy-Weinberg EquilibriumEquilibrium Can predict frequencies of Can predict frequencies of

genotypes in next generation genotypes in next generation using allele frequencies.using allele frequencies.

Possible genotypes: AA, Aa and Possible genotypes: AA, Aa and aaaa

Hardy-Weinberg Hardy-Weinberg EquilibriumEquilibrium Assume alleles A and a enter Assume alleles A and a enter

eggs and sperm in proportion to eggs and sperm in proportion to their frequency in population (i.e. their frequency in population (i.e. 0.6 and 0.4) 0.6 and 0.4)

Assume sperm and eggs meet at Assume sperm and eggs meet at random (one big gene pool).random (one big gene pool).

Hardy-Weinberg Hardy-Weinberg EquilibriumEquilibrium Then we can calculate genotype Then we can calculate genotype

frequencies.frequencies. AA: To produce an AA individual, AA: To produce an AA individual,

egg and sperm must each contain egg and sperm must each contain an A allele.an A allele.

This probability is 0.6 x 0.6 or 0.36 This probability is 0.6 x 0.6 or 0.36 (probability sperm contains A (probability sperm contains A times probability egg contains A).times probability egg contains A).

Hardy-Weinberg Hardy-Weinberg EquilibriumEquilibrium Similarly, we can calculate Similarly, we can calculate

frequency of aa.frequency of aa.

0.4 x 0.4 = 0.16.0.4 x 0.4 = 0.16.

Hardy-Weinberg Hardy-Weinberg EquilibriumEquilibrium Probability of Aa is given by Probability of Aa is given by

probability sperm contains A (0.6) probability sperm contains A (0.6) times probability egg contains a times probability egg contains a (0.4). 0.6 x 0.4 = 0.24(0.4). 0.6 x 0.4 = 0.24

Hardy-Weinberg Hardy-Weinberg EquilibriumEquilibrium But, there’s a second way to But, there’s a second way to

produce an Aa individual (egg produce an Aa individual (egg contains A and sperm contains a). contains A and sperm contains a). Same probability as before: 0.6 x Same probability as before: 0.6 x 0.4= 0.24.0.4= 0.24.

Overall probability of Aa = 0.24 + Overall probability of Aa = 0.24 + 0.24 = 0.48.0.24 = 0.48.

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

General formula for General formula for Hardy-WeinbergHardy-Weinberg Let p= frequency of dominant Let p= frequency of dominant

allele A and q = frequency of allele A and q = frequency of recessive allele a.recessive allele a.

So “p + q = 1”So “p + q = 1” Therefore, “pTherefore, “p2 2 + 2pq + q+ 2pq + q22 = 1” = 1” Frequency of the homozygous Frequency of the homozygous

dominant + frequency of the dominant + frequency of the heterozygous + frequency of the heterozygous + frequency of the homozygous recessive = 1homozygous recessive = 1

Conclusions from Conclusions from Hardy-Weinberg Hardy-Weinberg EquilibriumEquilibrium Allele frequencies in a population Allele frequencies in a population

will not change from one will not change from one generation to the next just as a generation to the next just as a result of assortment of alleles and result of assortment of alleles and zygote formation.zygote formation.

If the allele frequencies in a gene If the allele frequencies in a gene pool with two alleles are given by pool with two alleles are given by p and q, the genotype frequencies p and q, the genotype frequencies will be given by pwill be given by p22, 2pq, and q, 2pq, and q22..

Assumptions of Hardy-Assumptions of Hardy-WeinbergWeinberg 1. 1. No selectionNo selection..

– When individuals with certain When individuals with certain genotypes survive better than genotypes survive better than others, allele frequencies may others, allele frequencies may change from one generation to the change from one generation to the next.next.

Assumptions of Hardy-Assumptions of Hardy-WeinbergWeinberg 2. 2. No mutationNo mutation

– If new alleles are produced by If new alleles are produced by mutation or alleles mutate at mutation or alleles mutate at different rates, allele frequencies different rates, allele frequencies may change from one generation to may change from one generation to the next.the next.

Assumptions of Hardy-Assumptions of Hardy-WeinbergWeinberg 3. 3. No migrationNo migration

– Movement of individuals in or out of Movement of individuals in or out of a population will alter allele and a population will alter allele and genotype frequencies.genotype frequencies.

Assumptions of Hardy-Assumptions of Hardy-WeinbergWeinberg 4. 4. No chance eventsNo chance events..

– Luck plays no role. Eggs and sperm Luck plays no role. Eggs and sperm collide at same frequencies as the collide at same frequencies as the actual frequencies of p and q. actual frequencies of p and q.

– When assumption violated and by When assumption violated and by chance some individuals contribute chance some individuals contribute more alleles than others to next more alleles than others to next generation allele frequencies may generation allele frequencies may change. This mechanism of allele change. This mechanism of allele change called change called Genetic DriftGenetic Drift..

Assumptions of Hardy-Assumptions of Hardy-WeinbergWeinberg 5. 5. Individuals select mates at Individuals select mates at

randomrandom..– If this assumption violated allele If this assumption violated allele

frequencies will not change, but frequencies will not change, but genotype frequencies may.genotype frequencies may.

Hardy Weinberg equilibrium Hardy Weinberg equilibrium principle identifies the forces that principle identifies the forces that can cause evolution.can cause evolution.

If a population is not in H-W If a population is not in H-W equilibrium then one or more of equilibrium then one or more of the 5 assumptions is being the 5 assumptions is being violated.violated.

5.10

Solving Hardy-Solving Hardy-Weinberg ProblemsWeinberg Problems

What are we given?What are we given? What are we trying to find?What are we trying to find?

Let’s solve one:Let’s solve one:

84% of my students are tasters84% of my students are tasters What is the frequency of the What is the frequency of the

recessive allele in this population?recessive allele in this population?

What are we given?What are we given?

The frequency of the TT and TtThe frequency of the TT and Tt pp22 and 2pq and 2pq

What we are trying to What we are trying to find?find? The frequency of the recessive The frequency of the recessive

allele in the populationallele in the population qq

84% are TT and Tt84% are TT and Tt 16% are tt, or q16% are tt, or q22

qq22 = 16% or 0.16 = 16% or 0.16 q = 0.4q = 0.4 40% of the alleles are the 40% of the alleles are the

recessive gene for non-tasterrecessive gene for non-taster

Try this one on your Try this one on your own!own! Assume that there are only 6 Assume that there are only 6

people in this room with blue people in this room with blue eyes. How many people are eyes. How many people are heterozygous for brown eyes?heterozygous for brown eyes?

About 1% of West Africans have sickle About 1% of West Africans have sickle cell anemia. cell anemia.

A single mutation that causes a valineA single mutation that causes a valineamino acid to replace a glutamineamino acid to replace a glutaminein an alpha chain of the hemoglobin in an alpha chain of the hemoglobin molecule.molecule.

Mutation causes molecules to stick Mutation causes molecules to stick together.together.

Why isn’t mutant sickle cell geneWhy isn’t mutant sickle cell geneeliminated by natural selection?eliminated by natural selection?

Only individuals Only individuals homozygoushomozygous for forsickle cell gene get sickle cell anemia.sickle cell gene get sickle cell anemia.

Individuals with one copy of sickle cell geneIndividuals with one copy of sickle cell gene((heterozygotesheterozygotes) get sickle cell trait ) get sickle cell trait (mild form of disease).(mild form of disease).

Individuals with sickle cell allele (one or twoIndividuals with sickle cell allele (one or two copies) don’t get malaria.copies) don’t get malaria.

Heterozygotes have higher survival thanHeterozygotes have higher survival thaneither homozygote. Heterozygote advantage. either homozygote. Heterozygote advantage.

Sickle cell homozygotes die of sickle Sickle cell homozygotes die of sickle cell anemia.cell anemia.

““Normal” heterozygotes more likelyNormal” heterozygotes more likelyto die of malaria.to die of malaria.

Stabilizing selection for sickle cell allele.Stabilizing selection for sickle cell allele.

Maintaining multiple Maintaining multiple alleles in gene poolalleles in gene pool Another way in which multiple Another way in which multiple

alleles are maintained is alleles are maintained is frequency-dependent selection.frequency-dependent selection.

Frequency-dependent selection Frequency-dependent selection occurs when rare alleles have a occurs when rare alleles have a selective advantage. selective advantage.

Frequency-dependent Frequency-dependent selectionselection Color polymorphism in Elderflower Color polymorphism in Elderflower

OrchidOrchid

Two flower colors: yellow and purple. Two flower colors: yellow and purple. Offer no food reward to bees. Bees Offer no food reward to bees. Bees alternate visits to colors. alternate visits to colors.

How are two colors maintained in the How are two colors maintained in the population?population?

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

Frequency-dependent Frequency-dependent selectionselection

Experiment: provided five arrays Experiment: provided five arrays of potted orchids with different of potted orchids with different frequencies of yellow orchids in frequencies of yellow orchids in each.each.

Monitored orchids for fruit set and Monitored orchids for fruit set and removal of pollinaria (pollen removal of pollinaria (pollen bearing structures) bearing structures)

Frequency-dependent Frequency-dependent selectionselection

As predicted, reproductive As predicted, reproductive success of yellow varied with success of yellow varied with frequency.frequency.

Frequency-dependent Frequency-dependent selectionselection

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