Presentation on theme: "Mendelian Genetics in Populations – Hardy Weinberg equilibrium"— Presentation transcript:
1 Mendelian Genetics in Populations – Hardy Weinberg equilibrium The Hardy-Weinberg equilibrium principle yields two fundamental conclusions:Conclusion 1: The allele frequencies in a population will not change, generation after generation.Conclusion 2: If the allele frequencies in a population are given by p and q, the genotype frequencies will be given by p2, 2pq, q2.
2 Mendelian Genetics in Populations – Hardy Weinberg equilibrium The Hardy-Weinberg equilibrium has 5 assumptions1: There is no selection2: There is no mutation3: There is no migration (gene flow)4: There are no chance events (Chance events are unlikely to occur in a very large population. In a large population, eggs and sperm ‘collide’ at their actual frequencies of p and q.)5: Individuals choose their mates at random.If all of these assumptions are met, then nothing happens!The population does not change.
3 Mendelian Genetics in Populations - Selection Patterns of SelectionSelection for Recessive and Dominant allelesSelection for Heterozygotes and HomozygotesFrequency Dependent Selection
4 Selection on Recessive and Dominant alleles Gene called - l locusGenotypes: +/+ - phenotypically normal+/l - phenotypically normall/l lethalTrilobium castaneum (flour beetles)Peter Dawson (1970) starts 2 experimental populations with heterozygotes (+/l) as founders.Frequency of + and l are:The frequency of an allele in the next generation can be calculated by:From Box 6.5From Box 6.3
5 Fitness What is fitness, w? Your text book: Fitness is the extent to which an individual contributes genes to future generations.-an individuals score on a measure of performance expected to correlated with genetic contribution to future generations.e.g. lifetime reproductive successchance of survival to adulthood (reproduction)Absolute fitness - is the total number of surviving offspring an individual produces during its lifetime (lifetime reproductive success).Survivorship is a component of fitness.Absolute fitness = the chance of survival * the # of offspring.
6 Relative FitnessAbsolute fitness is standardize to obtain Relative fitness.The genotype with the highest absolute fitness has a relative fitness of 1.0.For every other genotype, their relative fitness is:𝑎𝑏𝑠𝑜𝑙𝑢𝑡𝑒 𝑓𝑖𝑡𝑛𝑒𝑠𝑠 𝑎𝑏𝑠𝑜𝑙𝑢𝑡𝑒 𝑓𝑖𝑡𝑛𝑒𝑠𝑠 𝑜𝑓 𝑡ℎ𝑒 𝑓𝑖𝑡𝑡𝑒𝑠𝑡 𝑔𝑒𝑛𝑜𝑡𝑦𝑝𝑒
7 Relative Fitness Example A beetle is polymorphic for color. It comes in black, brown and yellow morphs.Birds and lizards prey on them, so that due to differences in survivorship, the fitness of the color morphs differ.CB CB black % chance of survival to adulthoodCB CY brown - 93% chance of survival to adulthoodCY CY yellow - 11% chance of survival to adulthoodAssuming they have identical numbers of offspring, what is the relative fitness of each genotype?w CB CB /.93 = 0.72w CB CY = 1.0w CY CY -.11/.93 = 0.12
8 Absolute Fitness Problem: A species of snake has two forms: brown and green.They are determined by a single locus with two alleles.GG = brown, Gg = brown, gg = greenBrown phenotypes are cryptic and have a 80% chance of surviving to reproduce.Green phenotypes have a 60% chance of surviving to reproduce.The brown phenotype produces an average of 13 offspring.The green phenotype produces an average of 20 offspring.What are the absolute and relative fitnesses of each genotype?
9 Absolute Fitness Absolute fitness of Brown phenotypes GG and Gg Problem:A species of snake has two forms: brown and green.They are determined by a single locus with two alleles.GG = brown, Gg = brown, gg = greenBrown phenotypes have a 80% chance of surviving to reproduce.Green phenotypes have a 60% chance of surviving to reproduce.The brown phenotype produces an average of 13 offspring.The green phenotype produces an average of 20 offspring.What are the absolute and relative finesses of each genotype?Absolute fitness of Brown phenotypes GG and Gg.80 chance of survival x 13 offspring = 10.4 expected offspring.Absolute fitness of Green phenotype gg.60 chance of survival x 20 offspring = 12 expected offspring.w(gg) = 1w(Gg) = w(GG) = 10.4/12 = 0.87
10 Selection on Recessive and Dominant alleles When a recessive allele is common (and a dominant allele is rare), evolution is rapid.Why?If the dominant and recessive allele differ in fitness, then there will be a rapid reduction in the recessive allele if it has lower fitness.2) When a dominant allele is common (and a lethal recessive allele is rare), evolution is slow.Even lethal recessive alleles will persist because they “hide” in heterozygotes. They are virtually impossible to eliminate.If the dominant allele is lethal, what happens?That allele is eliminated in one generation.
11 Selection on Recessive and Dominant alleles 2) When a dominant allele is common (and a recessive allele is rare), evolution is slow.Even lethal recessive alleles will persist because they “hide” in heterozygotes. They are virtually impossible to eliminate.
12 Selection on Recessive and Dominant alleles When selection favors a recessive allele, evolution is slow at first. Why?The recessive allele goes to fixation (= 1.0)Most recessive alleles are in heterozygotes and cannot be selected for.Once recessive alleles become present as homozygotes, the rate of evolution increases dramatically.
13 Selection for Heterozygotes and Homozygotes Heterozygote superiority = heterosis = overdominanceFitness of the heterozygote is greater than that of either homozygote.
14 Selection for Heterozygotes Mukai and Burdick (1959)Single locus, two allelesVV, VL – viableLL - lethal2 experimental populationsV = 0.5L = 0.5But viable allele does not go close to fixation, as Dawson’s data did.Results begin to look like Dawson’s data with flour beetles.
15 Selection on Homozygotes Mukai and Burdick (1959)Starting with V = 0.975, both experimental data support the model and previous experiments.Using model from Box 6.5 and the following fitnesses:VV VL LL
16 Selection for Heterozygotes Generalizations about heterozygote superiority:1. Alleles will reach equilibrium at frequencies other than those predicted by H-W2. Because selection is favoring heterozygotes, both alleles will be maintained over time – instead of one allele being fixed and one eliminated (selection is maintaining genetic variability).3. Because both alleles are actively maintained over time, all three genotypes will be actively maintained over time.4. The general term for population with multiple phenotypes = balanced polymorphismheterosis is one mechanism that can produce this pattern (there are others)
17 Selection for Homozygotes Heterozygote inferiority = underdominanceHeterozygotes have lower fitness than do either homozygote.Because heterozygotes have low fitness, most matings will take place among homozygotes.Whichever allele (dominant or recessive doesn’t matter) is most common in a population will be selectively favored and will be fixed.
18 Selection for Homozygotes Do thought experiment: imagine population with two alleles A and a; Selection acts against heterozygotes (assume no heterozygotes survive)If A is more common than a, population will have high frequency of AA and lower frequency of aa.b. Assume random mating: who mates with whom?i. Because they’re more common, AA individuals will most likely mate with AA.ii. Because they’re rare, aa individuals are more likely to mate with AA than with aa.iii. Because most aa mate with AA, they produce heterozygous offspring.c. What happens to a alleles? a alleles will be found in heterozygotes and eliminated.d. What happens to the A allele? A becomes fixed.e. Same will happen if a more common than A.Note that fixation only depends on initial frequency, not on dominance or recessiveness.
19 Selection on Homozygotes Foster et al. (1972)Don’t get caught up with how researchers created the “alleles”.Frequencies of 0.5 for each allele is unstable.As soon as frequency shifts above or below 0.5, the allele rapidly goes to fixation or 0. (Consider outcome of thought experiment).
20 Selection on Homozygotes Foster et al. (1972)If fitness of homozygotes are unequal, then unstable equilibrium point shifts in favor of the allele with greater fitness.Heterozygote inferiority leads to a loss of genetic diversity within a population.Heterozygote inferiority may help maintain genetic diversity among populations. How?A: By driving different alleles to fixation in different populations.
21 Frequency Dependent Selection What happens if the direction of selection changes over time?1. When selection constantly favors one allele over another, that can result in fixation of that allele.2. A stable equilibrium would be achieved if the heterozygotes were favored.3. Negative frequency-dependent selection creates a condition of stable equilibrium by favoring one allele over another, but the favoritism alternates and is mediated by behavior!The punch line: In negative frequency dependent selection, rare alleles are selectively favored.
22 Frequency Dependent Selection Based on observations of Smithson and Macnair (1997)Naïve bumblebees visit stands of orchids to sample flowers.If a bee visits a purple flower and receives no reward, it looks next in a yellow flower.If it finds nothing in the yellow flower, it looks next in a purple flower.Finding nothing in the purple flower sends it back to the yellow flower.Bees visit equal numbers of purple and yellow flowers.As a consequence, orchids with the less common color are visited more often.More visits translates into greater reproductive success.The allele responsible for the rare color increases in frequency.
23 Frequency Dependent Selection Experiment by Gigord et al. (2001)Artificial arrays of potted orchids.Frequency of yellow flowers was varied.When frequency of yellow flowers was low, reproductive success was large.
24 Frequency Dependent Selection Experiment by Gigord et al. (2001)Artificial arrays of potted orchids.Frequency of yellow flowers was varied.When frequency of yellow flowers was low, reproductive success was large.When frequency of yellow flowers was high, reproductive success was low.
25 Frequency Dependent Selection Experiment by Gigord et al. (2001)Artificial arrays of potted orchids.Frequency of yellow flowers was varied.When frequency of yellow flowers was low, reproductive success was large.When frequency of yellow flowers was high, reproductive success was low.Dashed vertical lines indicate predicted equilibrium frequencies for the yellow allele as a function of:1) allele frequency and 2) fitness.Observed frequency of yellow flowers in 20 natural populations was 69± 3%Negative frequency dependent selection maintains genetic diversity in populations.
26 Mutation The second assumption of Hardy-Weinberg equilibrium is – No mutationMutation is ultimately the origin of the genetic variation that selection acts on – it provides the raw material for evolution.By itself, though (i.e., in the absence of selection for or against the mutant allele), does mutation cause evolutionary change?
27 Is this evolution? AA Aa aa 0.8098 0.18014 0.010018 Figure 6-26AA Aa aaGenotype frequencies change ever so slightly.Allele frequencies change ever so slightly.A high rate of mutation, but within the known range.Is this evolution?
28 Is this evolution? Eventually But it is not adaptive evolution. Figure 6-27Is this evolution?EventuallyBut it is not adaptive evolution.
29 Mutation Mutation is an important source of variation for selection. Used inbred, homozygous stock.Two conditionsTwo cages w/o NaCl in the diet.Four cages with access to media containing , 1, 2, 3, 4, 5, 6% NaCl5% and 6% NaCl lethalAfter 30 generations flies divided among cages with 0, 1, 2, 3, 4, 5, 6% NaCl in diet.
30 MutationFlies with access to all 6 NaCl conc. survive and produce progeny on each of the 6 NaCl conc.= adaptive evolution through mutation and selection.5% & 6% NaCl is lethal to the original stock
31 MutationEven unstressed flies developed mutations in the absence of selection that permitted them to survive and produce progeny up to 5% NaCl5% & 6% NaCl is lethal to the original stock
32 Mutation-Selection balance Most mutations are at least mildly deleterious, so selection acts to eliminate them.Yet, deleterious alleles remain in populations at frequencies higher than predicted by H-W – why?A: Mutation is an ongoing process - new deleterious alleles are always being created.If alleles are being created by mutation at the same rate they’re eliminated by selection, the allele will achieve an equilibrium frequency.
33 Mutation-Selection balance We can calculate the equilibrium frequency with a simple equation.𝑞 = 𝑢 𝑠For recessive alleles𝑞 = the equilibrium frequency of the mutant alleleµ = the mutation rate (the rate at which the new allele is created)s = the selection coefficient = a number between 0 and 1 that measures the strength of selection acting against the allele. (s = 1-w)If the favored phenotype produces 100 progeny, and only 90 are produced by the less favorable phenotype, then the fitness (w) of the less favorable phenotype is 0.9, and s = 1-w = 0.1.𝑞 = 𝑢 𝑠When the mutant allele is dominant, thenIf s = 1 then 𝑞 =𝑢
34 Mutation-Selection balance We can calculate the equilibrium frequency with a simple equation.When mutation rates are low and selection against the allele is high, the equilibrium frequency will be low.low 𝑞 = 𝑢↓ 𝑠↑When mutation rates are high and selection is relatively weak, the equilibrium frequency will be high.high 𝑞 = 𝑢↑ 𝑠↓
35 Mutation-Selection balance Cystic Fibrosis – is it maintained by selection-balance?1. CF is caused by recessive loss-of-function mutations in the CFTR (cystic fibrosis transmembrane conductance regulator) gene.a. CFTR is a cell surface protein expressed in mucus membrane liningsb. Acts as, among other things, a chloride channel (inability to regulate chloride concentrations causes many of the problems associated with CF).Gene also plays a role in allowing cells of lung lining to ingest and destroy Pseudomonas aeruginosa bacteria.Lung damage by cystic fibrosis (right).i. Inability to destroy bacteria means individuals homozygous for mutant CFTRs have chronic P. aeruginosa lung infections.ii. Ultimately leads to severe lung damage and early death.A lung epithelial cell ingesting P. aeruginosa. Cells in red are inside cell and surrounded by CFTR.
36 What is the allele frequency of the mutant allele? Mutation-Selection balanceSelection against loss-of-function mutations in CFTR is strong.a. Until recently, very few individuals with CF lived to reproductive age.b. Many of those who do survive into 30s and 40s are sterile.Mutant CFTR allele remains present at frequencies higher than predicted by H-W .CF present 1 in 2,500 newborns of European ancestry.What is the allele frequency of the mutant allele?
37 Is something else is going on? Mutation-Selection balance𝑞 = 𝑢 𝑠a. Assume selection coefficient of 1 (homozygotes never reproduce)b. Determine the mutation rate that would be required to produce equilibrium frequency of about 0.02.Result = mutation rate of 4 x 10-4Actual mutation rate seems to be about 6.7 x 10-7.This is substantially lower than would be required for mutation-selection balance.Is something else is going on?
38 Mutation-Selection balance Piers et al. (1998) hypothesized that CF heterozygotes are resistant to typhoid fever and therefore exhibit heterozygote superiority.The hypothesis is that typhoid bacteria (Salmonella typhi) use CFTR protein as a point of entry into cells:Homozygous wild-type individuals will be susceptible to typhoid.Homozygous mutant individuals will have CF.Heterozygotes will be resistant to typhoid and not have CF.
39 Mutation-Selection balance Piers et al. (1998) tested hypothesis by constructing mouse cells with 3 different CFTR genotypes using wild type and most common mutant CFTR allele, then exposing cells to S. typhi.ΔF508 is a common, single-codon deletion in the CFTR allele.Results strongly suggests that CF, like sickle-cell anemia, is maintained by heterozygote superiority.