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Mendelian Genetics in Populations – Hardy Weinberg equilibrium The Hardy-Weinberg equilibrium principle yields two fundamental conclusions: Conclusion.

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Presentation on theme: "Mendelian Genetics in Populations – Hardy Weinberg equilibrium The Hardy-Weinberg equilibrium principle yields two fundamental conclusions: Conclusion."— 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 p 2, 2pq, q 2.

2 Mendelian Genetics in Populations – Hardy Weinberg equilibrium The Hardy-Weinberg equilibrium has 5 assumptions 1: There is no selection 2: There is no mutation 3: 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 Selection Selection for Recessive and Dominant alleles Selection for Heterozygotes and Homozygotes Frequency Dependent Selection

4 Selection on Recessive and Dominant alleles Trilobium castaneum (flour beetles) Gene called - l locus Genotypes: +/+ - phenotypically normal +/l - phenotypically normal l/l - lethal 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 6.5 From 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 success chance 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 Fitness Absolute 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:

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. C B C B black - 67% chance of survival to adulthood C B C Y brown - 93% chance of survival to adulthood C Y C Y yellow - 11% chance of survival to adulthood Assuming they have identical numbers of offspring, what is the relative fitness of each genotype? w C B C B -.67/.93 = 0.72 w C B C Y = 1.0 w C Y C Y -.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 = green Brown 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 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 = green Brown 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) = 1 w (Gg) = w (GG) = 10.4/12 = 0.87

10 Selection on Recessive and Dominant alleles 1)When a recessive allele is common (and a dominant allele is rare), evolution is rapid. Why? 2) When a dominant allele is common (and a lethal recessive allele is rare), evolution is slow. 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. 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? Most recessive alleles are in heterozygotes and cannot be selected for. Once recessive alleles become present as homozygotes, the rate of evolution increases dramatically. The recessive allele goes to fixation (= 1.0)

13 Selection for Heterozygotes and Homozygotes Heterozygote superiority = heterosis = overdominance Fitness of the heterozygote is greater than that of either homozygote.

14 Selection for Heterozygotes Mukai and Burdick (1959) Single locus, two alleles VV, VL – viable LL - lethal 2 experimental populations V = 0.5 L = 0.5 Results begin to look like Dawson’s data with flour beetles. But viable allele does not go close to fixation, as Dawson’s data did.

15 Selection on Homozygotes Mukai and Burdick (1959) Using model from Box 6.5 and the following fitnesses: VVVLLL Starting with V = 0.975, both experimental data support the model and previous experiments.

16 Selection for Heterozygotes Generalizations about heterozygote superiority: 1. Alleles will reach equilibrium at frequencies other than those predicted by H-W 2. 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 polymorphism heterosis is one mechanism that can produce this pattern (there are others)

17 Selection for Homozygotes Heterozygote inferiority = underdominance Heterozygotes 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) a.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  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. Based on observations of Smithson and Macnair (1997)  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  Artificial arrays of potted orchids.  Frequency of yellow flowers was varied. Experiment by Gigord et al. (2001)  When frequency of yellow flowers was low, reproductive success was large.

24 Frequency Dependent Selection  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. Experiment by Gigord et al. (2001)

25 Frequency Dependent Selection  Observed frequency of yellow flowers in 20 natural populations was 69± 3%  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. Experiment by Gigord et al. (2001)  Dashed vertical lines indicate predicted equilibrium frequencies for the yellow allele as a function of: 1) allele frequency and 2) fitness. Negative frequency dependent selection maintains genetic diversity in populations.

26 Mutation  Mutation 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? The second assumption of Hardy-Weinberg equilibrium is – No mutation

27 Figure 6-26 A high rate of mutation, but within the known range. Allele frequencies change ever so slightly. AA Aa aa Genotype frequencies change ever so slightly. Is this evolution?

28 Figure 6-27 Is this evolution? Eventually But it is not adaptive evolution.

29 Mutation  Used inbred, homozygous stock.  Two conditions Two cages w/o NaCl in the diet. Four cages with access to media containing 0, 1, 2, 3, 4, 5, 6% NaCl 5% and 6% NaCl lethal  After 30 generations flies divided among cages with 0, 1, 2, 3, 4, 5, 6% NaCl in diet. Mutation is an important source of variation for selection.

30 Mutation 5% & 6% NaCl is lethal to the original stock Flies with access to all 6 NaCl conc. survive and produce progeny on each of the 6 NaCl conc. = adaptive evolution through mutation and selection.

31 Mutation 5% & 6% NaCl is lethal to the original stock Even unstressed flies developed mutations in the absence of selection that permitted them to survive and produce progeny up to 5% NaCl

32 Mutation-Selection balance A: Mutation is an ongoing process - new deleterious alleles are always being created.  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?  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. For recessive alleles When the mutant allele is dominant, then 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.

34 Mutation-Selection balance  When mutation rates are high and selection is relatively weak, the equilibrium frequency will be high.  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.

35 Mutation-Selection balance  Cystic Fibrosis – is it maintained by selection-balance? Lung damage by cystic fibrosis (right). 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 linings b.Acts as, among other things, a chloride channel (inability to regulate chloride concentrations causes many of the problems associated with CF). c.Gene also plays a role in allowing cells of lung lining to ingest and destroy Pseudomonas aeruginosa bacteria. A lung epithelial cell ingesting P. aeruginosa. Cells in red are inside cell and surrounded by CFTR. 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.

36 Mutation-Selection balance Selection 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 Mutation-Selection balance a. Assume selection coefficient of 1 (homozygotes never reproduce) b. Determine the mutation rate that would be required to produce equilibrium frequency of about Result = mutation rate of 4 x  Actual mutation rate seems to be about 6.7 x  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.


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