Lecture 12LECTURE 12POPULATION GENETICS IIISEPTEMBER 22, 2014Homework: Reading: Chapter 25.4-25.8 and 25.9-25.10. Page 720.Homework: Illustrate Summary Points (p. 721) #6-8. Solved problem 2. Questions: Ch 25 Q 12-15, 23, 24, 26Modifications of the Hardy-Weinberg law (continued)E. MutationThe wear and tear on the DNA due to replication, exposure to radiation and chemicals, results in sequence changes (mutations), i.e. new alleles. Mutations are the primary source of new alleles in a population.E. 1 Mutation rates per gene vary widely among genes. However mutation from a dominant wild type allele to a recessive loss-of-function allele is typically around 1:100,000 per gene per generation. Q: Interpret this number, assuming the human genome has 20,000 genes. A: The genome will accumulate large numbers of deleterious alleles, over evolutionary time-scales; which, as long as they remain heterozygous, are not effectively eliminated by selection and therefore persist in the gene pool (>3,000 human disease alleles).Q: Assuming there was no purifying selection (or genetic drift), how many generations would it take to lose half of all wild type alleles to deleterious mutations?A: About 70,000. In humans, about 1.75 million years.Q: We saw earlier that recessive alleles are not easily eliminated by selection. How many recessive lethalalleles might your genome harbor? None? One or two? A few more? See below for an answer.E. 2 Mutation rate per nucleotide  in humans: Approx 3.0 x 10-8 per generation.-> This is relatively high, perhaps because it takes 200 mitoses from one zygote to the next.Q: Given that our genome has 3 billion basepairs, how many NEW mutations does your genome carry?A: About 90 per haploid set; these are nucleotide changes that your parents do not have.E. 3 Balance of mutation and selection. It can be shown that the frequency (q) for a fairly uncommon mutated allele will be given byq2 = /s (see slide for derivation)Q: A typical spontaneous mutation rate for an essential human gene is =10-6 per generation. If homozygotes have no offspring (s=1), what will be the allele frequency in the population? What will be theexpected fraction of carriers and homozygotes? A: q= (/s)1/2 = 10-3 2pq=1/500 q2 = 10-6-> These are typical values for rare human disease alleles.Q: What if selection is weak (s=0.01)?A: The mutant allele will accumulate to 10x higher frequency.Q: Of the 20000 human genes, about 3000 are 'essential' for quality of life. Estimate, for how many of these genes do I carry a detrimental mutation? A: 3000 x 1/500 = 6 1-> In reality this number may be lower, because many deleterious alleles also have a reduced fitness in the heterozygous state.E. 4 Linkage disequilibrium: Preferential (nonrandom) association between two specific alleles of different genes. Reason: (a) Every new mutation arises in a specific haplotype context = displays LD. (b) A selective sweep boosts specific mutations and all variable sites that are linked to it nearby on the chromosome. (c) Migration may bring new haplotypes into a population.LD = PAB - pA x pBPAB -is the actual, observed, frequency of the AB haplotype (allele combination)pA x pB is the expected frequency of AB, the product of the actual allele frequencies of A and B. Once created, LD breaks down over time, as crossing over events seperate A from its linked allele B.-> Remember: 1cM genetic distance takes a median of almost 2000 years to break up by crossing over.By observing the degree of LD around a new mutation one can discern how long ago the underlying mutation arose (if we know which mutation it is).Q: Which human chromosome might be an excellent archive of the genetic history of human mutation, migration and selection?A: The Y-chromosome, because it does not lose its LD by crossing over.F. Genetic driftHW assumption: the population is infinitely large. This assumption is in place to eliminate sampling error when progeny genotypes are assembled by randomly drawing from the pool of parental gametes. Obviously, no population is infinite, but large populations will have negligible sampling error. Because of sampling error, (i) allele frequencies will fluctuate over several generations (genetic drift) and (ii) an allelehas a certain probability of becoming lost from the population (and the other allele may become 'fixed'). Analogy: Flip a coin 4 times. You can imagine getting 4 tails rather than the more likely 2:2 ratio of heads and tails. But if you flip the coin 40 times, the ratio of heads and tails will almost certainly not be 40:0 but close to 20:20. Drawing genes from a gene pool resembles a coin-flip experiment. The exact probabilities are governed by the Binomial distributionGiven: A population of N diploid individuals with allele frequencies for A and a given by p and q.The total number of alleles will be n=2N. We are asking, what is the likelihood (L) that the NEXT generation will have m number of A alleles (and n-m a alleles)?L = ‘n over m’ x pm x q(n-m)with 'n over m' standing for n! / m! x (n-m)!Q: Practice, what is the probability that allele a will be eliminated in the next generation? A: p2NGenetic drift plays an important role in population genetics and evolution because small population sizes are quite typical:a) endangered speciesb) species that don't roam widely but have low population densities 2c) species in which only a small fraction of males are reproductively successfuld) founder effects: a small group of individuals establishes a new foothold (e.g. on an island)e) population bottlenecks: a natural disaster decimates a population; crop domesticationNon-intuitive result: Elimination of rare alleles is very common, especially over long times. Experiment: see Buri's study of the brown-eye-allele in 107 small Drosophila populations. 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