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Chapter 7

Chapter 7. Evolution at Multiple Loci: Linkage, Sex, and Quantitative Genetics. Evolution at Multiple Loci. In the past two chapters we have considered the Hardy-Weinberg Equilibrium Principle for one locus at a time Can this model be extended to a two or higher locus case?

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Chapter 7

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  1. Chapter 7 Evolution at Multiple Loci: Linkage, Sex, and Quantitative Genetics

  2. Evolution at Multiple Loci • In the past two chapters we have considered the Hardy-Weinberg Equilibrium Principle for one locus at a time • Can this model be extended to a two or higher locus case? • Must make a more realistic model

  3. Multiple Loci • Genes do not exist in isolation • Multiple genes probably effect a single character • Physically associated on chromosome • Linkage disequilibrium

  4. Evolution at Two Loci • Consider two loci on the same chromosome: A and B • Alleles A and a; B and b • Track both allele frequencies and chromosome frequencies • Four possible chromosome genotypes: AB, Ab, aB, and ab • Haplotypes the multi-locus genotype of chromosome, mitochondria or gamete

  5. Evolution at Two Loci • Loci are in linkage equilibrium if the frequency of one allele does not affect the frequency of the other • Linkage disequilibrium = locus frequencies affect each other • May affect evolution of each other by genetic linkage • Genes may be inherited as a group • May be based on physical distance between the loci

  6. Evolution at Two Loci • Numerical example • Two hypothetical populations with 25 chromosomes each • We can calculate allele frequencies and chromosome frequencies

  7. Evolution at Two Loci • Numerical example • Allele frequencies same for both populations • Chromosome frequencies differ slightly • To see difference, can calculate frequency of allele B on chromosomes carrying A versus frequency of chromosomes carrying a • Can depict this graphically

  8. Evolution at Two Loci • Numerical example • Top population is in linkage equilibrium • Chromosome genotype of one locus is independent of other locus • Bottom population is in linkage disequilibrium • Nonrandom association between a genotype at one locus and another • If we know one genotype we have a clue about the other

  9. Evolution at Two Loci • Conditions for Linkage Equilibrium • The frequency of B on chromosomes carrying A is equal to the frequency of B on chromosomes carrying a • The frequency of any chromosome haplotype can be calculated by multiplying frequencies of constituent alleles • The quantity D, the coefficient of linkage disequilibrium, is equal to zero • D = gABgab - gAbgaB • gs are frequencies of chromosomes

  10. Evolution at Two Loci • Assess conditions for hypothetical example • Frequencies of chromosomes are equal • True for top, not for bottom • Frequencies of haplotypes can be calculated by multiplying allele frequencies • A X B = (0.6)(0.8) = 0.48 YES • A X B = (0.6)(0.8) = 0.48 NO AB = 0.44 • D = 0 • gABgab - gAbgaB = (0.48)(0.08) - (0.12)(0.32) YES • gABgab - gAbgaB = (0.44)(0.04) - (0.16)(0.36) NO

  11. Evolution at Two Loci • If the population is in linkage equilibrium, Hardy-Weinberg equations can be used for each locus independently • Assume no selection, no mutation, no migration, infinite population, panmixia

  12. Evolution at Two Loci • What creates linkage disequilibrium? • Selection on multilocus genotypes • Genetic drift • Population admixture

  13. Evolution at Two Loci • Selection on multilocus genotypes • Start with top population from example • 10 zygote types can be produced • Their frequencies can be predicted

  14. Evolution at Two Loci • Selection on multilocus genotypes • Individuals with genotype ab/ab have a size of 10 • For other genotypes, every copy of A or B add one unit to size • aB/aB is size 12 • AB/Ab is size 13 • Predators eat every individual less than size 13 • Linkage disequilibrium created by selection

  15. Evolution at Two Loci • Genetic drift • Imagine a population where the only haplotypes are AB and Ab • Allele a does not exist • The loci are in linkage equilibrium • If a single mutation caused A to mutate to a on an Ab chromosome, linkage disequilibrium would be created • ab would exist but not aB • Frequency of a would be tied to b but not B

  16. Evolution at Two Loci • Genetic drift • Imagine selection favors a over A • a increases in frequency • Degree of linkage disequilibrium increases • Even though mutation and selection acted, the linkage disequilibrium problem is really caused by sampling error • If there were an infinite population size, more A to a mutations would have occurred • aB chromosomes would not be missing • Drift is linkage disequilibrium culprit

  17. Evolution at Two Loci • Population admixture • Imagine two gene pools in linkage equilibrium

  18. Evolution at Two Loci • Population admixture • If the two gene pools combine, the ratios are thrown off and the new population falls into linkage disequilibrium

  19. Evolution at Two Loci • How to eliminate linkage disequilibrium • Sexual reproduction reduces linkage disequilibrium • Meiosis, crossing over, outbreeding • Meiosis breaks up old genotype combinations and creates new ones • Genetic Recombination • Randomizes genotypes of loci with respect to each other

  20. Evolution at Two Loci • Genetic Recombination • Rate of linkage disequilibrium decline is proportional to rate of recombination

  21. Evolution at Two Loci • Genetic Recombination • Study by Clegg • Documented decay of linkage disequilibrium in fruit flies • Two loci on Chromosome 3 • Set up populations with only AB and ab chromosomes at frequencies of 0.5 • In linkage disequilibrium • D = 0.25 • Lowest value possible

  22. Evolution at Two Loci • Genetic Recombination • Study by Clegg • Maintained populations for 50 generations with 1000 individuals • Mated with whomever they chose • Every generation sampled for the four genotypes and calculated rate of linkage disequilibrium • Linkage disequilibrium declined to almost zero with sexual reproduction

  23. Evolution at Two Loci • Why does linkage disequilibrium matter? • If two loci are in linkage disequilibrium, selection at one locus changes allele frequencies at the other • Cannot use Hardy-Weinberg to calculate allele or genotype frequencies • In practice the change in one locus due to linkage disequilibrium could erroneously be interpreted as selection on that locus

  24. Evolution at Two Loci • Why does linkage disequilibrium matter? • If in linkage equilibrium Hardy-Weinberg can still be used • Random sexual reproduction is very efficient at eliminating linkage disequilibrium • Most loci are in linkage equilibrium • Empirical study of 5000 human loci found that only 4% were in linkage disequilibrium

  25. Evolution at Two Loci • Why does linkage disequilibrium matter? • A study of Arabidopsis plants showed 12% linkage disequilibrium • Arabidopsis usually selfs • Must outbreed some time or would have higher D values

  26. Evolution at Two Loci • CCR5-D32 allele • Where did the allele come from? • Why is it mainly in Europe? • Stephens measured linkage disequilibrium in CCR5-D32 with two loci nearby on same chromosome • GAAT and AFMB • Neutral alleles • 192 Europeans • GAAT and AFMB are nearly in linkage equilibrium • CCR5-D32 in strong linkage disequilibrium with both

  27. Evolution at Two Loci • CCR5-D32 allele • Linked alleles • + - 197 - 215 • How did linkage disequilibrium arise? • Selection, genetic drift, or population admixture • Not selection because GAAT and AFMB are selectively neutral • Not population admixture or the allele would be elsewhere in the world • Must be genetic drift

  28. Evolution at Two Loci • CCR5-D32 allele • At some time in past only the wild type allele (+) existed • Then on the chromosome CCR5-GAAT-AFMB with alleles + - 197 - 215 a mutation occurred to D32 • Linkage is now breaking down • Some individuals with + - 197 - 217 are now found

  29. Evolution at Two Loci • CCR5-D32 allele • Stephens used rates of crossing over and mutation to calculate how fast the linkage disequilibrium would be expected to break down • Used this calculation to estimate how long ago D32 appeared • This allele first appeared between 275 and 1875 years ago • Probably about 700 years ago

  30. Evolution at Two Loci • CCR5-D32 allele • Unique mutation must have happened in Europe • Probably occurred elsewhere but was not favored by selection • Why was D32 favored in Europe? • Must have been strong selection to raise from nearly 0% to 20% in 700 years

  31. Evolution at Two Loci • CCR5-D32 allele • Perhaps D32 provides protection from other diseases • It has been hypothesized that it protects against the bacterium Yersinia pestis, the pathogen that caused the Black Death • Investigations are being performed now to test this theory

  32. Adaptive Significance of Sex • Why should organisms reproduce sexually? • Complicated, costly, dangerous • Some organisms can choose to reproduce sexually or asexually at any time • Why don’t they just reproduce asexually and save all of the effort?

  33. Adaptive Significance of Sex • Aphids have spring and summer populations of all females that reproduce by parthenogenesis • Produce live-born young identical to themselves • In the fall aphids produce males and females and mate • Lay eggs • When the eggs hatch they are all parthenogenetic females again

  34. Adaptive Significance of Sex • Tunicate Thalia democratica • Female gives birth to single asexual offspring • Nourished by a structure similar to a placenta • This asexual produces 20–80 genetically identical sexual embryos • Juveniles fertilized internally by sperm from mature sexual adults who developed testes • Grow to adults as they nourish their own offspring and complete life cycle

  35. Adaptive Significance of Sex • Which reproductive mode is better: Sexual or Asexual? • John Maynard Smith developed a null model to answer the question • Has two assumptions • A female’s reproductive mode does not affect the number of offspring she can make • A female’s reproductive mode does not affect the probability that her offspring will survive

  36. Adaptive Significance of Sex • Which reproductive mode is better: Sexual or Asexual? • Maynard Smith noted that all the offspring of a parthenogenetic female are female but the offspring of a sexual female are a mixture of daughters and sons • Therefore, an asexual female would produce twice as many grandchildren as a sexual female • Asexual females would constitute a larger and larger proportion of the population each generation

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