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Deviations from HWE I. Mutation A. Basics: 1. Consider a population with: f(A) = p = .6

Deviations from HWE I. Mutation A. Basics: 1. Consider a population with: f(A) = p = .6 f(a) = q = .4 2. Suppose 'a' mutates to 'A' at a realistic rate of: μ = 1 x 10 -5. Deviations from HWE I. Mutation A. Basics: 1. Consider a population with: f(A) = p = .6

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Deviations from HWE I. Mutation A. Basics: 1. Consider a population with: f(A) = p = .6

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  1. Deviations from HWE I. Mutation A. Basics: 1. Consider a population with: f(A) = p = .6 f(a) = q = .4 2. Suppose 'a' mutates to 'A' at a realistic rate of: μ = 1 x 10-5

  2. Deviations from HWE I. Mutation A. Basics: 1. Consider a population with: f(A) = p = .6 f(a) = q = .4 2. Suppose 'a' mutates to 'A' at a realistic rate of: μ = 1 x 10-5 3. Well, what fraction of alleles will change? 'a' will decline by: qm = .4 x 0.00001 = 0.000004 'A' will increase by the same amount.

  3. Deviations from HWE I. Mutation A. Basics: 1. Consider a population with: f(A) = p = .6 f(a) = q = .4 2. Suppose 'a' mutates to 'A' at a realistic rate of: μ = 1 x 10-5 3. Well, what fraction of alleles will change? 'a' will decline by: qm = .4 x 0.00001 = 0.000004 'A' will increase by the same amount. 4. So, the new gene frequencies will be: p1 = p + μq = .600004 q1 = q - μq = q(1-μ) = .399996

  4. Deviations from HWE I. Mutation A. Basics: 4. So, the new gene frequencies will be: p1 = p + μq = 1 - q + μq = 1- q(1-μ) = .600004 q1 = q - μq = q(1-μ) = .399996 5. How about with both FORWARD and backward mutation? Δq = νp - μq - so, if A -> a =v = 0.00008 and a->A = μ = 0.00001, and p = 0.6 and q = 0.4, then:

  5. Deviations from HWE I. Mutation A. Basics: 4. So, the new gene frequencies will be: p1 = p + μq = 1 - q + μq = 1- q(1-μ) = .600004 q1 = q - μq = q(1-μ) = .399996 5. How about with both FORWARD and backward mutation? Δq = νp - μq - so, if A -> a =v = 0.00008 and a->A = μ = 0.00001, and p = 0.6 and q = 0.4, then: Δq = νp - μq = 0.000048 - 0.000004 = 0.000044 q1 = .4 + 0.000044 = 0.400044

  6. Deviations from HWE I. Mutation A. Basics: 5. How about with both FORWARD and backward mutation? - Δq = νp - μq - and qeq = v/ v + μ

  7. Deviations from HWE I. Mutation A. Basics: 5. How about with both FORWARD and backward mutation? - Δq = νp - μq - and qeq = v/ v + μ - and qeq = v/ v + μ = 0.00008/0.00009 = 0.89

  8. Deviations from HWE I. Mutation A. Basics: 5. How about with both FORWARD and backward mutation? - Δq = νp - μq - and qeq = v/ v + μ - and qeq = v/ v + μ = 0.00008/0.00009 = 0.89 - so, if Δq = νp – μq, then: Δq = (.11)(0.00008) - (.89)(0.00001) = 0.0..... check.

  9. Deviations from HWE I. Mutation A. Basics: B. Other Considerations:

  10. Deviations from HWE I. Mutation A. Basics: B. Other Considerations: - Selection: Selection can BALANCE mutation... so a deleterious allele might not accumulate as rapidly as mutation would predict, because it it eliminated from the population by selection each generation. (We'll model these effects later).

  11. Deviations from HWE I. Mutation A. Basics: B. Other Considerations: - Selection: - Drift: The probability that a new allele (produced by mutation) becomes fixed (q = 1.0) in a population = 1/2N (basically, it's frequency in that population of diploids). In a small population, this chance becomes measureable and likely. So, NEUTRAL mutations have a reasonable change of becoming fixed in small populations... and then replaced by new mutation

  12. Deviations from HWE I. Mutation II. Migration A. Basics: - Consider two populations: p2 = 0.7 q2 = 0.3 p1 = 0.2 q1 = 0.8

  13. Deviations from HWE I. Mutation II. Migration A. Basics: - Consider two populations: p2 = 0.7 q2 = 0.3 p1 = 0.2 q1 = 0.8 suppose migrants immigrate at a rate such that the new immigrants represent 10% of the new population

  14. Deviations from HWE I. Mutation II. Migration A. Basics: - Consider two populations: p2 = 0.7 q2 = 0.3 p1 = 0.2 q1 = 0.8 suppose migrants immigrate at a rate such that the new immigrants represent 10% of the new population

  15. Deviations from HWE I. Mutation II. Migration A. Basics: - Consider two populations: p2 = 0.7 q2 = 0.3 p1 = 0.2 q1 = 0.8 suppose migrants immigrate at a rate such that the new immigrants represent 10% of the new population p(new) = p1(1-m) + p2(m)

  16. Deviations from HWE I. Mutation II. Migration A. Basics: - Consider two populations: p2 = 0.7 q2 = 0.3 p1 = 0.2 q1 = 0.8 suppose migrants immigrate at a rate such that the new immigrants represent 10% of the new population p(new) = p1(1-m) + p2(m) p(new) = 0.2(0.9) + 0.7(0.1) = 0.25

  17. Deviations from HWE I. Mutation II. Migration A. Basics: B. Advanced: - Consider three populations: p1 = 0.7 q1 = 0.3 p2 = 0.2 q2 = 0.8 p3 = 0.6 q3 = 0.4

  18. Deviations from HWE I. Mutation II. Migration A. Basics: B. Advanced: - Consider three populations: - How different are they, genetically? (this can give us a handle on how much migration there may be between them...) p1 = 0.7 q1 = 0.3 p2 = 0.2 q2 = 0.8 p3 = 0.6 q3 = 0.4

  19. Deviations from HWE I. Mutation II. Migration A. Basics: B. Advanced: - Consider three populations: - How different are they, genetically? (this can give us a handle on how much migration there may be between them...) - Compute Nei's Genetic Distance: D = -ln [ ∑pi1pi2/ √ ∑pi12 ∑pi22] p1 = 0.7 q1 = 0.3 p2 = 0.2 q2 = 0.8 p3 = 0.6 q3 = 0.4

  20. Deviations from HWE I. Mutation II. Migration A. Basics: B. Advanced: - Consider three populations: - How different are they, genetically? (this can give us a handle on how much migration there may be between them...) - Compute Nei's Genetic Distance: D = -ln [ ∑pi1pi2/ √ ∑pi12 ∑pi22] - So, for Population 1 and 2: - ∑pi1pi2 = (0.7*0.2) + (0.3*0.8) = 0.38 - denominator = √ (.49+.09) * (.04+.64) = 0.628 D12 = -ln (0.38/0.62) = 0.50 p1 = 0.7 q1 = 0.3 p2 = 0.2 q2 = 0.8 p3 = 0.6 q3 = 0.4

  21. - Compute Nei's Genetic Distance: D = -ln [ ∑pi1pi2/ √ ∑pi12 ∑pi22] - So, for Population 1 and 2: - ∑pi1pi2 = (0.7*0.2) + (0.3*0.8) = 0.38 - denominator = √ (.49+.09) * (.04+.64) = 0.628 D12 = -ln (0.38/0.628) = 0.50 - For Population 1 and 3: - ∑pi1pi2 = (0.7*0.6) + (0.3*0.4) = 0.54 - denominator = √ (.49+.09) * (.36+.16) = 0.55 D13 = -ln (0.54/0.55) = 0.02 (not very ‘distant’) - For Population 2 and 3: - ∑pi1pi2 = (0.2*0.6) + (0.8*0.4) = 0.44 - denominator = √ (.04+.64) * (.36+.16) = 0.61 D23 = -ln (0.44/0.61) = 0.33 p1 = 0.7 q1 = 0.3 p2 = 0.2 q2 = 0.8 p3 = 0.6 q3 = 0.4

  22. Deviations from HWE I. Mutation II. Migration III. Non-Random Mating A. Positive Assortative Mating "like phenotype mates with like phenotype"

  23. Deviations from HWE I. Mutation II. Migration III. Non-Random Mating A. Positive Assortative Mating "like phenotype mates with like phenotype" 1. Pattern:

  24. 1. Pattern: 2. Effect: - reduction in heterozygosity at this locus; increase in homozygosity.

  25. Deviations from HWE I. Mutation II. Migration III. Non-Random Mating A. Positive Assortative Mating B. Inbreeding 1. Overview:

  26. Deviations from HWE I. Mutation II. Migration III. Non-Random Mating A. Positive Assortative Mating B. Inbreeding 1. Overview: Inbreeding is “like mating with like”, but across the entire genome. So, heterozygosity should decline across all loci at about the same rate due to inbreeding, alone.

  27. B. Inbreeding 1. Overview: - So, the fractional demise of heterozygosity compared to HWE expectations can be used as a direct measure of inbreeding! F = “inbreeding coefficient” F = (Hexp - Hobs)/ Hexp = (2pq - H)/2pq When this is done on multiple loci, the values should all be similar (as inbreeding affects the whole genotype).

  28. B. Inbreeding 1. Overview: - Example: F = (2pq - H)/2pq p = .5, q = .5, expected HWE heterozygosity = 2pq = 0.5 OBSERVED in F1 = 0.3... so F = (.5 - .3)/.5 = 0.4 As Hobs 0, F  1.0

  29. Deviations from HWE I. Mutation II. Migration III. Non-Random Mating A. Positive Assortative Mating B. Inbreeding 1. Overview: 2. Effects:

  30. Deviations from HWE I. Mutation II. Migration III. Non-Random Mating A. Positive Assortative Mating B. Inbreeding 1. Overview: 2. Effects: - reduce heterozygosity across entire genome

  31. Deviations from HWE I. Mutation II. Migration III. Non-Random Mating A. Positive Assortative Mating B. Inbreeding 1. Overview: 2. Effects: - reduce heterozygosity across entire genome - rate dependent upon degree of relatedness

  32. Deviations from HWE I. Mutation II. Migration III. Non-Random Mating A. Positive Assortative Mating B. Inbreeding 1. Overview: 2. Effects: - reduce heterozygosity across entire genome - rate dependent upon degree of relatedness - change in genotypic frequencies but no change in gene frequencies as a result of non-random mating ALONE....

  33. Deviations from HWE I. Mutation II. Migration III. Non-Random Mating A. Positive Assortative Mating B. Inbreeding 1. Overview: 2. Effects: - reduce heterozygosity across entire genome - rate dependent upon degree of relatedness - change in genotypic frequencies but no change in gene frequencies as a result of non-random mating ALONE.... - BUT... increasing homozygosity may reveal deleterious recessives.

  34. Deviations from HWE I. Mutation II. Migration III. Non-Random Mating A. Positive Assortative Mating B. Inbreeding 1. Overview: 2. Effects: - reduce heterozygosity across entire genome - rate dependent upon degree of relatedness - change in genotypic frequencies but no change in gene frequencies as a result of non-random mating ALONE.... - BUT... increasing homozygosity may reveal deleterious recessives. - these may be selected against (changing gene frequencies)

  35. Deviations from HWE I. Mutation II. Migration III. Non-Random Mating A. Positive Assortative Mating B. Inbreeding 1. Overview: 2. Effects: - reduce heterozygosity across entire genome - rate dependent upon degree of relatedness - change in genotypic frequencies but no change in gene frequencies as a result of non-random mating ALONE.... - BUT... increasing homozygosity may reveal deleterious recessives. - these may be selected against (changing gene frequencies) - this reduces mean reproductive success (inbreeding depression)

  36. Deviations from HWE I. Mutation II. Migration III. Non-Random Mating IV. Genetic Drift A. Sampling Error

  37. Deviations from HWE I. Mutation II. Migration III. Non-Random Mating IV. Genetic Drift A. Sampling Error 1. samples from a variable population may not represent the population exactly. In biological populations, this is because not all adults mate. Two Major Patterns:

  38. 1) small samples deviate more, just by chance, from the original population than large samples.

  39. 2) small samples differ more from one another than large samples.

  40. Deviations from HWE I. Mutation II. Migration III. Non-Random Mating IV. Genetic Drift A. Sampling Error 1. Patterns 2. Instances where this is common: - “Bottlenecks” where population is reduced in size - “Founder Effect” where small group begins new population

  41. - “Genetic Bottleneck” If a population crashes (perhaps as the result of a plague) there will be both selection and drift. There will be selection for those resistant to the disease (and correlated selection for genes close to the genes conferring resistance), but there will also be drift at other loci simply by reducing the size of the breeding population. Cheetah have very low genetic diversity, suggesting a severe bottleneck in the past. They can even exchange skin grafts without rejection… European Bison, hunted to 12 individuals, now number over 1000. Fell to 100’s in the 1800s, now in the 100,000’s

  42. - “Founder Effect” and Huntington’s Chorea HC is a neurodegenerative disorder caused by an autosomal lethal dominant allele. The fishing villages around Lake Maracaibo in Venezuela have the highest incidence of Huntington’s Chorea in the world, approaching 50% in some communities. The gene was mapped to chromosome 4, and found the HC allele was caused by a repeated sequence of over 35 “CAG’s”. Dr. Nancy Wexler found homozygotes in Maracaibo and described it as the first truly dominant human disease (most are incompletely dominant and cause death in the homozygous condition).

  43. - “Founder Effect” and Huntington’s Chorea HC is a neurodegenerative disorder caused by an autosomal lethal dominant allele. The fishing villages around Lake Maracaibo in Venezuela have the highest incidence of Huntington’s Chorea in the world, approaching 50% in some communities. By comparing pedigrees, she traced the incidence to a single woman who lived 200 years ago. When the population was small, she had 10 children who survived and reproduced. Folks with HC now trace their ancestry to this lineage. Also a nice example of “coalescence” – convergence of alleles on a common ancestral allele.

  44. Deviations from HWE I. Mutation II. Migration III. Non-Random Mating IV. Genetic Drift A. Sampling Error B. Coalescence

  45. B. Coalescence - Not all reproducing entities will leave a descendant. Over time, most lineages will go extinct

  46. B. Coalescence - Not all reproducing entities will leave a descendant. Over time, most lineages will go extinct - After an elapsed time, many of the entities will be descendants of the same successful lineage that, just by chance, has left a descendant in each generation. So, over time, average relatedness among existing entities increases.

  47. B. Coalescence - Not all reproducing entities will leave a descendant. Over time, most lineages will go extinct - After an elapsed time, many of the entities will be descendants of the same successful lineage that, just by chance, has left a descendant in each generation. So, over time, average relatedness among existing entities increases. - Eventually, all the entities that are present will trace their ancestry back to a single ancestor; their genealogies 'coalesce' on a single ancestor

  48. B. Coalescence - Not all reproducing entities will leave a descendant. Over time, most lineages will go extinct - After an elapsed time, many of the entities will be descendants of the same successful lineage that, just by chance, has left a descendant in each generation. So, over time, average relatedness among existing entities increases. - Eventually, all the entities that are present will trace their ancestry back to a single ancestor; their genealogies 'coalesce' on a single ancestor. - If the entity is a single gene or a haploid genome, this means that eventually, all the entities in the populations are the same - 'similar by descent'... If this is an allele, the allele is now FIXED f = 1.0. ***When random change occurs, it will ultimately lead to fixation and inbreeding***

  49. Deviations from HWE I. Mutation II. Migration III. Non-Random Mating IV. Genetic Drift A. Sampling Error B. Coalescence C. Evolution by Drift

  50. C. Evolution by Drift - So, by chance, one allele in the population will become fixed. The probability = frequency in the population (p). Even one NEW allele with frequency 1/2N, has that chance of eventually becoming fixed...

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