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III. Modeling Selection A. Selection for a Dominant Allele B. Selection for an Incompletely Dominant Allele C.

III. Modeling Selection A. Selection for a Dominant Allele B. Selection for an Incompletely Dominant Allele C. Selection that Maintains Variation. C. Selection that Maintains Variation 1. Heterosis - selection for the heterozygote. C. Selection that Maintains Variation

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III. Modeling Selection A. Selection for a Dominant Allele B. Selection for an Incompletely Dominant Allele C.

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  1. III. Modeling Selection A. Selection for a Dominant Allele B. Selection for an Incompletely Dominant Allele C. Selection that Maintains Variation

  2. C. Selection that Maintains Variation 1. Heterosis - selection for the heterozygote

  3. C. Selection that Maintains Variation 1. Heterosis - selection for the heterozygote - Consider an 'A" allele. It's probability of being lost from the population is a function of:

  4. C. Selection that Maintains Variation 1. Heterosis - selection for the heterozygote - Consider an 'A" allele. It's probability of being lost from the population is a function of: 1) probability it meets another 'A' (p)

  5. C. Selection that Maintains Variation 1. Heterosis - selection for the heterozygote - Consider an 'A" allele. It's probability of being lost from the population is a function of: 1) probability it meets another 'A' (p) 2) rate at which these AA are lost (s).

  6. C. Selection that Maintains Variation 1. Heterosis - selection for the heterozygote - Consider an 'A" allele. It's probability of being lost from the population is a function of: 1) probability it meets another 'A' (p) 2) rate at which these AA are lost (s). - So, prob of losing an 'A' allele = ps

  7. C. Selection that Maintains Variation 1. Heterosis - selection for the heterozygote - Consider an 'A" allele. It's probability of being lost from the population is a function of: 1) probability it meets another 'A' (p) 2) rate at which these AA are lost (s). - So, prob of losing an 'A' allele = ps - Likewise the probability of losing an 'a' = qt

  8. C. Selection that Maintains Variation 1. Heterosis - selection for the heterozygote - Consider an 'A" allele. It's probability of being lost from the population is a function of: 1) probability it meets another 'A' (p) 2) rate at which these AA are lost (s). - So, prob of losing an 'A' allele = ps - Likewise the probability of losing an 'a' = qt - An equilibrium will occur, when the probability of losing A an a are equal; when ps = qt.

  9. C. Selection that Maintains Variation 1. Heterosis - selection for the heterozygote - An equilibrium will occur, when the probability of losing A an a are equal; when ps = qt.

  10. C. Selection that Maintains Variation 1. Heterosis - selection for the heterozygote - An equilibrium will occur, when the probability of losing A an a are equal; when ps = qt. - substituting (1-p) for q, ps = (1-p)t ps = t - pt ps +pt = t p(s + t) = t peq = t/(s + t)

  11. C. Selection that Maintains Variation 1. Heterosis - selection for the heterozygote - An equilibrium will occur, when the probability of losing A an a are equal; when ps = qt. - substituting (1-p) for q, ps = (1-p)t ps = t - pt ps +pt = t p(s + t) = t peq = t/(s + t) - So, for our example, t = 0.75, s = 0.5 - so, peq = .75/1.25 = 0.6

  12. C. Selection that Maintains Variation 1. Heterosis - selection for the heterozygote - so, peq = .75/1.25 = 0.6

  13. C. Selection that Maintains Variation 1. Heterosis - selection for the heterozygote - so, peq = .75/1.25 = 0.6 - so, if p > 0.6, it should decline to this peq

  14. C. Selection that Maintains Variation 1. Heterosis - selection for the heterozygote - so, peq = .75/1.25 = 0.6 - so, if p > 0.6, it should decline to this peq 0.6

  15. C. Selection that Maintains Variation 1. Heterosis - selection for the heterozygote 2. Multiple Niche Polymorphism -

  16. C. Selection that Maintains Variation 1. Heterosis - selection for the heterozygote 2. Multiple Niche Polymorphism - - equilibrium can occur if AA and aa are each fit in a given niche, within the population. The equilibrium will depend on the relative frequencies of the niches and the selection differentials...

  17. C. Selection that Maintains Variation 1. Heterosis - selection for the heterozygote 2. Multiple Niche Polymorphism - - equilibrium can occur if AA and aa are each fit in a given niche, within the population. The equilibrium will depend on the relative frequencies of the niches and the selection differentials... - can you think of an example??

  18. C. Selection that Maintains Variation 1. Heterosis - selection for the heterozygote 2. Multiple Niche Polymorphism - - equilibrium can occur if AA and aa are each fit in a given niche, within the population. The equilibrium will depend on the relative frequencies of the niches and the selection differentials... - can you think of an example?? Papilio butterflies... females mimic different models and an equilibrium is maintained; in fact, an equilibrium at each locus, which are also maintained in linkage disequilibrium.

  19. C. Selection that Maintains Variation 1. Heterosis - selection for the heterozygote 2. Multiple Niche Polymorphism 3. Frequency Dependent Selection

  20. C. Selection that Maintains Variation 1. Heterosis - selection for the heterozygote 2. Multiple Niche Polymorphism 3. Frequency Dependent Selection - the fitness depends on the frequency...

  21. C. Selection that Maintains Variation 1. Heterosis - selection for the heterozygote 2. Multiple Niche Polymorphism 3. Frequency Dependent Selection - the fitness depends on the frequency... - as a gene becomes rare, it becomes advantageous and is maintained in the population...

  22. C. Selection that Maintains Variation 1. Heterosis - selection for the heterozygote 2. Multiple Niche Polymorphism 3. Frequency Dependent Selection - the fitness depends on the frequency... - as a gene becomes rare, it becomes advantageous and is maintained in the population... - "Rare mate" phenomenon...

  23. - Morphs of Heliconius melpomene and H. erato Mullerian complex between two distasteful species... positive frequency dependence in both populations to look like the most abundant morph

  24. C. Selection that Maintains Variation 1. Heterosis - selection for the heterozygote 2. Multiple Niche Polymorphism 3. Frequency Dependent Selection 4. Selection Against the Heterozygote

  25. 4. Selection Against the Heterozygote

  26. 4. Selection Against the Heterozygote - peq = t/(s + t)

  27. 4. Selection Against the Heterozygote - peq = t/(s + t) - here = .25/(.50 + .25) = .33

  28. 4. Selection Against the Heterozygote - peq = t/(s + t) - here = .25/(.50 + .25) = .33 - if p > 0.33, then it will keep increasing to fixation.

  29. 4. Selection Against the Heterozygote - peq = t/(s + t) - here = .25/(.50 + .25) = .33 - if p > 0.33, then it will keep increasing to fixation. - However, if p < 0.33, then p will decline to zero... AND THERE WILL BE FIXATION FOR A SUBOPTIMAL ALLELE....'a'... !! UNSTABLE EQUILIBRIUM!!!!

  30. Population Genetics I. Basic Principles II. X-linked Genes III. Modeling Selection IV. OTHER DEVIATIONS FROM HWE

  31. Deviations from HWE I. Mutation A. Basics:

  32. Deviations from HWE I. Mutation A. Basics: 1. Consider a population with: f(A) = p = .6 f(a) = q = .4

  33. 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

  34. 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.

  35. 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

  36. 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

  37. 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:

  38. 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

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

  40. 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

  41. 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.

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

  43. 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.

  44. 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. - 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

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

  46. 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

  47. 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

  48. 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)

  49. 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

  50. 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

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