Assumptions of Hardy-Weinberg equilibrium

Transcription

1 Migration and Drift

2 Assumptions of Hardy-Weinberg equilibrium 1. Mating is random 2. Population size is infinite (i.e., no genetic drift) 3. No migration 4. No mutation 5. No selection

3 An example of directional selection Let p = q = 0.5 Genotype: A 1 A 1 A 1 A 2 A 2 A 2 Fitness: w 1 = pw 11 + qw 12 = w 2 = qw 22 + pw 12 = w = pw 1 + qw 2 = p = p(w 1 /w) = q = q(w 2 /w) = In ~150 generations the A 1 allele will be fixed

4 Conclusion: Natural selection can cause rapid evolutionary change!

5 Natural selection and mean population fitness

6 Natural selection and mean population fitness Question: How does w change during the process of directional selection?

7 Natural selection and mean population fitness Question: How does w change during the process of directional selection? Genotype: AA Aa aa Fitness: Here, selection is favoring a dominant allele.

8 Directional selection always maximizes mean population fitness!

9 Natural selection and mean population fitness Question: How does w change during the process of directional selection? Genotype: AA Aa aa Fitness: Here, selection is favoring a recessive allele.

10 Directional selection always maximizes mean population fitness!

11 Natural selection and mean population fitness Question: How does w change during the process of balancing selection?

12 Natural selection and mean population fitness Question: How does w change during the process of balancing selection? Genotype: AA Aa aa Fitness: 1-s 1 1-t

13 Natural selection and mean population fitness Question: How does w change during the process of balancing selection? Genotype: AA Aa aa Fitness: 1-s 1 1-t ^ Results in stable equilibrium point at p = t/(s + t)

14 Natural selection and mean population fitness Question: How does w change during the process of balancing selection? Example: suppose s = 0.40 and t = 0.60

15 Natural selection and mean population fitness Question: How does w change during the process of balancing selection? Example: suppose s = 0.40 and t = 0.60 Genotype: AA Aa aa Fitness:

16 Natural selection and mean population fitness Question: How does w change during the process of balancing selection? Example: suppose s = 0.40 and t = 0.60 Genotype: AA Aa aa Fitness: ^ Stable equilibrium point at p = t/(s + t)

17 Natural selection and mean population fitness Question: How does w change during the process of balancing selection? Example: suppose s = 0.40 and t = 0.60 Genotype: AA Aa aa Fitness: ^ Stable equilibrium point at p = t/(s + t) = 0.60

18 Balancing selection maximizes mean population fitness!

19 Balancing selection maximizes mean population fitness! but is only 0.75!

20 Conclusion: Natural selection always acts to maximize mean population fitness

21 Natural selection and mean population fitness

22 Natural selection and mean population fitness Sewall Wright envisoned populations occupying adaptive landscapes.

23 Natural selection and mean population fitness Sewall Wright envisoned populations occupying adaptive landscapes. Wright at the University of Chicago in 1925

24 Natural selection and mean population fitness Sewall Wright envisoned populations occupying adaptive landscapes. Wright in 1965

25 Natural selection and mean population fitness Sewall Wright envisoned populations occupying adaptive landscapes. these landscapes were covered with multiple adaptive peaks separated by valleys of reduced fitness

26 A hypothetical adaptive landscape

27

28 Natural selection and mean population fitness Sewall Wright envisoned populations occupying adaptive landscapes. these landscapes were covered with multiple adaptive peaks separated by valleys of reduced fitness his shifting balance theory considered how populations could move from one peak to another.

29 A hypothetical adaptive landscape How does a population move among peaks??

30 Mutation

31 Mutation Let p = frequency of A 1 allele

32 Mutation Let p = frequency of A 1 allele Let q = frequency of A 2 allele

33 Mutation Let p = frequency of A 1 allele Let q = frequency of A 2 allele Let p = q = 0.50

34 Mutation Let p = frequency of A 1 allele Let q = frequency of A 2 allele Let p = q = 0.50 µ A 1 A 2 Let µ = 1 x 10-5

35 Mutation Let p = frequency of A 1 allele Let q = frequency of A 2 allele Let p = q = 0.50 µ A 1 A 2 υ Let µ = 1 x 10-5 (and ignore υ)

36 Mutation denoting the change in A2 in one generation as Δq,

37 Mutation denoting the change in A2 in one generation as Δq, Δq = µ x p

38 Mutation denoting the change in A2 in one generation as Δq, Δq = µ x p = (1 x 10-5 )(0.5)

39 Mutation denoting the change in A2 in one generation as Δq, Δq = µ x p = (1 x 10-5 )(0.5) =

40 Mutation denoting the change in A2 in one generation as Δq, Δq = µ x p = (1 x 10-5 )(0.5) = the A 2 allele has increased in frequency to

41 Mutation denoting the change in A2 in one generation as Δq, Δq = µ x p = (1 x 10-5 )(0.5) = the A 2 allele has increased in frequency to it would take another 140,000 generations to reach 0.875

42 Mutation denoting the change in A2 in one generation as Δq, Δq = µ x p = (1 x 10-5 )(0.5) = the A 2 allele has increased in frequency to it would take another 140,000 generations to reach Conclusion: The rate of change due to mutation pressure is extremely small!

43 Some comments on mutation 1. Mutation is the raw material that fuels all evolutionary change.

44 Some comments on mutation 1. Mutation is the raw material that fuels all evolutionary change. 2. Mutations occur randomly!

45 Some comments on mutation 1. Mutation is the raw material that fuels all evolutionary change. 2. Mutations occur randomly! 3. Mutations occur too infrequently to cause significant allele frequency change.

46 Some comments on mutation 1. Mutation is the raw material that fuels all evolutionary change. 2. Mutations occur randomly! 3. Mutations occur too infrequently to cause significant allele frequency change. 4. Most mutations are deleterious and experience purifying selection.

47 Some comments on mutation 1. Mutation is the raw material that fuels all evolutionary change. 2. Mutations occur randomly! 3. Mutations occur too infrequently to cause significant allele frequency change. 4. Most mutations are deleterious and experience purifying selection. 5. A small (but unknown) proportion of mutations are beneficial and lead to adaptation.

48 Migration (gene flow)

49 Migration (gene flow) gene flow is simply the movement of genes among populations.

50 Migration (gene flow) gene flow is simply the movement of genes among populations. it can occur by the movement of gametes, or by the movement (and successful breeding) of individuals.

51 Migration (gene flow) gene flow is simply the movement of genes among populations. it can occur by the movement of gametes, or by the movement (and successful breeding) of individuals. its magnitude is determined by m

52 Migration (gene flow) gene flow is simply the movement of genes among populations. it can occur by the movement of gametes, or by the movement (and successful breeding) of individuals. its magnitude is determined by m m = the proportion of genes entering a population in individuals (genes) immigrating from a different population.

53 Sewall Wright s Continent-Island model

54 A simple model of migration

55 A simple model of migration let p I = frequency of A 1 allele on island

56 A simple model of migration let p I = frequency of A 1 allele on island let p C = frequency of A 1 allele on continent

57 A simple model of migration let p I = frequency of A 1 allele on island let p C = frequency of A 1 allele on continent let m = proportion of A 1 alleles moving to island each generation

58 A simple model of migration let p I = frequency of A 1 allele on island let p C = frequency of A 1 allele on continent let m = proportion of A 1 alleles moving to island each generation let p I = frequency of A 1 allele on island in the next generation

59 A simple model of migration let p I = frequency of A 1 allele on island let p C = frequency of A 1 allele on continent let m = proportion of A 1 alleles moving to island each generation let p I = frequency of A 1 allele on island in the next generation p I = (1-m)(p I ) + m(p c )

60 A simple model of migration let p I = frequency of A 1 allele on island let p C = frequency of A 1 allele on continent let m = proportion of A 1 alleles moving to island each generation let p I = frequency of A 1 allele on island in the next generation p I = (1-m)(p I ) + m(p c ) resident immigrant

61 A simple model of migration let Δp I = change in frequency of A 1 allele on island from one generation to the next

62 A simple model of migration let Δp I = change in frequency of A 1 allele on island from one generation to the next Δp I = p I - p I

63 A simple model of migration let Δp I = change in frequency of A 1 allele on island from one generation to the next Δp I = p I - p I = (1-m)(p I ) + m(p c ) - p I

64 A simple model of migration let Δp I = change in frequency of A 1 allele on island from one generation to the next Δp I = p I - p I = (1-m)(p I ) + m(p c ) - p I = m(p c p I )

65 An example:

66 An example: let p c = 0.75

67 An example: let p c = 0.75 let p I = 0.25

68 An example: let m = 0.10 let p c = 0.75 let p I = 0.25

69 An example: let m = 0.10 let p c = 0.75 let p I = 0.25 let s ignore back-migration

70 An example: let m = 0.10 let p c = 0.75 let p I = 0.25 Δp I = m(p c p I )

71 An example: let m = 0.10 let p c = 0.75 let p I = 0.25 Δp I = m(p c p I ) = 0.10( )

72 An example: let m = 0.10 let p c = 0.75 let p I = 0.25 Δp I = m(p c p I ) = 0.10( ) = 0.050

73 Now: let m = 0.10 p c = 0.75 p I = 0.30

74 Now: let m = 0.10 p c = 0.75 p I = 0.30 Δp I = m(p c p I ) = 0.10( ) = 0.045

75 Conclusions

76 Conclusions 1. Gene flow can cause rapid evolutionary change.

77 Conclusions 1. Gene flow can cause rapid evolutionary change. 2. The long-term outcome will be the elimination of genetic differences between populations!

78 Conclusions 1. Gene flow can cause rapid evolutionary change. 2. The long-term outcome will be the elimination of genetic differences between populations! But natural selection act to oppose gene flow

79 Example: Lake Erie water snakes (Nerodia sipedon)

80 Example: Lake Erie water snakes (Nerodia sipedon)

81 Example: Lake Erie water snakes (Nerodia sipedon)

82 Random drift

83 Assumptions of Hardy-Weinberg equilibrium 1. Mating is random 2. No selection 3. No mutation 4. No migration 5. Population size is infinite (i.e., no genetic drift)

84 The Neutral Theory of Evolution Motoo Kimura

85 Random genetic drift Definition: random changes in the frequencies of neutral alleles from generation to generation caused by accidents of sampling

86 Random genetic drift white = p = 0.50 red = q = 0.50

87 Random genetic drift white = p = 0.50 red = q = 0.50 Sample 40,000,000 balls

88 Random genetic drift white = p = 0.50 red = q = ,000,167 white 19,999,833 red

89 Random genetic drift white = p = 0.50 red = q = ,000,167 white 19,999,833 red now p = q =

90 Random genetic drift white = p = 0.50 red = q = 0.50 Sample 200 balls

91 Random genetic drift white = p = 0.50 red = q = white 106 red

92 Random genetic drift white = p = 0.50 red = q = white 106 red now p = q = 0.530

93 Some properties of random genetic drift

94 Some properties of random genetic drift 1. Magnitude inversely proportional to effective population size (N e ).

95 Some properties of random genetic drift 1. Magnitude inversely proportional to effective population size (N e ). 2. Ultimately results in loss of variation from natural populations.

96 Some properties of random genetic drift 1. Magnitude inversely proportional to effective population size (N e ). 2. Ultimately results in loss of variation from natural populations. 3. The probability of fixation of a neutral allele is equal to its frequency in the population.

97 Some properties of random genetic drift 1. Magnitude inversely proportional to effective population size (N e ). 2. Ultimately results in loss of variation from natural populations. 3. The probability of fixation of a neutral allele is equal to its frequency in the population. 4. Will cause isolated populations to diverge genetically.

98 Some properties of random genetic drift 1. Magnitude inversely proportional to effective population size (N e ). 2. Ultimately results in loss of variation from natural populations. 3. The probability of fixation of a neutral allele is equal to its frequency in the population. 4. Will cause isolated populations to diverge genetically. 5. Is accentuated during population bottlenecks and founder events.

99 What is effective population size?

100 What is effective population size? in any one generation, N e is roughly equivalent to the number of breeding individuals in the population.

101 What is effective population size? in any one generation, N e is roughly equivalent to the number of breeding individuals in the population. this is equivalent to a contemporary effective size.

102 What is effective population size? in any one generation, N e is roughly equivalent to the number of breeding individuals in the population. this is equivalent to a contemporary effective size. N e is also strongly influenced by long-term history.

103 What is effective population size? in any one generation, N e is roughly equivalent to the number of breeding individuals in the population. this is equivalent to a contemporary effective size. N e is also strongly influenced by long-term history. this is equivalent to a species evolutionary effective size.

104 Factors affecting effective population size

105 Factors affecting effective population size 1. Fluctuations in population size

106 Factors affecting effective population size 1. Fluctuations in population size - here, N e is equal to the harmonic mean of the actual population numbers:

107 Factors affecting effective population size 1. Fluctuations in population size - here, N e is equal to the harmonic mean of the actual population numbers: 1/N e = 1/t(1/N 1 + 1/N 2 + 1/N 3 + 1/N t )

108 Factors affecting effective population size 1. Fluctuations in population size - here, N e is equal to the harmonic mean of the actual population numbers: 1/N e = 1/t(1/N 1 + 1/N 2 + 1/N 3 + 1/N t ) Example: Over 3 generations, N = 2000, 30, 2000

109 Factors affecting effective population size 1. Fluctuations in population size - here, N e is equal to the harmonic mean of the actual population numbers: 1/N e = 1/t(1/N 1 + 1/N 2 + 1/N 3 + 1/N t ) Example: Over 3 generations, N = 2000, 30, 2000 Arithmetic mean =

110 Factors affecting effective population size 1. Fluctuations in population size - here, N e is equal to the harmonic mean of the actual population numbers: 1/N e = 1/t(1/N 1 + 1/N 2 + 1/N 3 + 1/N t ) Example: Over 3 generations, N = 2000, 30, 2000 Arithmetic mean = Harmonic mean = 87.4

111 Factors affecting effective population size 2. Unequal numbers of males and females

112 Factors affecting effective population size 2. Unequal numbers of males and females let N m = No. of males, N f = No. of females:

113 Factors affecting effective population size 2. Unequal numbers of males and females let N m = No. of males, N f = No. of females: N e = 4N m N f N m + N f

114 Factors affecting effective population size 2. Unequal numbers of males and females let N m = No. of males, N f = No. of females: N e = 4N m N f N m + N f Example: Breeding populations of northern elephant seals:

115 Factors affecting effective population size 2. Unequal numbers of males and females let N m = No. of males, N f = No. of females: N e = 4N m N f N m + N f Example: Breeding populations of northern elephant seals: 15 alpha males each controlling a harem of 20 females:

116 Factors affecting effective population size 2. Unequal numbers of males and females let N m = No. of males, N f = No. of females: N e = 4N m N f N m + N f Example: Breeding populations of northern elephant seals: 15 alpha males each controlling a harem of 20 females: census size (N) = 315

117 Factors affecting effective population size 2. Unequal numbers of males and females let N m = No. of males, N f = No. of females: N e = 4N m N f N m + N f Example: Breeding populations of northern elephant seals: 15 alpha males each controlling a harem of 20 females: census size (N) = 315 effective size (N e ) = 57.1

118 Factors affecting effective population size 3. Large variance in reproductive success reduces N e because a small number of individuals have a disproportional effect on the reproductive success of the population.

119 Genetic Bottlenecks genetic bottlenecks refer to severe reductions in effective population size. N e Time

120 Genetic Bottlenecks genetic bottlenecks refer to severe reductions in effective population size.

121 Genetic Bottlenecks genetic bottlenecks refer to severe reductions in effective population size. Examples: the northern elephant seal (Mirounga angustirostis) and the cheetah (Acinonyx jubatus).

122 Founder effects occur when a new population is founded from a small number of individuals.

123 Founder effects occur when a new population is founded from a small number of individuals. Consequences:

124 Founder effects occur when a new population is founded from a small number of individuals. Consequences: 1. New population has a fraction of genetic variation present in the ancestral population.

125 Founder effects occur when a new population is founded from a small number of individuals. Consequences: 1. New population has a fraction of genetic variation present in the ancestral population. 2. Initial allele frequencies differ because of chance.

126 Founder effects occur when a new population is founded from a small number of individuals. Consequences: 1. New population has a fraction of genetic variation present in the ancestral population. 2. Initial allele frequencies differ because of chance. Example: the silvereye, Zosterops lateralis

127 Founder effects in the silvereye, Zosterops lateralis

128 Timing of island hopping

129 and reductions in allelic diversity

130 The interplay between drift, migration, and selection 1. Gene flow vs. drift

131 The interplay between drift, migration, and selection 1. Gene flow vs. drift random drift and gene flow act in opposition to each other!

132 The interplay between drift, migration, and selection 1. Gene flow vs. drift random drift and gene flow act in opposition to each other! random drift allow genetic divergence of two populations.

133 The interplay between drift, migration, and selection 1. Gene flow vs. drift random drift and gene flow act in opposition to each other! random drift allow genetic divergence of two populations. gene flow prevent divergence.

134 The interplay between drift, migration, and selection 1. Gene flow vs. drift random drift and gene flow act in opposition to each other! random drift allow genetic divergence of two populations. gene flow prevent divergence. if N e m > 1, gene flow overrides drift and prevents divergence

135 The interplay between drift, migration, and selection 1. Gene flow vs. drift random drift and gene flow act in opposition to each other! random drift allow genetic divergence of two populations. gene flow prevent divergence. if N e m > 1, gene flow overrides drift and prevents divergence if N e m < 1, random drift can lead to genetic divergence.

136 The interplay between drift, migration, and selection 2. Gene flow and selection

137 The interplay between drift, migration, and selection 2. Gene flow and selection gene flow and selection usually act in opposition.

138 The interplay between drift, migration, and selection 2. Gene flow and selection gene flow and selection usually act in opposition. selection favor different alleles in different populations ( local adaptation ).

139 The interplay between drift, migration, and selection 2. Gene flow and selection gene flow and selection usually act in opposition. selection favor different alleles in different populations ( local adaptation ). gene flow prevent adaptive divergence.

140 The interplay between drift, migration, and selection 2. Gene flow and selection gene flow and selection usually act in opposition. selection favor different alleles in different populations ( local adaptation ). gene flow prevent adaptive divergence. if m > s, gene flow can overpower local adaptation

141 The interplay between drift, migration, and selection 2. Gene flow and selection gene flow and selection usually act in opposition. selection favor different alleles in different populations ( local adaptation ). gene flow prevent adaptive divergence. if m > s, gene flow can overpower local adaptation if s > m, then selection can allow local adaptation

142 The interplay between drift, migration, and selection 3. Drift and selection

143 The interplay between drift, migration, and selection 3. Drift and selection - random genetic drift and natural selection act in opposition.

144 The interplay between drift, migration, and selection 3. Drift and selection - random genetic drift and natural selection act in opposition. selection deterministic change in allele frequency

145 The interplay between drift, migration, and selection 3. Drift and selection - random genetic drift and natural selection act in opposition. selection deterministic change in allele frequency random drift random changes in allele frequency

146 The interplay between drift, migration, and selection 3. Drift and selection - random genetic drift and natural selection act in opposition. selection deterministic change in allele frequency random drift random changes in allele frequency if N e s > 10, selection controls the fate of the allele

147 The interplay between drift, migration, and selection 3. Drift and selection - random genetic drift and natural selection act in opposition. selection deterministic change in allele frequency random drift random changes in allele frequency if N e s > 10, selection controls the fate of the allele if N e s < 1, drift will overpower the effect of selection

148 A hypothetical adaptive landscape How does a population move among peaks??

149 Assumptions of Hardy-Weinberg equilibrium 1. Mating is random 2. No selection 3. No mutation 4. No migration 5. Population size is infinite (i.e., no genetic drift)