MENDELIAN GENETICS in POPULATIONS I:
SELECTION and MUTATION as MECHANISMS of EVOLUTION

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Chapter 6 in the 4th edition, Chapter 5 in the 3rd.

review questions

• An introduction to Hardy-Weinberg from Kimball's Biology Place
• Population genetics follows allele and genotypic frequencies across generations.
• population: a group of interbreeding organisms and their offspring [Fig. 5.1] 
• gene pool: the collection of alleles present within a population 
• allele frequency: the proportion of an individual allele within the gene pool 
• genotype frequency: the proportion of a genotype within the population 
• Hardy-Weinberg equilibrium: null model for gene frequencies in the absence of evolution.

5.1    THE HARDY-WEINBERG EQUILIBRIUM PRINCIPLE

• Does the gene pool predict the distribution of genotypes within a population?

A Numerical Example

• hypothetical population through one cycle from gametes in generation 1 to gametes in generation 2 (fig. 5.1)
• F₁ gene pool with fr(A) = 0.6 and fr(a) = 0.4 (fig. 5.2) yields zygotes with A•A = 0.36, A•a = 0.48, and a•a = 0.16 [Fig. 5.2, 5.3 Box 5.1]
• F₂ gene pool has gametes with fr(A) = 0.6 and fr(a) = 0.4 (Figs. 5.4, 5.5)

The General Case

1. fr(A₁) = p
2. fr(A₂) = q
3. p + q = 1
4. the frequency of genotypes is [Figs. 5.6, 5.7]:
   1. homozygote A1: fr(A₁A₁) = p²
   2. heterozygote A1A2: fr(A₁A₂) = pq + pq = 2pq
   3. homozygote A2: fr(A₂A₂) = q²
5. p = p² + ½ (2pq) = p² + pq
6. q = (q² + ½ (2pq) = q² + pq
7. p + q = 1 = (p + q)² = 1 = p² + 2pq + q² (the Hardy-Weinberg Principle)
8. Same trick works with multiple loci: e.g., 3 alleles [box 5.2]
   1. p + q + r = 1 
   2. p² + q² + r² + 2pq + 2pr + 2qr = 1

 Key points:

1. Conclusion 1: At equilibrium, allele frequencies do not change from generation to generation
2. Conclusion 2: allele frequencies predict genotype frequencies (p² + 2pq + q²)
3. if population displaced from equilibrium, return to equilibrium in one generation
4. Assumptions for Hardy-Weinberg:
   1. No selection on any genotype
   2. No mutation
   3. No migration
   4. No random events affecting population
   5. Mating within population at random (panmixis)
   6. In other words, no evolution.

Changes in the Frequency of the CCR5-Δ32 Allele

• Will the AIDS epidemic cause that allele to become more frequent in human populations?

5.2    SELECTION

Adding selection to the H-W analysis: Changes in allele frequencies

• Fitness of a genotype depends on relationship between genotype and phenotype
• Selection can cause allele frequencies to change across generations when individuals with some genotypes survive at higher rates than individuals with other genotypes [Fig. 5.9]
•  Alleles that confer reproductive success are selected for and can become fixed in populations [Fig. 5.10].

Empirical Research on Allele Frequency Change by Selection

• Frequency change in the Alcohol Dehydrogenase (ADH) gene alleles in laboratory populations of Drosophila exposed to ethyl alcohol
• ADH^S decreases, ADH^F increases, no change in controls [Fig. 5.11]

Adding Selection to Hardy-Weinberg Analysis: Calculation of Genotype Frequencies

• selection violates conclusions 1 and/or 2.
• heterozygote superiority [Fig. 5.12]
  • no change in allele frequencies (conclusion 1 holds)
  • but a change in genotype frequencies (conclusion 2 is violated) 
• figure 5.9: change in both allele and genotype frequencies

Changes in the Frequency of the CCR5-Δ32 allele revisited:

• will the AIDS epidemic cause an increase in frequency of this allele?
• three scenarios to model the effect of AIDS on allele frequency (fig. 5.13):
  1. Scenario 1: high frequency of CCR5-Δ32 plus strong selection favoring the allele
     • allele is fixed at the end of 40 generations 
     • this combination of conditions doesn’t occur anywhere at present
  2. Scenario 2: high frequency of beneficial allele plus low infection and mortality rates
     • this is the situation in European populations
     • result = virtually no change in allele frequency in 40 generations
     • selection is too weak to cause appreciable change in such a short period of time
  3. Scenario 3: low frequency of CCR5-Δ32 + high infection and mortality rates (= strong selection)
     • this is the situation in many sub-Saharan African countries
     • result = virtually no change in allele frequency in 40 generations
     • reason = most copies of the allele are present in heterozygotes
• in terms of AIDS epidemic, we can’t expect the frequency of this allele to increase appreciably in the near term
• in general, selection will have major effects
  1. over long periods of time even when frequency of favored allele is low and selection is weak
  2. over short periods of time only when frequency of favored allele is high and selection is relatively strong

5.3    PATTERNS OF SELECTION

Selection on Dominant and Recessive Alleles

• selection in Tribolium (flour) beetles [Fig. 5.14]
  • when a recessive allele is common (and a dominant is rare), evolution by natural selection is rapid
  • when the recessive allele is rare, most copies will be hidden in heterozygotes and natural selection will be unable to change frequencies and fix alleles even if selection is very strong
• An algebraic treatment of selection on recessive and dominant alleles [Box 5.7]
  • if selection favors a recessive allele it will increase slowly at first.  As the recessives increases the rate of evolution will accelerate until the recessive is fixed [Fig. 5.15]
  • selection against lethal dominants can eliminate them in one generation

Selection on Heterozygotes and Homozygotes

• the heterozygote can have a fitness between both homozygotes [Box 5.8]
• heterozygote superiority = heterosis = overdominance
  1. Drosophila: equilibrium frequency for viable and lethal alleles [Fig. 5.16].
  2. sickle cell anemia and malaria.
• heterozygote inferiority or underdominance
  1. compound chromosomes in fruit flies [Fig. 5.17] 
     1. are either fixed if the frequency of C(2) > 0.8 
     2. eliminated if C(2) < 0.8
     3. in equilibrium only if C(2) = 0.8. 
     4. Heterozygotes are inviable

1. selection can promote increased heterozygosity [Fig. 5.9]
2. selection can promote reduced variability [Figs.5.9, 5.10, 5.11]
3.   many other patterns such as

Frequency-Dependent Selection

• selection can maintain two different alleles in a population if each allele is advantageous when it is rare
• frequency of left-handed scale-eating fish [Fig. 5.19] over time [Fig. 5.20].
  1. as left handed increase, prey become wary of being bit on the left
  2. left decrease and right increase leading to an increase of left.
  3. fluctuation around equilibrium value

Compulsory Sterilization

• read about it and draw your own conclusions

5.4    MUTATION

Adding Mutation to the Hardy-Weinberg Analysis

• mutation by itself is not a potent evolutionary forces

Example:

1. μ = 0.0001 per generation will change A=0.9, a=0.1 to 
2. a =.10009 and 
3. aa from .01 to .01002 in one generation [Fig. 5.22]
4. over many generations there can be a small, but appreciable effect [Fig. 5.23, Box 5.9]
   • p_n =  p_oe^-μn
   • bacteria have mutation rates of 2 X 10^-6
   • after 5,000 generations: p₅₀₀₀ = (1)e^-0.01 = .99 for A₁ (a decrease of .01)

Mutation and Selection

• mutation provides variation that can be strongly acted on by selection
• changes over time in cell size on E. coli grown on a limiting medium [Fig. 5.24] 

Mutation-Selection Balance

• as selection removes deleterious alleles, mutation resupplies them.
• A balance between the two may explain the persistence of deleterious alleles in populations
• μ = rate at which A₁ →  A₂
• w_xy = relative fitness of A_xA_y  = 1 - s
• s is the selection coefficient: 0<s<1; as s → 1, relative fitness of w_xy → 0 
• equilibrium frequency of q = (μ/s)^1/2 [see Box 5.10 for derivation]
• if A₂ is a lethal dominant, then = μ/s = μ [see Box 5.10 for derivation]
• spinal muscular atrophy
  • a loss of function allele with q = .01 in Caucasian populations
  • s is estimated to be 0.9
  • μ = s* ² = 0.9 x 10^-4 per allele per generation
  • this agrees with the observation that 7 of 340 affected individuals carried a new mutation not present in either parent.
  • This is a mutation rate of 1.1 x 10^-4 per allele per generation [Box 5.11]

Example: Cystic Fibrosis

• CF is caused by recessive loss-of-function mutations in the CFTR (cystic fibrosis transmembrane conductance regulator) gene
• gene plays a role in allowing cells of lung lining to ingest and destroy Pseudomonas aeruginosa bacteria
• inability to destroy bacteria means individuals homozygous for mutant CFTRs have chronic P. aeruginosa lung infections [Fig. 5.25]
• ultimately leads to severe lung damage and early death
• homozygous recessive (cc) lethal
• 1/2000 (0.0005) people in northern Europe have CF
  •  if in H-W equilibrium, then q² = 0.0005 and q = 0.0224 
  • if c is maintained by mutation selection balance, and cc has 0 fitness, s = 1, then
  • q = 0.0224 = (μ/1)^½
  • μ = 0.0005 = 5 x 10^-4, an unusually high mutation rate, suggesting incorrect assumptions
• actual mutation rate is 6.7 x 10^-7
• perhaps c is maintained by heterozygote superiority
• cells heterozygous for CF have a substantial resistance to the bacteria that cause typhoid [Fig. 5.26]

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