Chapter 8: Evolution at multiple loci

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Chapter 8 Evolution at multiple loci

• Evolution at two loci Linkage equilibrium and
  linkage disequilibrium.
• Locus is location on a chromosome where a gene
  occurs.
• Single locus Hardy-Weinberg models are simple.
  However, many traits are controlled by combined
  influence of many genes.

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• Pair of loci located on same chromosome.
• (Recall locus is location on chromosome of a
  gene).
• Gene at locus A has two alleles A and a
• Gene at locus B has two alleles B and b

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• In two-locus Hardy-Weinberg analysis we track
  allele and chromosome frequencies.
• Thus 4 possible chromosome genotypes
• AB, Ab, aB, ab
• Multilocus genotype referred to as a haplotype
  (from haploid genotype).

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• Does selection on locus A affect our ability to
  make predictions about evolution at locus B?
• Sometimes. Depends on whether loci are in
  linkage equilibrium or linkage disequilibrium.

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• Two loci in a population are in linkage
  equilibrium when genotype of a chromosome at one
  locus is independent of the genotype at the other
  locus on the same chromosome.
• I.e. knowing genotype at one locus is of no use
  in predicting genotype at the other locus.

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Example

• Two hypothetical populations each containing 25
  chromosomes.
• Allele frequencies are identical in both
  populations.
• A 0.6, a 0.4 B 0.8, b 0.2

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• If studying only locus A or locus B we would
  conclude populations were identical.
• However, populations not identical when we look
  at haplotypes.

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• Population 1 Population 2
• AB 0.48 AB 0.44
• Ab 0.12 Ab 0.16
• aB 0.32 aB 0.36
• ab 0.08 ab 0.04

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• Population 1 is in linkage equilibrium.
• Frequency of B on chromosomes carrying A is 12/15
  or 0.8, frequency of B on chromosomes carrying a
  is 8/10 or 0.8.
• Frequency of B is same on chromosomes carrying A
  as on chromosomes carrying a.

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• Population 2 is in linkage disequilibrium.
• Frequency of B on chromosomes carrying A is 11/15
  or 0.73, frequency of B on chromosomes carrying a
  is 9/10 or 0.9.

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Conditions for linkage equilibrium

• 1. Frequency of B on chromosomes carrying allele
  A is equal to frequency of B on chromosomes
  carrying allele a.
• 2. Frequency of a chromosome haplotype can be
  calculated by multiplying frequencies of
  constituent alleles, i.e. frequency of AB is
  freq. A X freq. B.

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Conditions for linkage equilibrium

• 3. Coefficient of linkage disequilibrium (D) is
  equal to zero. See Box 8.1 and satisfy yourself
  that the equation below makes sense.
• D gABgab - gAbgaB
• (gAB frequency of chromosome AB, etc.)

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Coefficient of linkage disequilibrium

• D can range from - 0.25 to 0.25.
• 0.25 when AB and ab only genotypes and both at
  frequency of 0.5
• Similarly -0.25 when Ab and aB only genotypes and
  both at frequency of 0.5
• If D 0, then population in linkage equilibrium
  and value of D is a measure of the degree of
  linkage disequilibrium.

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What creates linkage disequilibrium in
populations?

• Three mechanisms
• Selection on multilocus genotypes.
• Genetic drift
• Population mixing

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Selection on multilocus genotypes.

• Scenario Locus A and locus B in linkage
  equilibrium. Gametes combine at random to from
  zygotes.

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Selection on multilocus genotypes.

• Assume genotype ab/ab is of size 10 units.
• For all other genotypes every copy of A or B adds
  one unit of size (e.g. Ab/aB is size 12).
• Assume predators eat all genotypes of lt 13 units
  size.

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Selection on multilocus genotypes.

• Survivors (65.3 of population) in linkage
  disequilibrium by all 3 criteria because some
  genotypes missing.
• E.g. criterion 3 D gABgab - gAbgaB
• D 0.44160 - (0.05760.1536) - 0.0088

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Genetic drift

• Scenario Small population with two genotypes AB
  and Ab. No copies of allele a.
• Single Ab chromosome mutation converts an A to an
  a. This single ab chromosome puts population in
  linkage disequilibrium.
• Scenario is drift because only in a small
  population would you expect to have only a single
  mutation of A to a. In large population you would
  expect many mutations of A to a and a to A.

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Before mutation
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Genetic drift followed by selection

• If selection favors a and its frequency
  increases, degree of linkage disequilibrium
  increases too.

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After mutation
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After mutation and selection
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Population mixing

• If two populations, which are in linkage
  equilibrium, are merged the resulting population
  may not be in linkage equilibrium.

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What eliminates linkage disequilibrium from
population?

• Sexual reproduction steadily reduces linkage
  disequilibrium.
• Crossing over during meiosis breaks up old
  combinations of alleles and creates new
  combinations.

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Genetic recombination

• Genetic recombination tends to randomize
  genotypes in relation to other genotypes (i.e.,
  it reduces linkage disequilibrium.)
• Rate of decline in linkage disequilibrium is
  proportional to rate of recombination.

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r is recombination rate, r is related to how far
apart two loci are on a chromosome.
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Empirical example of genetic recombination

• Clegg et al. (1980) established two fruit fly
  populations that were in linkage disequilibrium.
  
• Population 1 AB and ab each 0.5 frequency.
• Population 2 aB and Ab each 0.5 frequency.

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Empirical example of genetic recombination

• Populations of about 1,000 individuals maintained
  for 48-50 generations.
• Flies allowed to mate freely.
• Populations sampled every 1-2 generations to
  count frequencies of 4 haplotypes.

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Empirical example of genetic recombination

• Crossing-over created missing haplotypes in each
  population and linkage disequilibrium
  disappeared.
• In general, in random-mating populations sex is
  efficient enough at eliminating linkage
  disequilibrium that most alleles are in linkage
  equilibrium most of the time.

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Practical reasons to measure linkage
disequilibrium

• There are two major uses of measures of linkage
  disequilibrium.
• Can be used to reconstruct history of genes and
  populations
• Can be used to identify alleles recently favored
  by positive selection

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Reconstructing history of the CCR5-?32 locus

• Where did the CCR5-?32 allele come from and when
  did it originate?
• CCR5-?32 is the allele that provides a selective
  advantage against HIV.

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Reconstructing history of the CCR5-?32 locus

• CCR5-?32 is located on chromosome 3 and near two
  short-tandem repeat sites called GAAT and AFMB.
• GAAT and AFMB are non-coding and have no effect
  on fitness. Both GAAT and AFMB have a number of
  different alleles.

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Reconstructing history of the CCR5-?32 locus

• Stephens et al. (1998) examined haplotypes of 192
  Europeans.
• Found that GAAT and AFMB alleles in close to
  linkage equilibrium with each other.

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Reconstructing history of the CCR5-?32 locus

• However, CCR5 is in strong linkage disequilibrium
  with both GAAT and AFMB.
• Almost all chromosomes carrying CCR5-?32 also
  carry allele 197 at GAAT and allele 215 at AFMB.

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Reconstructing history of the CCR5-?32 locus

• Most likely reason for observed linkage
  disequilibrium is genetic drift.
• Hypothesis in past was originally only one CCR5
  allele the CCR5 allele, a mutation on a
  chromosome with the haplotype CCR5--GAAT-197--AFMB
  -215 created the CCR5?32 allele.

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Reconstructing history of the CCR5-?32 locus

• The CCR5?32 allele was favored by selection and
  rose to high frequency dragging the other two
  alleles with it.
• Since its appearance and spread, crossing over
  and mutation have been breaking down the linkage
  disequilibrium. Now about 15 of ?32-197-215
  haplotypes have changed to other haplotypes.

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Reconstructing history of the CCR5-?32 locus

• Based on rates of crossing over and mutation
  rates, Stephens et al. (1998) estimate the
  CCR5-?32 allele first appeared about 700 years
  ago (range of estimates 275-1875 years)

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Reconstructing history of the CCR5-?32 locus

• Because the CCR5-?32 increased in frequency so
  rapidly selection must have been strong.
• Most obvious candidate is an epidemic disease.
• Myxoma virus a relative of smallpox uses CCR5
  protein on cell surface to enter host cell, which
  suggests the epidemic disease that favored
  CCR5-?32 may have been smallpox.
• However, timing of origin also closely matches
  period of bubonic plague.

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Using linkage disequilibrium to detect strong
positive selection.

• A new mutant allele will be in linkage
  disequilibrium when it first appears. If it
  persists, it may increase in frequency.
• Over time linkage disequilibrium will break down
  as a result of recombination from crossing over.
• Linkage disequilibrium breaks down fastest for
  loci further apart on a chromosome because
  crossing over take place more often between
  distant loci.

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Using linkage disequilibrium to detect strong
positive selection.

• High linkage disequilibrium indicates an allele
  originated recently.
• Also, expect a recently mutated allele to be rare
  unless selection strongly favors it.

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Using linkage disequilibrium to detect strong
positive selection.

• If an allele is common, but has high linkage
  disequilibrium, especially with loci that are
  located far away on the chromosome, this suggests
  that the allele has been strongly selected for
  and must have originated recently.
• If the allele had arisen a long time ago, sex
  should have eliminated the linkage
  disequilibrium.

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Using linkage disequilibrium to detect positive
selection.

• An allele of G6PD (Glucose-6-phosphate
  dehydrogenase), G6PD-202A has a high frequency
  (18 in African populations) and has a high
  degree of linkage disequilibrium.
• Thus, it appears to have been strongly selected
  for recently.

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G6PD and malaria

• There are many common G6PD deficiencies and their
  distribution corresponds closely with the
  distribution of malaria.
• Appears that G6PD-202A confers strong protection
  against malaria.

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Adaptive significance of sex

• Many risks and costs associated with sexual
  reproduction.
• Searching for a mate requires time and energy and
  exposes organisms to predators.
• Mate may require investment (food, territory,
  defense).
• Risk of sexually transmitted disease.

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Adaptive significance of sex

• Why not reproduce asexually?
• Many organisms can reproduce both sexually and
  asexually.
• E.g. plants, aphids.

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Adaptive significance of sex

• In populations that can reproduce both asexually
  and sexually will one mode of reproduction
  replace the other?

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Adaptive significance of sex

• John Maynard Smith explored the question.
• Considered population in which some organisms
  reproduce asexually and the others sexually.
• Made 2 assumptions.

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Maynard Smiths assumptions

• 1. Mode of reproduction does not affect number
  of offspring she can produce.
• 2. Mode of reproduction does not affect
  probability offspring will survive.
• (asexually reproducing organisms produce only
  females, sexually reproducing produce both males
  and females.)

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Adaptive significance of sex

• Asexually reproducing females under Maynard
  Smiths assumptions leave twice as many
  grandchildren as sexually reproducing females.
• This is because each generation of sexually
  reproducing organisms contains only 50 females.

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Adaptive significance of sex

• Ultimately, asexual reproduction should take
  over.
• However, in nature this is not the case.
• Most organisms reproduce sexually and both sexual
  and asexual modes of reproduction are used in
  many organisms

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Adaptive significance of sex

• Sex must confer benefits that overcome the
  mathematical reproductive advantage of asexual
  reproduction.
• One or both of Maynard Smiths assumptions must
  be incorrect.

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Adaptive significance of sex

• Assumption 1 (mode of reproduction does not
  affect number of offspring she can produce) is
  violated in species where males helps females
  (humans, birds, many mammals, some fish).
• However, not likely a general explanation because
  in most species male does not help.

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Adaptive significance of sex

• Most likely advantage of sex is that it increases
  offsprings prospects of survival.

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Dunbrack et al. (1995) experiment

• Lab populations of flour beetles
• Mixed populations of red and black strains.
• Strains designated as sexual or asexual in
  experimental replicates.

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Dunbrack et al. (1995) experiment

• Asexual strain in culture. Every generation each
  adult replaced by 3 new individuals from
  reservoir population of sexual strain. This
  simulates a 3X reproductive advantage, but there
  is no evolution in response to the environment.
• Sexual strain allowed to breed and remain in
  culture. Could evolve.

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Dunbrack et al. (1995) experiment

• Two strains prevented from breeding with each
  other.
• Populations tracked for 30 generations.
• 8 replicates in experiment. Four different
  concentrations of malathion (insecticide).
• Controls No evolution, but one strain had 3x
  reproductive advantage.

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Dunbrack et al. (1995) experiment

• Control results.
• Asexually reproducing strain outcompeted the
  sexually reproducing strain.

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Dunbrack et al. (1995) experiment

• Experimental cultures Initially asexual strain
  increased in frequency, but eventually sexual
  strain took over.
• Rate at which sexual strain took over was
  proportional to malathion concentration.

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Dunbrack et al. (1995) experiment

• Conclusion Assumption 2 of Maynard Smiths null
  model is incorrect.
• Descendants produced by sexual reproduction
  achieve higher fitness than those produced
  asexually.

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Sex in populations means genetic recombination

• Sex involves
• Meiosis with crossing over
• Matings with random individuals
• Random meeting of sperm and eggs
• Consequence is genetic recombination. New
  combinations of genes brought together each
  generation.

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Why is sex beneficial?

• 1. Genetic drift plus mutation make sex
  beneficial. Escapes Mullers ratchet.
• 2. Selection imposed by changing environments
  makes sex beneficial

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Genetic drift plus mutation Mullers ratchet

• An asexually reproducing female will pass a
  deleterious mutation to all her offspring.
• Back mutation only way to eliminate it.
• Mullers ratchet accumulation of deleterious
  alleles in asexually reproducing populations.

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Mullers ratchet

• Small, asexually reproducing population.
• Deleterious mutations occur occasionally.
• Mutations selected against.
• Population contains groups of individuals with
  zero, one, two, etc. mutations.

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Mullers ratchet

• Few individuals in each group. If by chance no
  individual with zero mutations reproduces in a
  generation, then the zero mutation group is lost.
• Rate of loss of groups by drift will be higher
  than rate of back mutation so population will
  over time accumulate deleterious mutations in a
  ratchet fashion.

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Mullers ratchet

• Burden of increased number of deleterious
  mutations (genetic load) may eventually cause
  population to go extinct.
• Sexual reproduction breaks ratchet. E.g. two
  individuals each with one copy of a deleterious
  mutation will produce 25 of offspring that are
  mutation free.

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Anderson and Hughes (1996) test of Mullers
ratchet in bacteria.

• Propagated multiple generations of bacterium, but
  each generation derived from one individual
  (genetic drift).
• 444 cultures. At end of experiment (2 months) 1
  of cultures had reduced fitness (lower than
  wild-type bacteria), none had increased fitness.
  Results consistent with Mullers ratchet.

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Selection favors sex in changing environments.

• Effects of Mullers ratchet are slow and take
  many generations to affect asexually reproducing
  populations.
• However, advantage of sex is apparent in only a
  few generations. What short-term benefit does sex
  provide?

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Selection favors sex in changing environments.

• In constant environments asexual reproduction is
  a good strategy (if mother is adapted to
  environment, offspring will be too).
• However, if environment changes, offspring may be
  poorly adapted and all will be poorly adapted
  because they are identical.

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Selection favors sex in changing environments.

• Sexually reproducing females produce variable
  offspring so if the environment changes some may
  be well adapted to the new environment.

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Selection favors sex in changing environments.

• Red Queen Hypothesis evolutionary arms race
  between hosts and parasites.
• (Red Queen runs to stand still)
• Parasites and hosts are in a perpetual struggle.
  Host evolving defenses, parasite evolving ways to
  evade them.
• Different multilocus host genotypes are favored
  each generation. Sex creates the genotypes.

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Do parasites favor sex in hosts?

• Lively (1992) studied New Zealand freshwater
  snail. Host to parasitic trematodes.
• Trematodes eat hosts gonads and castrate it!
  Strong selection pressure.
• Snail populations contain both obligate sexually
  and asexually reproducing females.

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Do parasites favor sex in hosts?

• Proportion of sexual vs asexual females varies
  from population to population.
• Frequency of trematode infections varies also.

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Do parasites favor sex in hosts?

• If evolutionary arms race favors sex, then
  sexually reproducing snails should be commoner in
  populations with high rates of trematode
  infections.
• Results match prediction.

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White slice indicates frequency of males and
thus sexual reproduction
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