Evolution Involving More Than One Locus

Lecture 04

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Linkage Disequilibrium (s²)

Models of evolution at two or more loci depend on haplotype frequencies

• Probability of genes co-occurring if there is no linkage or selection, etc. is the product of the gene frequency for each allele

• When deviations occur, they add up to 0 (as the total must still equal 1)

• D is the Linkage Disequilibrium between these loci (notice they are in equilibrium when D = 0)

Disequilibrium

• Physical linkage on a chromosome is only one reason for disequilibrium
  • Disequilibrium is undone by recombination and will decline each generation

D_t+1  =  (1 - r)*D_t

• Where D is disequilibrium proportion and r is the frequency of recombination
• The probability of recombination for linked genes depends on the distance between genes and increases as the distance increases
• Disequilibrium can be maintained  by:
  • Non-Random Mating - phenotypes preferring to mate with same phenotype will associate genes and cause permanent D
  • Selection - if particular haplotypes are fittest, selection will promote their association
    • if fitness of a haplotype is the product of the individual fitnesses of the alleles in the haplotype, the process of decline of the disequilibrium produced is described by the equation above and, given time, the fittest genes will not be any more associated than their frequencies would predict
    • if the fitness is produced by epistasis, then fitness is determined by the presence of both alleles and may decline rapidly when an allele is not found associated with the "right" partner.  In this case, fitness can lead to permanent disequilibrium (equilibrium is reached with D > 0)
  • Drift - random chance can cause associations, which will then be subject to the process of decline described by the equation above.
• It should also be noted that mitotic asexuality will also preserve linkage disequilibrium, as no recombination occurs

Hitch-hiking may affect an allele's frequency

For closely linked loci, fitness of alleles at one allele may affect the frequency of alleles at the linked locus

• Start with a population that is homozygous for allele A at locus 1 and heterozygous for alleles B and B at locus 2
  • Alleles B and B are equally fit and only drift changes their frequency each generation
• A new, most fit allele (say, A₂) arises by mutation at locus 1 and the individual with the mutation happens to have allele B₂ at locus 2
  • A₂ is strongly selected for and increases in frequency rapidly
  • Allele B₂ is the hitch-hiker that will also increase in frequency, not because selection favors it but because selection favors a neighboring locus

Although recombination will break the association between A₂ and B₂ by producing A₂B₁ haplotypes, the process is slow for closely linked loci and will only offset the action of strong selection over the long term

Selective Sweeps are hitch-hiking gone wild

• When an allele arises by mutation that is most fit, it can proceed to fixation rapidly (this is seen to happen in microbial populations with some regularity)
  • The regions near the new allele all hitch-hike to fixation where recombination is so slow that no new haplotypes arise during the sweep
  • for loci farther away from the new allele, recombination will preserve alleles as it produces new haplotypes before fixation
• So selective sweeps can lower genetic variation at more than just one locus

Wright's Adaptive Landscapes can describe complex fitness epistasis for multiple loci

• Easiest to see as a graphical system, with one axis always fitness and the other axis the frequency of alleles at a locus (more loci, more axes)
  • the fitness curve will have peaks and valleys
• selection will always proceed up a fitness peak
  • if local peak is not most fit peak, the population reaches a local equilibrium with a lower average fitness than the potential maximum fitness
• This is where Wright brings in population size
  • in small populations (or populations subdivided into small sub-populations), drift may move a population from one valley side to the other, and so the population will begin to climb toward a  new peak
  • This is the Shifting Balance Theory

Quantitative Genetics

• I will present a powerpoint with some material on this subject

Last updated February 8, 2008