Selection at Multiple Loci
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© 1997
David H.A. Fitch
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Deviations from the null hypotheses:  Selection at multiple loci

I.  Selection at two loci (that are epistatic for fitness) and its effect on linkage disequilibrium

A.  Correcting the model of linkage disequilibrium to account for selection (i.e., for differences in the fitnesses of different haplotypes)

1.  If specific interactions between alleles at different loci result in different fitnesses, there is "epistasis for fitness", and selection will affect haplotype frequencies

2.  The average fitness of haplotype AB is:

     wAB = Sum of all (fijWij),

where i and j are haplotypes that make genotype ij and fij and Wij are the frequency and fitness of all genotypes containing haplotype AB.

3.  After one generation, the rate of increase of the AB haplotype depends on:

  1. The current frequency of the AB gamete, fAB
  2. The average selective advantage of the AB gamete, wAB (which depends on the degree of epistasis for fitness)
  3. The mean fitness of all of the genotypes in the population, w
  4. And the degree to which the recombination rate (r) reduces the frequency of AB in proportion to its excess (D), which occurs in heterozygous genotypes (which have fitness WH)

i.e., the change in frequency of the AB haplotype is equal to:

     [fAB(wAB-w) - rDWH] / w

After a bit of algebra, the absolute value of the disequilibrium coefficient can be found:

     |D|  =  | (fABwAB-wfAB') / rWH |

4.  That is,
a.  The greater is fitness due to the epistatic interaction between alleles A and B, wAB, and/or the smaller is r between the loci, the greater will be the linkage disequilibrium, |D|.
b.  Alternatively, |D| decreases with greater r and less epistasis for fitness.

B. Other effects on linkage disequilibrium

1.  Note that genetic drift can also cause linkage disequilibrium (one allele combination may drift to excess or fixation, and founder populations are likely to have high |D|

2.  Hitchhiking:  A locus that could be neutral or slightly deleterious and a closely linked locus under strong selection will often show linkage disequilibrium

C.  Examples of selection and disequilibrium in natural populations:  Closely linked genes that contribute to the same character or function often show strong linkage disequilibrium (and coadaptation between particular alleles at these different loci may result)
1.  For example, Batesian mimicry
2.  And heterostyly

II.  Selection on quantitative traits:  heritability and response to selection

A.  Heritability is the fraction of the phenotypic variance that is due to the additive component of genetic variation

1.  Total phenotypic variance (VP) results from variance among the phenotypic means of each genotype (VG), the phenotypic variance due to environmental differences (VE), and the phenotypic variance due to the interaction between particular genotypes and environments (VGE); VGE is generally ignored

2.  VG is due to variances due to additive, dominance and epistatic (interactive) effects:

     VG = VA + VD + VI

3.  Heritability (in the "narrow sense") is defined as the fraction of the phenotypic variance that is due to additive genetic effects:

     hN2 = VA / VG

B.  Response to selection depends on heritability of the phenotype

1.  Because the phenotypic resemblance between parents and offspring is due almost entirely to the additive effects of genes, VA is the main component of VP that causes the response of a population to selection

2.  Thus, heritability can be estimated by plotting the mean phenotype of parents against that of their progeny:

     R = hN2S

3.  For example, a heritability of one will result in progeny that look exactly like their parents, and a rapid response of the change in mean phenotypic to selection (i.e., rate of phenotypic evolution)

4.  This is the basis of Darwin's mechanism for directional evolutionary change, or anagenesis

III.  Evolution and selection

A.  Directional selection:  The phenotypic mean increases or decreases over time

1.  For example, when drought reduced the food supply, Geospiza fortis populations evolved larger body size (h = 0.76) in only a few generations (Why?)

2.  As another example, experimental selection for increased bristle number (average combined h = 0.2) in Drosophila melanogaster produced an enormously significant change in bristle number.
a.  At points, the response to selection plateaued (Provide a hypothesis to explain this)
b.  After relaxation of selection at these plateaus for a few generations, the response to selection could be positive again (Why!?)

B.  Stabilizing selection:  The phenotypic mean is static over time (actually the lack of phenotypic evolution)

1.  One mechanism is provided by countervailing selective forces

2.  For example, one genotype may provide better fitness in the absence of a predator (e.g., for sexual selection), but an opposite genotype involving the same loci may provide better fitness in the presence of a predator

C.  Diversifying selection:  Divergence of populations expressing different phenotypes

1.  May be common where there is frequency-dependent selection
a.  For example, different phenotypes in a resource-limited population are specialized for different resources, such as differently sized beaks and differently sized seeds
b.  For example, Batesian mimicry in Papilio dardanus

2.  Actually Darwin's proposed mechanism for evolutionary divergence (cladogenesis)

IV.  Maintenance of polymorphism in the face of selection

Under both directional and stabilizing selection, genetic variance is generally predicted to decrease.  So why is this variance often large?  Some possible explanations may be:

A.  Mutation might balance the decrease in variance due to selection; however, because mutation is a weak evolutionary force, this will only occur if:
1.  Selection for a particular trait is weak
2.  Recurrent mutation rates are rapid
3.  Many loci contribute to the trait (i.e., the number of targets for mutation is large)

B.  Dominance interactions between alleles may hide recessive (possibly low-fitness) traits (and thus preserve polymorphism) for a long time

C.  Genetic correlations may exist between different traits that affect fitness to different extents (e.g., resulting in a "tradeoff"); adumbrated by Darwin's principle of the "Correlation of Growth"
Two kinds of genetic correlations are possible:
1.  Linkage disequilibrium (different traits are governed by different loci); maintained if:
a.  Loci are tightly linked, and/or
b.  Selection strongly favors the correlation
2.  Pleiotropy (different traits are governed by one locus)

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 Nonrandom
Mating  Genetic
Drift  Selection:
One Locus  Selection:
Many Loci
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[Nonrandom Mating] [Genetic Drift] [Selection: One Locus] [Selection: Many Loci]

[Deviations from the Null Hypotheses]

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