Zoology 510, Class Notes for Ridley, Chapter 8
Two-Locus and Multi-Locus Population Genetics

 

Brief Outline

• Introductory comments
• Overview
• Checklist of important concepts and terms
• Section-by-section comments
  • 8.1. Mimicry in Papilio memnon, two-locus selection.
  • 8.2. Coadaptation of loci.
  • 8.3. Mimicry in Heliconius, multiple loci. .
  • 8.4. Haplotype frequencies.
  • 8.5. Linkage equilibrium.
  • 8.6. HLA genes, multi-locus system.
  • 8.7. Causes for linkage disequilibrium.
  • 8.8. Two-locus models.
  • 8.9. Hitchhiking.
  • 8.10. Fitness consequences of linkage disequilibrium.
  • 8.11. Merits of linkage.
  • 8.12. Adaptive topography.
  • 8.13. Shifting balance theory.

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Introductory comments.

• In chapter 5, we considered the effects of selection acting on a single locus.
• Some additional effects -- including haplotype frequencies, linkage disequilibrium, coadaptation of loci, genetic hitchhiking, adaptive landscape, and shifting balance theory -- come into play when multiple loci are considered.
• In this chapter, we shall emphasize qualitative appreciation of these multi-locus effects, rather than quantitative modelling.

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Overview.

• Examples (mimicry among butterflies, human lymphocyte antigen gene complex) illustrate the significance of linkage among loci.
• In the absence of other influences (in an "ideal", infinite randomly mating population), random assortment and chromosomal recombination are expected to establish linkage equilibrium in which haplotype frequencies are simply those expected from independent recombination of alleles at various loci.
• Any departure from linkage equilibrium is called linkage disequilibrium, and indicates that some other factors (e.g., selection, inbreeding) may be at work.
• Stable linkage disequilibrium (consistent association of alleles at different loci that are not proportional to the alleles' individual frequencies) can arise from tight chromosomal linkage (e.g., supergenes in which crossover is unlikely) or from population structure, especially in combination with selection for or against particular haplotypes.
• Selection which favors or disfavors particular haplotypes can influence linkage patterns.

CHECK LIST of important CONCEPTS and TERMS

• Mimicry
  • Mimetic polymorphism
• Supergene
• Coadaptation of loci
• Haplotypes
• Linkage equilibrium
  • Haplotype frequencies
  • D = linkage disequilibrium
• HLA genes, histocompatibility
• Epistasis (epistatic fitness interactions)
• Hitchhiking
• Adaptive topography (adaptive landscape)
• Shifting balance theory

Chapter 8, Section-by-Section Comments

8.1. "Mimicry in Papilio is controlled by more than one genetic locus."

• Many organisms mimic other organisms, as an element of protective adaptation.  Mimicry is an interesting subject in its own right.  Here Ridley uses mimetic polymorphism, in which one species may have several different morphs, to introduce the concept of Mendelian traits controlled by multiple loci.
• The first examples involve swallowtail butterflies, genus Papilio .
• Close to home, both yellow tiger and black morphs of Papilio glaucus are fairly common in southern Illinois.  (I don't notice the model very often; it is supposedly more common farther south.)
• The tropical species Papilio memnon has several different morphs resemble several different (presumed) models (see Ridley's color plate 2, following p. 458, to compare mimics and their models).
  • Possible advantages for a population which produces several mimetic and non-mimetic morphs instead of just one:
    • Reducing the number of mimics for any particular model, so potential predators don't encounter more mimics than models.
    • Making it harder for a predator to learn to discriminate between mimic and model.
  • The various morphs appear to be controlled by many Mendelian alleles at a single locus, but...
  • Rare mixed morphs suggest that recombination can occur among several tightly linked genes.
  • The genetics of this case have not been confirmed; the example is illustrative but partly hypothetical.

• Tightly linked sets of functionally related genes are sometimes called supergenes.
• Since a recombinant within a supergene behaves a lot like a new allele, one might reasonably consider supergene recombination as a form of mutation.  (But that would be decidedly unconventional, and then supergenes wouldn't count as examples of multilocus selection.)
• Summary concept:  Gene linkage can be adaptively significant.

8.2. "The genotypes at different loci in Papilio memnon are coadapted."

• Supergenes are coadapted sets of linked genes.
• To say that linked genes are coadapted is to say that particular alleles at one locus work best with particular alleles at the linked loci, such that each linked set of alleles works well together.
• Coadaptation is maintained by tight linkage.
  • Crossing over tends to break up coadapted gene complexes.
  • Without tight linkage, especially favorable combinations of alleles would not be stable.
  • Without tight linkage, the best each locus could do would be to find a compromise which worked fairly well with all the various alleles at other loci.
• Summary concept:  Linkage binds loci into supergenes which are coadapted.

8.3. "Mimicry in Heliconius is controlled by more than one gene, but not by a supergene."

• In the tropical butterfly Heliconius, mimicry is based on coadapted sets of alleles which are not tightly linked.
  • Different haplotypes are fixed in different subpopulations.
  • Because subpopulations with different morphs are geographically separated, there is no opportunity for recombination.
• Summary concept:  Haplotype coadaptation can be maintained by population structure.  It does not require physical linkage on chromosomes.

8.4. "Two-locus genetics is concerned with haplotype frequencies."

• The haplotype specifies alleles at separate loci that occur together in a single individual.
• Haplotype frequencies are used to determine whether alleles at two or more loci are in linkage equilibrium.

8.5. "The frequencies of haplotypes may or may not be in linkage equilibrium."

• In an "ideal", infinite randomly mating population, random assortment and chromosomal recombination will eventually establish linkage equilibrium in which haplotype frequencies are simply those expected from independent recombination of alleles at various loci.
• Linkage disequilibrium occurs whenever there are any departures from the expectations of linkage equilibrium.
• Linkage disequilibrium can be expressed numerically, as the difference between actual haplotype frequencies and those expected at equilibrium.
  • The algebra is straightforward but tedious.
  • D is linkage disequilibrium.

  • NOTE ERROR IN TEXT:  The paragraph at the bottom of p. 200 should read:

    D is conventionally defined by multiplying the frequencies of A₁B₁ and A₂B₂ and subtracting that total from the productof the frequencies of A₁B₂ and A₂B₁.

  • For two alleles at two loci,
    • D = ad - bc
    • Here a and d are the frequencies for one pair of complementary haplotypes (conventially but arbitrarily called the "coupling" pair), while b and c are the frequencies for the pair of complementary haplotypes (conventially called the "repulsion" pair) that result from recombination between the two loci (see pp. 200-201).

• Recombination works to reestablish linkage equilibrium.  How fast depends on the rate of recombination.
  • The change in linkage disequilibrium that results in one generation from crossing over at rate r is then given by D' = (1 - r) D

• The explanation on p. 203 is quite clear and to the point.
  • "...like the Hardy-Weinburg theorem, linkage equilibrium provides a theoretical baseline telling us whether anything interesting is occurring in a population.  ...if two loci are in linkage disequilibrium, we may also suspect that one or more of these factors [selection, non-random mating, or sampling effects] are at work."

8.6. "The human HLA genes are a multi-locus gene system."

• The human lymphocyte antigen system is amazing in several ways, most notably for its tremendous number of alleles at each of several linked loci, for combinatorial assembly of the peptide products those loci to produce an almost unlimited range of antibodies, and for somatic mutation to produce still greater antibody diversity.
• The HLA system also provides examples of linkage disequilibrium, which probably have significance for disease resistance.

8.7. "Linkage disequilibrium can exist for several reasons."

• Linkage can persist for some time while equilibrium is being approached.
• Random sampling will disturb linkage equilibrium (analogous to the way drift produces departures from Hardy-Weinburg equilibrium).
• Non-random mating (including any of the process which cause inbreeding, such as population structure or preferential mating among similar haplotypes) can produce linkage disequilibrium, even when the relevant loci are on different chromosomes.
• Selection can act against particular haplotypes.

8.8. "Two-locus models of natural selection can be built."

• Don't get stuck on the models in this section.   Concentrate on understanding the distinction between independent and epistatic fitness effects.  For each type of interaction, Ridley offers hypothetical examples to illustrate how the effect might work.
• Ridley introduces multiplicative and additive fitness effects, which are both simple, mathematically tractable versions of independent fitness interactions.
  • For such independent effects, the contribution to fitness by alleles at one locus does not depend on which alleles happen to be present at other loci
  • Of course, overall fitness depends on all loci, but each locus contributes independently.
  • When loci affect fitness independently, normal (ideal) processes are expected to maintain stable haplotype frequencies with no linkage disequilibrium.

• Ridley also introduces epistatic fitness interactions, in which the contribution to fitness by an allele depends on which other alleles are present at other loci.
  • Epistasis depends on the presence of more than allele at each of two or more loci.  Without polymorphic alleles, epistatic fitness effects cannot occur.
  • The example offered is the Papilio mimetic polymorphism.
  • Selection can only cause linkage disequilibrium if epistasis occurs (but remember there are other, non-selective, causes for linkage disequilibrium).

• It remains unknown how common or significant epistatic fitness effects actually are.  Plausibly (but speculatively), the genome may be organized to minimize deleterious effects of epistasis.

8.9. "Hitchhiking occurs in two-locus selection models."

• Hitchhiking is a very simple concept, with potentially complex consequences.
• Selection for alleles at one locus can carry along "hitchhiker" alleles at linked loci.
  • The easiest case to imagine is for neutral alleles to hitchhike by tight linkage to strongly selected alleles.
• Fixation of neutral alleles by hitchhiking may offer one possible explanation for rates of heterozygosity which are lower than expected by neutral theory.

8.10. "Linkage disequilibrium can be advantageous, neutral, or disadvantageous."

• Hitchhiking of neutral alleles is a simple example of a neutral effect for linkage disequilibrium.
• Hitchhiking of weakly deleterious alleles is a simple example of a deleterious effect for linkage disequilibrium.
• Stable mimetic polymorphism based on epistatic fitness interactions illustrates one possible advantage for linkage disequilibrium.
• "The distinction between advantageous and disadvantage linkage disequilibriumis crucial to understanding one of the major problems of evolutionary biology -- why recombination exists" (p. 212). See the next section below.

8.11. "Why does the genome not congeal?"

• If the effects of linkage disequilibrium are advantageous, then recombination may be harmful.
  • Recombination can break up beneficial allele combinations.
  • Even though recombination can also create new advantageous combinations, it will just as easily take them apart again.
• But if the effects of linkage disequilibrium are disadvantageous, then recombination can be beneficial.
  • Recombination can separate beneficial alleles from linked deleterious alleles.
• Recombination is genetically variable, and should be subject to selection.
  • Speculatively, and perhaps more to the point, recombination rates may vary in a site-specific manner (e.g., by inversion), so supergenes can be individually protected from recombination even while the advantages of recombination prevail elsewhere.

8.12. "Wright invented the influential concept of an adaptive topography."

• The idea of a three-dimensional landscape, on which height indicates fitness, provides a convenient (but possibly misleading) metaphor for thinking about evolution.
• As an example of this metaphor, Box 7.3, p. 182, applies the adaptive landscape idea to explain Fisher's model of adaptive evolution.
• On the adaptive landscape, peaks correspond to genotypes with high fitness.
• Selection is expected to move populations uphill, to find local high points.
• But selection acting alone can strand a population on a local peak, even if it is surrounded by much higher peaks (better adapted genotypes).
• Hence Wright also introduced the "shifting balance theory" (next section, below) to explain how populations to move away from local peaks if there are higher peaks nearby.

8.13. "The shifting balance theory of evolution."

• Sewall Wright was one of the founders of the "modern synthesis".
• Sewall Wright's shifting balance theory proposes that the "balance" among allele frequencies at many loci can shift as a result of random sampling variations (i.e., drift).  Such shifts will enable a population to "explore" the adaptive landscape, especially if the population is subdivided into many small subpopulations, in each of which drift can operate at a higher rate.  Such exploration would enable a population to escape from a low, local peak to reach a nearby, higher peak.  (Selection acting alone would hold the population on the local peak.)

• Thus, according to Wright, drift is actually important for adaptation.

• R.A. Fisher (another of the founders of the "modern synthesis"), disagreed with Wright over the importance of drift in adaptive.  Fisher believed that a complex multidimensional fitness landscape would not have isolated local peaks on which a population would become stranded.

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