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BIOL2007 - EVOLUTION AT MORE THAN ONE GENE SO FAR Evolution at a single locus No interactions between genes One gene - one trait REAL evolution: 10,000 - 100,000 genes producing mRNA linkage, a physical interaction mechanistic interactions in gene action. GENE INTERACTIONS
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e.g. polymorphic Batesian mimicry (palatable mimics)
Gene interactions affect genotypic frequencies at many loci.
A/a (say) controls: forewing colour pattern
B/b controls: hindwing pattern
AB, ab combinations favoured at expense of Ab, aB
Inbreeding, selection, migration etc. cause a deviation from Hardy-Weinberg equilibrium at a single locus.
Similarly, selection (also migration, drift) can cause deviation from multilocus equilibria, and lead to prevalence of particular 2-locus combinations.
Expected gametic frequencies, if two genes are independently inherited and randomly combined, can be obtained from allelic frequencies in population:
Alleles A a
allele pA 1-pA
B pB pApB (1-pA)pB
b 1-pB pA(1-pB) (1-pA)(1-pB) Sum = 1
Non-randomness of the gametic frequencies means a deviation from two locus equilibrium
frequencies= expectation + deviation
pAB= pApB+ D
pAb= pA(1-pB)- D
paB=(1-pA)pB - D
pab=(1-pA)(1-pB) + D
(Obviously, the sum pAB +pAb + paB + pab = 1 )
… also known as … linkage disequilibrium.
Also: D = pABpab - pAbpaB
Frequency of gamete AB, pAB= pApB+ D
D can vary between a maximum of +0.25 and a minimum of –0.25, but the range is often smaller if the frequency of alleles is not exactly 0.5.
To get an idea of the fraction of maximal possible disequilibrium, D is standardized in various ways. A common way is to use the correlation coefficient:
Can also useRAB2, which measures fraction of variance explained by relation between the two genes.
Even two loci: difficult maths
But real evolution: 10s or hundreds of loci affect traits.
Think of three loci, A,B,C,
3 possible 2-way gametic disequilibria: DAB,DAC,DBC… and one 3-way disequilibrium, DABC
(the effect of the DAB on C, of DAC on B etc.)
More loci, more multi-order disequilibria! Maths complex!
But, if D small, can assume few interactions between loci, and loci evolve independently; can use quantitative genetics approximations(see Kevin Fowler’s lectures next week)
Rest of this lecture: pairs of loci.
Recombination reduces disequilibrium
All deviation from Hardy-Weinberg is completely lost in 1 generation of random mating
Deviation from 2 locus equilibrium more persistent. Recombination at a maximum of 50% of gametes.
D can therefore decline by at most 50% in each generation.
If c= % recombination, then:
Dt= Dt-1 (1 -c)
after many generations (t): Dt = D0(1 -c)t
A: Drift - random sampling of gametic frequencies, ~
e.g. Tightly linked markers: humans and Drosophila
At tightly linked sites, loss of D slow; drift, even in very large populations can therefore have an effect.
B:Selection - epistatic selection (for gene combinations)
For example: mimetic butterflies, Primula flower morphs…
C: Migration - mixing of populations with different frequencies
Supergene controls 3 major components:
Dominants are all 'thrum' form.
Style length: G – short style & short papillae on stigma surface
Pollen size: P – 'thrum' pollen ~ 1.5x dia 'pin' pollen
Anther position: A – 'thrum' anther position at mouth of corolla-tube
(Matings between pin & pin and thrum & thrum are also largely incompatible).
... occasional recombinants ('homostyles') occur naturally
Why are all thrum phenotypes dominant?
Why does each morph only have one allele at each gene (i.e. linkage disequilibrium complete, D≈1), and not recombinant phenotypes?
1) Studying migration or dispersal
·between populations with different gene frequencies
Mixing will produce disequilibrium which will persist for some generations
For example, genetic disease locus D and marker loci m
In humans 1 million b.p. givesc≈ 1% = 1 map unit (centimorgan)
Can use “association studies” or “disequilibrium mapping”, to find disease genes and markers in populations. Humans: disequilibria significant between marker loci (e.g. microsatellites, SNPs) and between markers and genetic disease loci ~ 1Mb apart, due to drift
Linkage disequilibria useful for fine-scale gene mapping. D can quickly narrow search for the "candidate loci". Successfully used in recent studies. "Hapmap" project.
Physical distance (kB)
(now generally dis-
believed for humans, but is probable
in other species)
Awadalla et al.
Science 286: 2524-5
Gene interactions: pleiotropy, epistasis
Evolution may affect frequencies of two- and more locus associations, as well as just gene frequencies.
Deviation from 2-locus equilibrium is known as gametic disequilibrium or linkage disequilibrium, measured by D
D is destroyed by recombination, c, so Dt= D0(1 -c)t
D can increased by selection, migration, drift
D is involved in maintaining 'supergenes'.
D can be used in linkage mapping, studies of migration in natural populations
Futuyma: Chapter 9: 205-207, Chapter 13: 303-304
Freeman & Herron: Chapter 7