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

Pleiotropy • single gene affects multiple traits

Epistasis • multiple genes interact to affect a trait• multiple traits interact to produce fitness• therefore, natural selection for gene combinations

e.g. polymorphic Batesian mimicry (palatable mimics)

PLEIOTROPY AND EPISTASIS

Papilio memnon, a Batesian mimicmodelspecies mimicspolymorphic Batesian mimicry

(palatable mimics):

frequency-dependent selection for rare female-limited mimic

selection for coordinated phenotype: gene combinations In general, selection • is epistatic• acts on combinations of genes, rather than single loci male is

non-mimetic

How do EPISTASIS AND PLEIOTROPY affect our view of evolution? Gene interactions affect genotypic frequencies at many loci.

A/a (say) controls: forewing colour pattern B/b controls: hindwing patternAB, 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.

HOW DO WE MEASURE DISEQUILIBRIUM?

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

freq.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

D is the gametic disequilibrium coefficient, or measure of deviation from 2 locus equilibrium:  Gametic  random 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 )

gametic disequilibrium, D … also known as … linkage disequilibrium.

Also: D = pABpab - pAbpaB

STANDARDIZATION

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:

)1)(1(BABA

ABABpppp

DR

Can also use RAB2, which measures fraction of variance explained by relation between the two genes.

MORE THAN TWO LOCI

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.

FACTORS THAT CAN DECREASE D 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.

Disequilibrium actually declines by a fraction given by the recombination rate) every generationIf c = % recombination, then:  Dt = Dt-1 (1 -c)

after many generations (t): Dt = D0(1 -c)t 

LinkagedisequilibriumRAB

FACTORS THAT CAN INCREASE D

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

eN21

Primula verisPrimula veris – Cowslip – Cowslip

Primula veris – Cowslip – Heterostyly

"Pin" morph"Thrum" morph

Primula veris – Cowslip

"Pin" morph"Thrum" morph

Primula veris – Cowslip

"Pin" morph"Thrum" morph

Primula veris – Cowslip

"Pin" morph"Thrum" morph

"Pin" morph"Thrum" morph

Primula veris – CowslipSupergene 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 naturallyWhy 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?

Human Leucocyte Antigens (HLA): • Part of Major Histocompatibility Complex (MHC), a large complex of loci involved in the immune system.

• Involved in antibody/antigen reactions, involved in recognition, presents antigen to T-cell – for lysis

• Highly polymorphic, involved in immunity to disease

• Probable frequency-dependent selection for rare forms

Disequilibria over 10s-100s of millions of b.p., suggesting selection for combinations of loci.

USES for gametic disequilibria

1) Studying migration or dispersal

      between populations with different gene frequencies      between species

Mixing will produce disequilibrium which will persist for some generations

2) Linkage mapping of loci when c = 0.01 or less difficultFor example, genetic disease locus D and marker loci m

In humans 1 million b.p. gives c ≈ 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.

Linkage diseq. on human chromosome 22

Physical distance (kB)

Papilio memnon, a Batesian mimicmodelspecies mimics

male isnon-mimetic

3) Human mitochondrial DNA recombination?

(now generally dis-believed for humans, but is probablein other species)

Awadalla et al.Science 286: 2524-

5

SUMMARYGene 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, driftD is involved in maintaining 'supergenes'.D can be used in linkage mapping, studies of migration in natural populations

READINGS:Futuyma: Chapter 9: 205-207, Chapter 13: 303-304 Freeman & Herron: Chapter 7