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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
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
PLEIOTROPY AND EPISTASIS
e.g. polymorphic Batesian mimicry (palatable mimics)
Papilio memnon, a Batesian mimic
polymorphic Batesian mimicry
(palatable mimics):
model
species
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
nonmimetic
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 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.
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
allele
freq.
B
pB
b
1-pB
A
pA
a
1-pA
pApB
pA(1-pB)
(1-pA)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
pAb
paB
pab
=
=
=
=
pApB
pA(1-pB)
(1-pA)pB
(1-pA)(1-pB)
+D
-D
-D
+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:
D
AB
RAB 
pA pB(1 pA)(1 pB)
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 generation
If c = % recombination, then:
Dt = Dt-1 (1 -c)
after many generations (t):
Dt = D0(1 -c)t
Linkage
disequilibrium
RAB
FACTORS THAT CAN INCREASE D
1
A: Drift - random sampling of gametic frequencies, ~ 2N
e
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
Primula veris – Cowslip
Primula veris – Cowslip – Heterostyly
"Thrum" morph
"Pin" morph
Primula veris – Cowslip
"Thrum" morph
"Pin" morph
Primula veris – Cowslip
"Thrum"
morph
"Pin" morph
Primula veris – Cowslip
"Thrum"
morph
"Pin" morph
"Thrum" morph
"Pin" morph
Primula veris – Cowslip
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?
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 difficult
For 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 mimic
model
species
mimics
male is
non-mimetic
3) Human
mitochondrial DNA
recombination?
(now generally disbelieved for humans,
but is probable
in other species)
Awadalla et al.
Science 286: 2524-5
SUMMARY
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
READINGS:
Futuyma: Chapter 9: 205-207, Chapter 13: 303-304
Freeman & Herron: Chapter 7