New Courses in the Fall

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New Courses in the Fall Biodiversity --
Pennings Evolution of Development --
Azevedo Lab/Field Positions
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Dynamics of Unlinked Loci two loci, each on a
different chromosome A A1, A2 f (A1)
p, f (A2) q B B1, B2 f (B1) r, f (B2) s
Under Hardy-Weinberg Equilibrium, the expected
genotype frequencies for each locus are A
f (A1A1) p2 f (A1A2) 2pq f (A2A2)
q2 B f (B1B1) r2 f (B1B2) 2rs f (B2B2)
s2
If the population is in HWE, the 2-locus genotype
frequencies are the joint probabilities f
(A1A1B1B1) p2r2 f (A1A2B1B1) 2pqr2 f
(A2A2B1B1) q2r2 f (A1A1B1B2) 2rsp2 f
(A1A2B1B2) 2pq2rs f (A2A2B1B2) 2rsq2 f
(A1A1B2B2) p2s2 f (A1A2B2B2) 2pq s2 f
(A2A2B2B2) q2s2
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Significant Deviation From 2-locus HWE ---gt
significant non-random association of
genotypes linkage disequilibrium (w/ or w/o
physical linkage) measuring the degree of
association use expected vs. observed
distribution of gamete types
gamete exp. freq. obs. freq. if loci are
independent, A1B1 pr a exp.
freq. obs. freq. A1B2 ps b
i.e., pr a 0, etc. A2B1 qr
c A2B2 qs d
what if pr a ? 0 ??
D / gametic disequilibrium parameter / deviation
from random association between alleles D a
pr more generally, D ad - bc
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significant deviation from 2-locus HWE ---gt
significant non-random association of
genotypes linkage disequilibrium (w/ or w/o
physical linkage) measuring the degree of
association use expected vs. observed
distribution of gamete types gamete exp.
freq. obs. freq. if loci are
independent, A1B1 pr a D exp.
freq. obs. freq. A1B2 ps b - D
i.e., pr a 0, etc. A2B1 qr c -
D A2B2 qs d D what if pr a ? 0
?? D / gametic disequilibrium parameter /
deviation from random association between
alleles D a pr more generally, D
ad bc D lt 0.25 magnitude of D measures
how much association between alleles at
different loci, scaled by their frequency
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Recombination Erodes Linkage Disequilibrium
Dt (1 r)tDo
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Linkage Disequilibrium in Natural Populations May
Be Transient Or Permanent
Transient --recent fusion of populations with
different allele frequencies and incomplete
mixing (admixture) --recent mutation (single
copy, by definition in LDE with specific
alleles at other loci) --popn bottlenecks or
founder events --genetic drift
Permanent --very low recombination (e.g.,
chromosomal inversions) --non-random
mating --selection What kinds of selection
maintain linkage disequilibrium ??
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simplest model -- one trait, one gene, one
fitness survival A---gtpr(escape) once predator
attacks wij B---gtpr(detection) xij
multiplicative fitness pr(survival)
pr(detection) x pr(escape) A1A1 A1A2 A2A2 B1
B1 w11x11 w12x11 w22x11 B1B2 w11x12 w12x12 w
22x12 B2B2 w11x22 w12x22 w22x22
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Another Example survival A---gteach A2 allele
1 additional offspring wij B---gt each B2
allele 1 additional offspring xij additive
fitness fecundity wij xij
A1A1 A1A2 A2A2 B1B1 w11 x11 w12
x11 w22 x11 B1B2 w11 x12 w12 x12 w22
x12 B2B2 w11 x22 w12 x22 w22 x22
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Snail Shell Color background color brown
or light (pink, tan, yellow) presence of
bands banded or unbanded snails occur in
mixed woods open (sunny, short grass) and
shaded (trees, long grass) brown snails
overheat in the open, do best in shade, light do
better in the open brown snails with stripes
are more conspicuous, eaten by predators
light snails without stripes are more conspicuous

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survival depends simultaneously on color and
pattern A A1 light, A2 brown B B1
banded, B2 unbanded epistatic
fitness A1A1 A1A2 A2A2 B1B1 z11
z11 z21 B1B2 z11 z11 z21 B2B2 z12 z21 z2
2 where z12 lt z11, z12 lt z22, and z21 lt
z11, z21 lt z22
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fitness epistasis generates strong linkage
disequilibrium in polymorphic mimetic
swallowtail butterflies such as Papilio dardanus
and P. memnon
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Epistatic interactions between the alcohol
dehydrogenase (Adh) and a-glycerol phosphase
dehydrogenase loci in Drosophila
AdhS a-GpdhS
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with ethanol Adh genotype SS SF
FF a-Gpdh SS 0.60 1.29 0.93 genotype SF 0.96
1.00 0.84 FF 0.91 0.97 0.86 without
ethanol Adh genotype SS SF
FF a-Gpdh SS 0.99 1.06 0.86 genotype SF 1.08 1
.00 0.94 FF 0.77 1.16 0.75
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AdhS a-GpdhS
computer simulations
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AdhS/S common
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with ethanol Adh genotype SS SF
FF a-Gpdh SS 0.60 1.29 0.93 genotype SF 0.96
1.00 0.84 FF 0.91 0.97 0.86 without
ethanol Adh genotype SS SF
FF a-Gpdh SS 0.99 1.06 0.86 genotype SF 1.08 1
.00 0.94 FF 0.77 1.16 0.75
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How Important Are Epistatic Interactions
?? epistasis implies multiple adaptive peaks
-increased variance of F2 hybrids
-well-documented examples where
different physiological mechanisms produce
the same phenotype Do We See Evidence of
Epistasis at the Genome Level ??
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linkage disequilibrium may slow the rate at which
a beneficial mutation increases under
selection --linkage to deleterious alleles
higher substitution rates associated with higher
recombination
replacement silent
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using LDE to detect positive selection allelic
variation in G6pd (glucose
6-phosphate dehydrogenase)
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the distribution of G6pd-202A corresponds to the
distribution of malaria individuals carrying
this allele have reduced risk
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Detecting Positive Selection ---gt fate of a new
allele under mutation and drift - alleles that
are rare (young) with high LDE - alleles that
are rare (old) with low LDE - alleles that are
common (old) with low LDE recent positive
selection - allele is common with high
LDE Sabeti et al. 2002 Nature
419832 X-chromosomes of 230 men nine alleles
of G6pd (based on 11 SNP loci), incl.
G6pd-202A genotype each chromosome at 14 addl
SNP loci up to 413Kb away LDE as extended
haplotype homozygosity (EHH) defined
as pr(same genotype at all marker loci to point
x)
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G6pd Has Significantly Higher LDE Than Other
Alleles
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Genes may interact additively, multiplicatively,
or epistatically Epistatic selection favors
individuals with specific combinations of
alleles at different loci Epistasis is suggested
by violation of two-locus HWE Linkage
disequilibrium is the non-random association of
alleles at different loci D measures the
degree of non-random association, scaled by
allele frequencies in the population Transient
LDE can be produced by drift or admixture
permanent LDE is caused by non-random mating or
selection LDE may be relatively uncommon but
direct estimation from pairs of loci likely to
interact is difficult