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New Courses in the Fall
Biodiversity -- Pennings
Evolution of Development -- Azevedo
Lab/Field Positions
Dynamics of Unlinked Loci
two loci, each on a different chromosome
A:
A1, A2
f (A1) = p,
B:
B1, B2
f (B1) = r,
f (A2) = q
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
Significant Deviation From 2-locus HWE
---> 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
significant deviation from 2-locus HWE
---> 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
A1B1
A1B2
A2B1
A2B2
exp. freq.
pr
ps
qr
qs
obs. freq.
a+D
b-D
c-D
d+D
if loci are independent,
exp. freq. = obs. freq.
i.e., pr – a = 0, etc.
what if pr – a  0 ??
D / gametic disequilibrium parameter / deviation from random
association between alleles
D = a – pr; more generally, D = ad – bc; *D* < 0.25
magnitude of D measures how much association between alleles
at different loci, scaled by their frequency
Recombination Erodes Linkage Disequilibrium:
Dt = (1 – r)tDo
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 ??
simplest model -- one trait, one gene, one fitness
survival:
A--->pr(escape) once predator attacks
B--->pr(detection)
xij
multiplicative fitness
pr(survival) = pr(detection) x pr(escape)
B1B1
B1B2
B2B2
A1A1
A1A2
A2A2
w11x11
w11x12
w11x22
w12x11
w12x12
w12x22
w22x11
w22x12
w22x22
wij
Another Example
survival:
A--->each A2 allele = 1 additional offspring wij
B---> each B2 allele = 1 additional offspring xij
additive fitness
fecundity = wij + xij
B1B1
B1B2
B2B2
A1A1
A1A2
A2A2
w11 + x11
w11 + x12
w11 + x22
w12 + x11
w12 + x12
w12 + x22
w22 + x11
w22 + x12
w22 + x22
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
banded
brown
light
dead
alive
fitness depends
simultaneously on
unbanded
alive
dead
both traits
= epistasis
survival depends simultaneously on color and pattern
A: A1 = light, A2 = brown
B: B1 = banded, B2 = unbanded
epistatic fitness
B1B1
B1B2
B2B2
A1A1
A1A2
A2A2
z11
z11
z12
z11
z11
z21
z21
z21
z22
where z12 < z11, z12 < z22, and z21 < z11, z21 < z22
fitness epistasis generates strong linkage disequilibrium in polymorphic
mimetic swallowtail butterflies such as Papilio dardanus and P. memnon
Epistatic interactions between the alcohol dehydrogenase (Adh)
and a-glycerol phosphase dehydrogenase loci in Drosophila
AdhS
a-GpdhS
with ethanol
a-Gpdh
genotype
Adh genotype
SS
SF
FF
SS
SF
FF
without ethanol
a-Gpdh
genotype
SS
SF
FF
0.60
0.96
0.91
1.29
1.00
0.97
0.93
0.84
0.86
Adh genotype
SS
SF
FF
0.99
1.08
0.77
1.06
1.00
1.16
0.86
0.94
0.75
AdhS
a-GpdhS
computer
simulations
AdhS/S
common
with ethanol
a-Gpdh
genotype
Adh genotype
SS
SF
FF
SS
SF
FF
without ethanol
a-Gpdh
genotype
SS
SF
FF
0.60
0.96
0.91
1.29
1.00
0.97
0.93
0.84
0.86
Adh genotype
SS
SF
FF
0.99
1.08
0.77
1.06
1.00
1.16
0.86
0.94
0.75
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 ??
linkage disequilibrium may slow the rate at which a beneficial
mutation increases under selection
--linkage to deleterious alleles
replacement
higher substitution
rates associated with
higher recombination
silent
using LDE to detect positive selection: allelic variation in G6pd
(glucose 6-phosphate
dehydrogenase)
the distribution of G6pd-202A corresponds to the distribution
of malaria; individuals carrying this allele have reduced risk
Detecting Positive Selection ---> 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 419:832
X-chromosomes of 230 men
nine alleles of G6pd (based on 11 SNP loci), incl. G6pd-202A
genotype each chromosome at 14 add’l SNP loci up to 413Kb away
LDE as extended haplotype homozygosity (EHH); defined as
pr(same genotype at all marker loci to point x)
G6pd Has Significantly Higher LDE Than Other Alleles
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