1. New Courses in the Fall
Biodiversity -- Pennings
Evolution of Development -- Azevedo
Lab/Field Positions

3. 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

4. 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,
A1B pr a exp. freq. = obs. freq.
A1B ps b i.e., pr – a = 0, etc.
A2B qr c
A2B 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

5. 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,
A1B pr a + D exp. freq. = obs. freq.
A1B ps b - D i.e., pr – a = 0, etc.
A2B qr c - D
A2B 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* < 0.25
magnitude of D measures how much association between alleles
at different loci, scaled by their frequency

6. Recombination Erodes Linkage Disequilibrium: Dt = (1 – r)tDo

8. 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 ??

9. simplest model -- one trait, one gene, one fitness
survival: A--->pr(escape) once predator attacks wij
B--->pr(detection) xij
multiplicative fitness
pr(survival) = pr(detection) x pr(escape)
A1A1 A1A2 A2A2
B1B1 w11x11 w12x11 w22x11
B1B2 w11x12 w12x12 w22x12
B2B2 w11x22 w12x22 w22x22

10. Another Example
survival: A--->each A2 allele = 1 additional offspring wij
B---> 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

11. 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

12. brown light
banded dead alive fitness depends
simultaneously on
unbanded alive dead both traits
= epistasis

13. 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 z22
where z12 < z11, z12 < z22, and z21 < z11, z21 < z22

14. fitness epistasis generates strong linkage disequilibrium in polymorphic
mimetic swallowtail butterflies such as Papilio dardanus and P. memnon

15. Epistatic interactions between the alcohol dehydrogenase (Adh)
and a-glycerol phosphase dehydrogenase loci in Drosophila
AdhS a-GpdhS

16. with ethanol
Adh genotype
SS SF FF
a-Gpdh SS
genotype SF FF
without ethanol
a-Gpdh SS
genotype SF FF

17. AdhS a-GpdhS
computer
simulations

18. AdhS/S
common

19. with ethanol
Adh genotype
SS SF FF
a-Gpdh SS
genotype SF FF
without ethanol
a-Gpdh SS
genotype SF FF

20. 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 ??

21. 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

22. using LDE to detect positive selection: allelic variation in G6pd
(glucose 6-phosphate
dehydrogenase)

23. the distribution of G6pd-202A corresponds to the distribution
of malaria; individuals carrying this allele have reduced risk

24. 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 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)

25. G6pd Has Significantly Higher LDE Than Other Alleles

26. 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