New Courses in the Fall

Biodiversity -- Pennings

Evolution of Development -- Azevedo

Lab/Field Positions

Dynamics of Unlinked Loci

two loci, each on a different chromosomeA: A1, A2 f (A1) = p, f (A2) = qB: 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

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 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 - DA2B2 qs d + D what if pr – a 0 ??

D gametic disequilibrium parameter deviation from randomassociation between alleles

D = a – pr; more generally, D = ad – bc; D < 0.25

magnitude of D measures how much association between allelesat different loci, scaled by their frequency

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

Linkage Disequilibrium in Natural Populations May Be TransientOr 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 driftPermanent

--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 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

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

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

brown light

banded dead alive fitness depends

simultaneously on

unbanded alive dead both traits

= epistasis

survival depends simultaneously on color and pattern

A: A1 = light, A2 = brownB: 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

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 -glycerol phosphase dehydrogenase loci in Drosophila

AdhS -GpdhS

with ethanol Adh genotype SS SF FF

-Gpdh SS 0.60 1.29 0.93genotype SF 0.96 1.00 0.84

FF 0.91 0.97 0.86

without ethanol Adh genotype SS SF FF

-Gpdh SS 0.99 1.06 0.86genotype SF 1.08 1.00 0.94

FF 0.77 1.16 0.75

computersimulations

AdhS -GpdhS

AdhS/S

common

with ethanol Adh genotype SS SF FF

-Gpdh SS 0.60 1.29 0.93genotype SF 0.96 1.00 0.84

FF 0.91 0.97 0.86

without ethanol Adh genotype SS SF FF

-Gpdh SS 0.99 1.06 0.86genotype SF 1.08 1.00 0.94

FF 0.77 1.16 0.75

How Important Are Epistatic Interactions ??

epistasis implies multiple adaptive peaks

-increased variance of F2 hybrids

-well-documented examples where differentphysiological mechanisms produce thesame phenotype

Do We See Evidence of Epistasis at the Genome Level ??

replacement silent

linkage disequilibrium may slow the rate at which a beneficial mutation increases under selection

--linkage to deleterious alleles

higher substitutionrates associated withhigher recombination

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 mennine alleles of G6pd (based on 11 SNP loci), incl. G6pd-202Agenotype each chromosome at 14 add’l SNP loci up to 413Kb awayLDE 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 combinationsof 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; permanentLDE is caused by non-random mating or selection

LDE may be relatively uncommon; but direct estimation from pairsof loci likely to interact is difficult