Lecture 5: Genetic Variation and Inbreeding
September 7, 2012
Announcements
I will be out of town Thursday Sept 20 through Sunday, Sept 24
No office hours
Friday, Sept 21: Prof. Hawkins will give a guest lecture about transposable elements
Computer Lab Access Schedule is posted on the door and on the website
Hari will be holding his office hours in the lab
Updated hours will be on class homepage
Last Time Hardy-Weinberg Equilibrium
Using Hardy-Weinberg: Estimating allele frequencies for dominant loci
Variance of allele frequencies for dominant loci
Hypothesis testing
Measures of Diversity are a Function of Populations and Locus Characteristics
Assuming you assay the same samples, order the following markers by increasing average expected values of Ne and HE:
RAPD SSR
Allozyme
Today More Hardy-Weinberg Calculations
Merle Patterning in Dogs
First Violation of Hardy-Weinberg assumptions: Random Mating
Effects of Inbreeding on allele frequencies, genotype frequencies, and heterozygosity
Example: Merle patterning in dogs
Clarke et al. 2006 PNAS 103:1376
Merle or “dilute” coat color is a desired trait in collies, shetland sheepdogs (pictured), Dachshunds and other breeds
Homozygotes for mutant gene lack most coat color and have numerous defects (blindness, deafness)
Caused by a retrotransposon insertion in the SILV gene
Example: Merling Pattern in collies Homozygous wild-type
N=6,498 M1M1
Heterozygotes
N=3,500 M1M2
Homozygous mutants
N=2 M2M2
Is the Merle coat color mutation dominant, semi-dominant (incompletely dominant), or recessive?
Do the Merle genotype frequencies differ from those expected under Hardy-Weinberg Equilibrium?
Why does the merle coat coloration occur in some breeds
but not others?
How did we end up with so many dog breeds anyway?
Nonrandom Mating: Inbreeding Inbreeding: Nonrandom mating
within populations resulting in greater than expected mating between relatives
Assumptions (for this lecture): No selection, gene flow, mutation, or genetic drift
Inbreeding very common in plants and some insects
Pathological results of inbreeding in animal populations
Recessive human diseases Endangered species
http://i36.photobucket.com/albums/e4/doooosh/microcephaly.jpg
Important Points about Inbreeding Inbreeding affects ALL LOCI in genome
Inbreeding results in a REDUCTION OF HETEROZYGOSITY in the population
Inbreeding BY ITSELF changes only genotype frequencies, NOT ALLELE FREQUENCIES and therefore has NO EFFECT on overall genetic diversity within populations
Inbreeding equilibrium occurs when there is a balance between the creation (through outcrossing) and loss of heterozygotes in each generation
Inbreeding can be quantified by probability (f) an individual contains two alleles that are
Identical by Descent
A1A2 A3A4
A1A3 A2A3
A3A3 A2A3
A1A2 A3A4
A1A3 A2A3 A3A5
A3A3 A2A3
Identical by descent (IBD) Identical by state (IBS) Identical by descent (IBD)
P
F1
F2
Nomenclature D=X=P: frequency of AA or A1A1 genotype
R=Z=Q: frequency of aa or A2A2 genotype
H=Y: frequency of Aa or A1A2 genotype
p is frequency of the A or A1 allele
q is frequency of the a or A2 allele
All of these should have circumflex or hat when they are estimates:
p̂
Effect of Inbreeding on Genotype Frequencies
fp is probability of getting two A1 alleles IBD in an individual
p2(1-f) is probability of getting two A1 alleles IBS in an individual
Inbreeding increases homozygosity and decreases heterozygosity by equal amounts each generation
Complete inbreeding eliminates heterozygotes entirely
)1(2 fpfpD −+=
fpqpD += 2
22 fppfpD −+=22 fpfppD −+=
)1(2 pfppD −+=
fpqqR += 2
fpqpqH 22 −=
Fixation Index The difference between observed and expected
heterozygosity is a convenient measure of departures from Hardy-Weinberg Equilibrium
E
O
E
OE
HH
HHHF −=
−= 1
Where HO is observed heterozygosity and
HE is expected heterozygosity (2pq under Hardy-Weinberg Equilibrium)
Assume completely inbred fraction (f) and noninbred fraction (1-f) in population
)0()1(2 ffpqH +−=
!
H = 2pq(1" f )
!
f =1" H2pq
If departures from Hardy Weinberg are entirely due to inbreeding, f can be estimated from Fixation Index, F
!
F =1" HO
HE
IBD IBS
Effects of Inbreeding on Allele Frequencies
Allele frequencies do not change with inbreeding
Loss of heterozygotes exactly balanced by gain of homozygotes
00201 qfppD +=
!
H1 = 2p0q0 " 2 fp0q0
iii HDp21
+=
!
p1 = (p02 + fp0q0) +
12(2p0q0 " 2 fp0q0)
!
= p02 + p0q0
!
= p02 + p0(1" p0)
!
= p02 + p0 " p0
2
!
p1 = p0
Extreme Inbreeding: Self Fertilization Common mode of
reproduction in plants: mate only with self
Assume selfing newly established in a population
½ of heterozygotes become homozygotes each generation
Homozygotes are NEVER converted to heterozygotes
Self Fertilization
AA
aa
Aa
Aa
A
a
a A Aa Self-Fertilizations
AA
AA
AA
AA
A
A
A A AA Self-Fertilizations
½ Aa each generation ½ AA or aa (allele fixed
within lineage)
http://www.life.illinois.edu/ib/335/BreedingSystems/BreedingSystems.html
Decline of Heterozygosity with Self Fertilization
Steady and rapid decline of heterozygosity to zero 01 2
1 HH =
121
−= tt HH
.21
0HHt
t ⎟⎠
⎞⎜⎝
⎛=
AA or aa
Aa
Partial Self Fertilization
Mixed mating system: some progeny produced by selfing, others by outcrossing (assumed random)
Rate of outcrossing = T
Rate of selfing = S
T+S=1
Heterozygosity declines to equilibrium point
.2
2 1−+= tt
HSpqTH
aa
AA
Aa
What determines the equilibrium frequency of heterozygotes in a population with mixed selfing and
outcrossing?