Lecture 5: Genetic
Variation and
Inbreeding
January 24, 2014
Last Time
Hardy-Weinberg Equilibrium
Using Hardy-Weinberg: Estimating allele
frequencies for dominant loci
Variance of allele frequencies for
dominant loci
Hypothesis testing
Today
Measures of diversity
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
Expected Heterozygosity
If a population is in Hardy-Weinberg Equilibrium, the
probability of sampling a heterozygous individual at a
particular locus is the Expected Heterozygosity:
 2pq
for 2-allele, 1 locus system
OR
 1-(p2 + q2) or 1-Σ(expected homozygosity)
n
HE 1
more general: what’s left over after
calculating expected homozygosity

2
p i,
i 1
Homozygosity is overestimated at small
sample sizes. Must apply correction factor:
Correction for bias in
parameter estimates by
small sample size
HE
n

2 

 1   p i ,
2N 1
i 1

2N
Maximum Expected Heterozygosity
 Expected heterozygosity is maximized when all
allele frequencies are equal
 Approaches 1 when number of alleles = number
of chromosomes
2N
H E (max)  1  
i 1
2
2N 1
 1 
 1 

  1 2N 
 
2N
 2N 
 2N 
 Applying small sample correction factor:
HE
2
n
2N  2N 1

2 

1   p i  

 1
2N 1
i 1
 2N 1 2N 
2N
Also see Example 2.11 in Hedrick text
Observed Heterozygosity
 Proportion of individuals in a population that are
heterozygous for a particular locus:
HO 
N
N
ij

H
ij
Where Nij is the number of
diploid individuals with
genotype AiAj, and i ≠ j,
And Hij is frequency of
heterozygotes with those
alleles
 Difference between observed and expected heterozygosity
will become very important soon
 This is NOT how we test for departures from HardyWeinberg equilibrium!
Alleles per Locus
 Na: Number of alleles per locus
 Ne: Effective number of alleles per locus
 Same as ne in your text
If all alleles occurred at equal frequencies, this is the number
of alleles that would result in the same expected
heterozygosity as that observed in the population
Ne 
1
,
Na

i 1
2
pi
Example: Assay two microsatellite loci for
WVU football team (N=50)
Calculate He, Na and Ne
Locus A
Locus B
Allele
Frequency
Allele
Frequency
A1
0.01
B1
0.3
A2
0.01
B2
0.3
A3
0.98
B3
0.4
HE
n

2 

 1   p i ,
2N 1
i 1

2N
Ne 
1
,
Na

i 1
p
2
i
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
Example: Merle patterning in dogs
 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
Clarke et al. 2006 PNAS 103:1376
Example: Merling Pattern in collies
Homozygous wild-type
M1M1
N=6,498
Heterozygotes
Homozygous mutants
M1M2
M2M2
N=3,500
N=2
 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
P
A1A2
F1
A3A4
A1A3
F2
A 3A 3
A 2A 3
A2A3
Identical by descent (IBD)
A 1A 2
A3A4
A1A3
A2A3
A3A5
A3A3
A2A3
Identical by state (IBS)
Identical by descent (IBD)
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:
pˆ
Effect of Inbreeding on Genotype Frequencies
D  fp  p (1  f )
2
D  fp  p  fp
2
D  p  fp  fp
2
2
2
D  p  fp (1  p )
2
D  p  fpq
2
R  q  fpq
2
H  2 pq  2 fpq
 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
Fixation Index
 The difference between observed and expected
heterozygosity is a convenient measure of
departures from Hardy-Weinberg Equilibrium
F 
HE  HO
HE
 1
HO
HE
Where HO is observed heterozygosity and
HE is expected heterozygosity (2pq under Hardy-Weinberg
Equilibrium)