Transcript ppt
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-(p 2 + q 2 ) or 1-Σ(expected homozygosity) more general: what ’ s left over after calculating expected homozygosity
H E
1 Homozygosity is overestimated at small sample sizes. Must apply correction factor:
i n
1
p
2
i
, Correction for bias in parameter estimates by small sample size
H E
2 2
N N
1 1
i n
1
p
2
i
,
Maximum Expected Heterozygosity
Expected heterozygosity is maximized when all allele frequencies are equal
Approaches 1 when number of alleles = number of chromosomes
H E
(max ) 1
i
2
N
1 1 2
N
2 1 2
N
1 2
N
Applying small sample correction factor:
2 2
N
1 2
N H E
2 2
N N
1 1
i n
1
p
2
i
2 2
N N
1 2
N
1 2
N
1 Also see Example 2.11 in Hedrick text
Observed Heterozygosity
Proportion of individuals in a population that are heterozygous for a particular locus:
H O
N ij N
H ij
Where N ij is the number of diploid individuals with genotype A i A j, and i ≠ j,
And H ij 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 Hardy Weinberg equilibrium!
Alleles per Locus
N a
: Number of alleles per locus
N e
: Effective number of alleles per locus
Same as n e 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
N e
1
i N
1
a p i
2 ,
Example: Assay two microsatellite loci for WVU football team (N=50)
Calculate H e, N a and N e
Locus A Locus B Allele
A1 A2 A3
Frequency
0.01
0.01
0.98
Allele
B1 B2 B3
Frequency
0.3
0.3
0.4
H E
2 2
N N
1 1
i n
1
p
2
i
,
N e
1
i N
1
a p i
2 ,
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 N e and H E :
RAPD SSR Allozyme
Example: Merle patterning in dogs
Merle or “ dilute other breeds ” coat color is a desired trait in collies, shetland sheepdogs (pictured), Dachshunds and 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 Heterozygotes Homozygous mutants
M 1 M 1
N=6,498
M 1 M 2
N=3,500
M 2 M 2
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
A 1 A 2 A 3 A 4 A 1 A 2 A 3 A 4
F 1
A 1 A 3 A 2 A 3 A 1 A 3 A 2 A 3 A 3 A 5
F 2
A 3 A 3 A 2 A 3 Identical by descent (IBD) A 3 A 3 A 2 A 3 Identical by state (IBS) Identical by descent (IBD)
Nomenclature
D=X=P: frequency of AA or A 1 A 1 genotype
R=Z=Q: frequency of aa or A 2 A 2 genotype
H=Y: frequency of Aa or A 1 A 2 genotype
p is frequency of the A or A 1 allele
q is frequency of the a or A 2 allele
All of these should have circumflex or hat when they are estimates:
ˆ
p
Effect of Inbreeding on Genotype Frequencies
D
D
fp fp
p p
2 2 ( 1
fp f
2 )
fp is probability of getting two A 1 alleles IBD in an individual
D
p
2
fp
fp
2
D
p
2
fp
( 1
p
)
p
2 (1-f) is probability of getting two A 1 alleles IBS in an individual
D
p
2
fpq H R
q
2 2
pq
fpq
2
fpq
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
H E
H O H E
1
H O H E
Where H
O
is observed heterozygosity and
H E
is expected heterozygosity (2pq under Hardy-Weinberg Equilibrium)