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Population Structure
Partitioning of Genetic Variation
Banner-tailed kangaroo rat (Dipodomys spectabilis)
Distribution of populations
R2
SSW
1 km
Distribution of populations
1 km
Distribution of populations
1 km
Distribution of populations
1 km
Population Structure
Hierarchical Population Structure– Partitioning of the
genetic variation between the different groupings of individuals
Hierarchical levels– Total population
– Subpopulation
– Breeding groups
– Individuals
Distribution of populations
pA=1.0pa=1.0
Are the two populations inHaWeE? We trap animals in the box
and catch approximatelyequal numbers of animals from the two population.
Is the population now in HaWeE?
No, deficient in heterozygotes!
Population subdivision results in fewer heterozygotes than wewould expect if only 1 population
Ursus maritimus
North Beaufort Sea
South Beaufort Sea
Western Hudson Bay
Davis Strait
North Beaufort Sea
South Beaufort Sea
Western Hudson Bay Davis Strait
Western Population
Eastern Population
North Beaufort Sea
South Beaufort Sea
Western Hudson Bay
Davis Strait
Total Population
Heterozygosity within Populations
Calculate H at each hierarchical level– Populations
– Hlocus = (1-(∑pi2))
– HS = (I=1∑n Hlocus)/n n = Number of loci
Heterozygosity within populations
SB NB WH DS
G1A 0.742 0.755 0.451 0.406
G1D 0.612 0.631 0.602 0.607
G10B 0.767 0.740 0.433 0.639
G10C 0.244 0.391 0.691 0.486
G10L 0.317 0.332 0.491 0.348
G10M 0.796 0.758 0.782 0.736
G10P 0.697 0.687 0.777 0.754
G10X 0.838 0.741 0.711 0.820
H= 0.627 0.632 0.617 0.599
Heterozygosity within Regions
Calculate H at each hierarchical level– Regions– Estimate average allele
frequency within each region– Hlocus
= 1-( j=1∑a(I=1∑Rpi/R)2
R = # regions a = # alleles
– HR = (I=1∑n Hlocus)/n n = Number of loci Weight this value by the
number of populations in each region.
Heterozygosity within Regions
Western Eastern
G1A 0.766 0.435
G1D 0.624 0.605
G10B 0.772 0.548
G10C 0.321 0.607
G10L 0.327 0.422
G10M 0.801 0.764
G10P 0.697 0.784
G10X 0.811 0.770
H= 0.640 0.617
Heterozygosity Total
Calculate H at each hierarchical level– Total– Estimate average allele
frequency within each region
– Hlocus
= 1-( j=1∑a(I=1∑SPpi/SP)2
SP = # subpopulations a = # alleles
– HT = (I=1∑n Hlocus)/n n = Number of loci
Heterozygosity Total
Total
G1A 0.709
G1D 0.618
G10B 0.750
G10C 0.488
G10L 0.376
G10M 0.800
G10P 0.760
G10X 0.816
H= 0.665
Comparison of Hexp at various levels
0.5
0.55
0.6
0.65
0.7
0.75
SB NB WH DS WEST EAST TOTAL
Who Cares?? Study of statistical differences among local populations
is an important line of attack on the evolutionary problem. While such differences can only rarely represent first steps toward speciation in the sense of the splitting of the species, they are important for the evolution of the species as a whole. They provide a possible basis for intergroup selection of genetic systems, a process that provides a more effective mechanism for adaptive advance of the species as a whole than does the mass selection which is all that can occur under panmixia. Sewall Wright.
Translation
Population subdivision reduces population size.
Reduced population size increases genetic drift which decreases genetic diversity or increases inbreeding
Different populations will then diverge from each other with the possibility of speciation
Inbreeding
Inbreeding – Animals prefer to mate
with individuals more closely related to them than a random individual
– Decreases heterozygosity
– Reduces genetic variation
– Sexual Selection
Inbreeding– Animals mate at random
but there are a limited number of mates from which to choose due to population subdivision.
– Decreases heterozygosity
– Reduces genetic variation
– Genetic Drift
Wright’s F-stats Fixation Index (F)
– Quantifies inbreeding due to population structure
Reduction in H due to structure
– Estimates the reduction in H expected at one level of the hierarchy relative to another more inclusive level.
– FSR - Decrease in H given that the regions are divided into subpopulations
– FST - Decrease in H given the that the whole system is not panmictic.
– FST = ? in panmictic population?
– FST = ? in completely isolated populations?
€
FSR=HR −HS
HR
FRT =HT −HR
HT
FST =HT −HS
HT
€
FSR=HR −HS
HR
FRT =HT −HR
HT
FST =HT −HS
HT
€
HS =0.627+0.632+0.617+0.5994
=0.619
HR =0.640+0.617
2=0.628
HT =0.665
€
FSR=0.628−0.6190.628
=0.014
FRT =0.665−0.628
0.665=0.056
FST =0.665−0.619
0.665=0.069
Of the total genetic variation found in the4 major polar bear populations only 7% is due to the subdivision of the population.
Interpreting F-stats
FST = 0 - 0.05
– Little genetic differentiation
FST = 0.05 - 0.15
– Moderate genetic differentiation
FST = 0.15 - 0.25
– Great genetic differentiation
FST = > 0.25
– Very great differentiation
Interpreting F-stats
FST = 0 - 0.05
– Little genetic diff.
FST = 0.05 - 0.15
– Moderate genetic diff.
FST = 0.15 - 0.25
– Great genetic diff.
FST = > 0.25
– Very great diff.
Recall– F=1/(1+4Nm)– Nm={(1/F)-1}*0.25– If F = 0.15
Nm = {(1/0.15)-1}*0.25 Nm = (6.67-1)*0.25 Nm = 1.4
One migrant per generation will prevent great genetic differentiation or fixation of different alleles
Isolation BreakingThe Wahlund Principle
If Population subdivision leads to a reduction in the number of expected heterozygotes it must also result in a greater number of homozygotes than expected.
When isolation is broken homozygosity decreases
pA=1.0pa=1.0
Isolation BreakingThe Wahlund Principle
pA= 0.5pa=0.5
aa = 0.5Aa = 0.0AA = 0.5
aa = 0.25Aa = 0.5AA = 0.25
pA=1.0pa=1.0
Isolation BreakingThe Wahlund Principle
pA= 1.0pa=1.0
P(a) = q1
P(aa) = q12
P(a) = q1
P(aa) = q12
Average = (q12 + q2
2)/2 (12 + 02)/2 = 0.5
P(a) = q1 + q2
P(aa) = {(q1 + q2)/2}2
={(1.0 + 0.0)/2}2
=0.25Frequency of homozygotes decreases after fusion
pA=1.0pa=1.0
Isolation BreakingThe Wahlund Principle
pA= 1.0pa=1.0
Fusing separated populations reduces the average frequency ofeach homozygote by an amount equal to the variance in allelefrequency among the original populations following random mating.
Var(q) = 0.5(q1 - qavg)2 + 0.5(q2 - qavg)2
= 0.5(1.0 - 0.5)2 + 0.5(0 - 0.5)2 = 0.5*0.25 + 0.5*0.25 = 0.25
aa = 0.5
aa = 0.5 => 0.25
F and Wahlund
The reduction in homozygosity due to fusion – 2* 2
(assumes 2 alleles what would it be with more alleles??)
This must equal the increase in heterozygosity
HT - HS of
FST = (HT-HS)/HT
FST = (2*2)/HT
HT = 2pq
FST = 2 / 2pq
Thus the F-stats at each of the hierarchical levels are related to the variances of the allele frequencies grouped at the levels of interest.
Given this we can calculate the average genotype frequencies across populations….
Genotypes in Subdivided populations
In subdivided populations it is possible to calculate the average genotype frequencies across all populations
The genotypes across the subpopulations don’t obey HaWeE– Excess homozygotes
The genotypes within the subpopulations do obey HaWeE.
€
AA=p 2+p q FST
Aa=2p q −2p q FST
aa=q 2+p q FST
Remember, FST = 2 / 2pq and FST is the reduction in heterozygosity due to subdivision
The other Inbreeding
Selective mating between close relatives– The effect of inbreeding is
to reduce the heterozygosity of a population
– Defined as, “F - The proportionate reduction in heterozygosity relative to random mating”.
Analagous to our population subdivision but it is within a subpopulation
F = (HO - HI)/HO
– HO = 2pq Why? HI = HO-HOF
=HO(1-F) =2pq(1-F)
Inbreeding
In inbreed populations it is possible to calculate the expected genotype frequencies in an analagous fashion to subdivision
The genotypes don’t obey HaWeE– Deficiency of
heterozygotes = 2pqF These are allocated
equally amongst the two homozygotes because each heterozygote as an “A” and an “a”
€
AA=p2+pqF
Aa=2pq−2pqF
aa=q2+pqF
Remember, F is the reduction in heterozygosity due to inbreeding
€
AiAi =pi2(1−F )+piF
AiAj =2piqi(1−F )
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