population structure partitioning of genetic variation

Population Structure

Partitioning of Genetic Variation

Banner-tailed kangaroo rat (Dipodomys spectabilis)

Distribution of populations

R2

SSW

1 km


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


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


pA= 0.5pa=0.5

aa = 0.5Aa = 0.0AA = 0.5

aa = 0.25Aa = 0.5AA = 0.25

pA=1.0pa=1.0


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


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.

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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”

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AA=p2+pqF

Aa=2pq−2pqF

aa=q2+pqF

Remember, F is the reduction in heterozygosity due to inbreeding

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AiAi =pi2(1−F )+piF

AiAj =2piqi(1−F )

population structure partitioning of genetic variation

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