Transcript F-statistics

Quantifying the distribution of variation
Variation
within individuals
within subpopulations
among subpopulations (in total population)
Quantifying the distribution of variation
Variation
within individuals
within subpopulations
among subpopulations (in total population)
Quantifying the distribution of variation
I = individuals
S = subpopulations
T = total population
H is observed heterozygosity (# heterozygotes/N) in a population
HI is observed heterozygosity (# heterozygotes/N) averaged over
individuals in all subpopulations
HS is expected heterozygosity in each subpopulation if it was in
H-W equilibrium, averaged across subpopulations
HT is expected heterozygosity if subpopulations are combined as one
population
Quantifying the distribution of variation
I = individuals
S = subpopulations
T = total population
H is observed heterozygosity (# heterozygotes/N) in a population
HI is observed heterozygosity (# heterozygotes/N) averaged over
individuals in all subpopulations
HS is expected heterozygosity in each subpopulation if it was in
H-W equilibrium, averaged across subpopulations
HT is expected heterozygosity if subpopulations are combined as one
population
HT
HS
HS
HS
Quantifying the distribution of variation
HI observed heterozygosity averaged over individuals in all subpopulations
HS expected heterozygosity in each subpopulation (if it was in H-W equilib.)
averaged across subpopulations
HT expected heterozygosity if subpopulations are combined as one population
p
AA AA Aa aa aa
0.5
H
1/5 = 0.2
Aa Aa Aa Aa AA
0.6
4/5 = 0.8
Quantifying the distribution of variation
HI observed heterozygosity averaged over individuals in all subpopulations
HS expected heterozygosity in each subpopulation (if it was in H-W equilib.)
averaged across subpopulations
HT expected heterozygosity if subpopulations are combined as one population
p
AA AA Aa aa aa
0.5
H
1/5 = 0.2
HI
Aa Aa Aa Aa AA
0.6
4/5 = 0.8
(0.2 + 0.8)/2 = 0.5
Quantifying the distribution of variation
HI observed heterozygosity averaged over individuals in all subpopulations
HS expected heterozygosity in each subpopulation (if it was in H-W equilib.)
averaged across subpopulations
HT expected heterozygosity if subpopulations are combined as one population
p
AA AA Aa aa aa
0.5
H
1/5 = 0.2
HI
HS (av. of 2pq)
Aa Aa Aa Aa AA
0.6
4/5 = 0.8
(0.2 + 0.8)/2 = 0.5
2 x 0.5 x 0.5 = 0.5
2 x 0.6 x 0.4 = 0.48
(0.5 + 0.48)/2 = 0.49
If all subpopulations were in H-W equilibrium, HI would = HS
Quantifying the distribution of variation
HI observed heterozygosity averaged over individuals in all subpopulations
HS expected heterozygosity in each subpopulation (if it was in H-W equilib.)
averaged across subpopulations
HT expected heterozygosity if subpopulations are combined as one population
p
AA AA Aa aa aa
0.5
H
1/5 = 0.2
HI
HS (av. of 2pq)
HT (2 x pav x qav)
Aa Aa Aa Aa AA
0.6
4/5 = 0.8
(0.2 + 0.8)/2 = 0.5
2 x 0.5 x 0.5 = 0.5
2 x 0.6 x 0.4 = 0.48
(0.5 + 0.48)/2 = 0.49
2 x 0.55 x 0.45 = 0.495
Quantifying the distribution of variation
HI observed heterozygosity averaged over individuals in all subpopulations
HS expected heterozygosity in each subpopulation (if it was in H-W equilib.)
averaged across subpopulations
HT expected heterozygosity if subpopulations are combined as one population
p
AA AA Aa aa aa
0.5
H
1/5 = 0.2
HI
Aa Aa Aa Aa AA
0.6
4/5 = 0.8
(0.2 + 0.8)/2 = 0.5
HS (av. of 2pq)
HT (2 x pav x qav)
2 x 0.5 x 0.5 = 0.5
2 x 0.6 x 0.4 = 0.48
(0.5 + 0.48)/2 = 0.49
2 x 0.55 x 0.45 = 0.495
If all subpopulations were the same, HS would = HT
HI observed heterozygosity averaged over individuals in all subpopulations
HS expected heterozygosity in each subpopulation averaged across subpopulations
HT expected heterozygosity if subpopulations are combined as one population
FIT – reduction in heterozygosity of individuals relative to
whole population
FIT = HT – HI
HT
HI observed heterozygosity averaged over individuals in all subpopulations
HS expected heterozygosity in each subpopulation averaged across subpopulations
HT expected heterozygosity if subpopulations are combined as one population
FIT – reduction in heterozygosity of individuals relative to
whole population
FIT = HT – HI
HT
- any departure from single panmictic population will lead to significant value
- used to detect departures from Hardy-Weinberg equilibrium in total population
HI observed heterozygosity averaged over individuals in all subpopulations
HS expected heterozygosity in each subpopulation averaged across subpopulations
HT expected heterozygosity if subpopulations are combined as one population
FIS - inbreeding coefficient of individual relative to its subpopulation (change in H due to non-random mating)
FIS = HS – HI
HS
HI observed heterozygosity averaged over individuals in all subpopulations
HS expected heterozygosity in each subpopulation averaged across subpopulations
HT expected heterozygosity if subpopulations are combined as one population
FIS - inbreeding coefficient of individual relative to its subpopulation
FIS = HS – HI
HS
used to detect departures from Hardy-Weinberg equilibrium in "good"
populations
positive value = heterozygote deficiency (Wahlund effect)
zero value = all sub-populations in Hardy-Weinberg equilibrium
(random mating within subpopulations)
negative value = heterozygote excess
HI observed heterozygosity averaged over individuals in all subpopulations
HS expected heterozygosity in each subpopulation averaged across subpopulations
HT expected heterozygosity if subpopulations are combined as one population
FST - inbreeding coefficient of sub-population relative
to the whole population = fixation index
FST = HT – HS
HT
HI observed heterozygosity averaged over individuals in all subpopulations
HS expected heterozygosity in each subpopulation averaged across subpopulations
HT expected heterozygosity if subpopulations are combined as one population
FST - inbreeding coefficient of sub-population relative
to the whole population = fixation index
FST = HT – HS
HT
measures degree of population differentiation within species (always positive)
0.00 = sub-popns have same allele frequencies
0.05-0.15 = moderate differentiation
0.15-0.25 = great differentiation
>0.25 = extremely different
1.0 = popns fixed for different alleles
Dispersal and gene flow
Taxa (# species)
Amphibians (33)
Reptiles (22)
Mammals (57)
Fish (79)
Insects (46)
Birds (23)
Fst
0.32
0.26
0.24
0.14
0.10
0.05
Plants – animal poll. 0.22
Plants – wind poll. 0.10
Quantifying the distribution of variation
HI observed heterozygosity averaged over individuals in all subpopulations
(# heterozygotes/ total N)
HS expected heterozygosity in each subpopulation (if it was in H-W equilib.)
averaged across subpopulations
(# heterozygotes/total N)
HT expected heterozygosity if subpopulations are combined as one population
AA, AA, AA , AA BB, BB, BB, BB
HI
0
HS
0
HT
0.5
AA, AB, AB, BB AA, AB,AB, BB
0.5
0.5
0.5
AB, AB, AB, AB AB, AB, AB, AB
1
0.5
0.5
AA, BB, BB, BB AB, AB, AA, BB
0.25
0.44
0.47
Quantifying the distribution of variation
FIS - inbreeding coefficient of individual relative to its subpopulation
FIS = HS – HI
HS
positive value = heterozygote deficiency
zero value = all sub-populations in
Hardy-Weinberg equilibrium
negative value = heterozygote excess
AA, AA, AA , AA BB, BB, BB, BB
HI
0
HS
0
HT
0.5
FIS
0
AA, AB, AB, BB AA, AB,AB, BB
0.5
0.5
0.5
0
AB, AB, AB, AB AB, AB, AB, AB
1
0.5
0.5
-1
AA, BB, BB, BB AB, AB, AA, BB
0.25
0.44
0.47
0.43
9 populations examined at 21 loci
FIS = 0.49
high level of inbreeding?
dioecious – so likely due to clustering
of relatives
Pacific yew (Taxus brevifolia)
Quantifying the distribution of variation
FIT - reduction in heterozygosity of individuals relative to
whole population
FIT = HT – HI
HT
used to detect departures from Hardy-Weinberg
equilibrium in total population
FIT
AA, AA, AA , AA BB, BB, BB, BB
HI
0
HS
0
HT
0.5
AA, AB, AB, BB AA, AB,AB, BB
0.5
0.5
0.5
0
AB, AB, AB, AB AB, AB, AB, AB
1
0.5
0.5
-1
AA, BB, BB, BB AB, AB, AA, BB
0.25
0.47
0.46
0.44
1
Quantifying the distribution of variation
FST - inbreeding coefficient of sub-population relative
to the whole population
FST = HT – HS
HT
measures degree of population differentiation
within species (always positive)
FST
AA, AA, AA , AA BB, BB, BB, BB
HI
0
HS
0
HT
0.5
AA, AB, AB, BB AA, AB,AB, BB
0.5
0.5
0.5
0
AB, AB, AB, AB AB, AB, AB, AB
1
0.5
0.5
0
AA, BB, BB, BB AB, AB, AA, BB
0.25
0.47
0.07
0.44
1
9 populations examined at 21 loci
FST = 0.078
Low to moderate level of population
differentiation
Pacific yew (Taxus brevifolia)