1. Lecture 13: Population Structure
October 8, 2012

2. Last Time Effective population size calculations
Historical importance of drift: shifting balance or noise?
Population structure

3. Today Course feedback The F-Statistics Sample calculations of FST
Defining populations on genetic criteria

4. Midterm Course Evaluations
Based on five responses: It’s not too late to have an impact!
Lectures are generally OK
Labs are valuable, but better organization and more feedback are needed
Difficulty level is OK
Book is awful

5. F-Coefficients
Quantification of the structure of genetic variation in populations: population structure
Partition variation to the Total Population (T), Subpopulations (S), and Individuals (I) T S

6. F-Coefficients
Combine different sources of reduction in expected heterozygosity into one equation:
Overall deviation from H-W expectations
Deviation due to subpopulation differentiation
Deviation due to inbreeding within populations

7. F-Coefficients and IBD
View F-statistics as probability of Identity by Descent for different samples
Probability of IBD within an individual
Overall probability of IBD
Probability of IBD for 2 individuals in a subpopulation

8. F-Statistics Can Measure Departures from Expected Heterozygosity Due to Wahlund Effect
where HT is the average expected heterozygosity in the total population
HS is the average expected heterozygosity in subpopulations
HI is observed heterozygosity within a subpopulation

9. Recessive allele for flower color
Calculating FST
Recessive allele for flower color
B2B2 = white; B1B1 and B1B2 = dark pink
Subpopulation 1:
F(white) = 10/20 = 0.5
F(B2)1 = q1= = 0.707
p1= = 0.293
White: 10, Dark: 10
Subpopulation 2:
F(white)=2/20=0.1
F(B2)2 = q2 = = 0.32
p2 = = 0.68
White: 2, Dark: 18

10. Calculating FST Calculate Average HE of Subpopulations (HS)
For 2 subpopulations:
HS = Σ2piqi/2 = (2(0.707)(0.293) + 2(0.32)(0.68))/2
HS= 0.425
Calculate Average HE of Subpopulations (HS)
White: 10, Dark: 10
Calculate Average HE for Merged Subpopulations (HT):
F(white) = 12/40 = 0.3
q = 0.3 = 0.55; p=0.45
HT = 2pq = 2(0.55)(0.45)
HT = 0.495
White: 2, Dark: 18

11. Bottom Line: FST = (HT-HS)/HT = (0.495 - 0.425)/ 0.495 = 0.14
14% of the total variation in flower color alleles is due to variation among populations
AND
Expected heterozygosity is increased 14% when subpopulations are merged (Wahlund Effect)
White: 10, Dark: 10
White: 2, Dark: 18

12. Nei's Gene Diversity: GST
Nei's generalization of FST to multiple, multiallelic loci
Where HS is mean HE of m subpopulations, calculated for n alleles with frequency of pj
Where pj is mean allele frequency of allele j over all subpopulation

13. Unbiased Estimate of FST
Weir and Cockerham's (1984) Theta
Compensates for sampling error, which can cause large biases in FST or GST (e.g., if sample represents different proportions of populations)
Calculated in terms of correlation coefficients
Calculated by FSTAT software:
Goudet, J. (1995). "FSTAT (Version 1.2): A computer program to calculate F- statistics." Journal of Heredity 86(6):
Often simply referred to as FST in the literature
Weir, B.S. and C.C. Cockerham Estimating F-statistics for the analysis of population structure. Evolution 38:

14. Linanthus parryae population structure
Annual plant in Mojave desert is classic example of migration vs drift
Allele for blue flower color is recessive
Use F-statistics to partition variation among regions, subpopulations, and individuals
FST can be calculated for any hierarchy:
FRT: Variation due to differentiation of regions
FSR: Variation due to differentiation among subpopulations within regions
Schemske and Bierzychudek 2007 Evolution

15. Linanthus parryae population structure

16. Hartl and Clark 2007

17. FST as Variance Partitioning
Think of FST as proportion of genetic variation partitioned among populations
where V(q) is variance of q across subpopulations
Denominator is maximum amount of variance that could occur among subpopulations

18. Analysis of Molecular Variance (AMOVA)
Analogous to Analysis of Variance (ANOVA)
Use pairwise genetic distances as ‘response’
Test significance using permutations
Partition genetic diversity into different hierarchical levels, including regions, subpopulations, individuals
Many types of marker data can be used
Method of choice for dominant markers, sequence, and SNP

19. Phi Statistics from AMOVA
Correlation of random pairs of haplotypes drawn from a region relative to pairs drawn from the whole population (FRT)
Correlation of random pairs of haplotypes drawn from an individual subpopulation relative to pairs drawn from a region (FSR)
Correlation of random pairs of haplotypes drawn from an individual subpopulation relative to pairs drawn from the whole population (FST)

20. What if you don’t know how your samples are organized into populations (i.e., you don’t know how many source populations you have)? What if reference samples aren’t from a single population? What if they are offspring from parents coming from different source populations (admixture)?

21. What’s a population anyway?

22. Defining populations on genetic criteria
Assume subpopulations are at Hardy-Weinberg Equilibrium and linkage equilibrium
Probabilistically ‘assign’ individuals to populations to minimize departures from equilibrium
Can allow for admixture (individuals with different proportions of each population) and geographic information
Bayesian approach using Monte-Carlo Markov Chain method to explore parameter space
Implemented in STRUCTURE program:
Londo and Schaal 2007 Mol Ecol 16:4523

23. Example: Taita Thrush data*
Three main sampling locations in Kenya
Low migration rates (radio-tagging study)
155 individuals, genotyped at 7 microsatellite loci
Slide courtesy of Jonathan Pritchard

29. Posterior probability of K
Estimating K
Structure is run separately at different values of K. The program computes a statistic that measures the fit of each value of K (sort of a penalized likelihood); this can be used to help select K.
Assumed value of K
Posterior probability of K
12345
~ ~
Taita thrush data

30. Another method for inference of K
The K method of Evanno et al. (2005, Mol. Ecol. 14: ):
Eckert, Population Structure, 5-Aug

31. Inferred population structure
Africans Europeans MidEast Cent/S Asia Asia Oceania America
Each individual is a thin vertical line that is partitioned into K colored segments according to its membership coefficients in K clusters.
Rosenberg et al Science 298:

32. Inferred population structure – regions
Rosenberg et al Science 298: