Lecture 13: Population Structure October 8, 2012.

Lecture 13: Population Structure

October 8, 2012

Last Time

Effective population size calculations

Historical importance of drift: shifting balance or noise?

Population structure

Today Course feedback

The F-Statistics

Sample calculations of FST

Defining populations on genetic criteria

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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)

TS

F-Coefficients

Combine different sources of reduction in expected heterozygosity into one equation:

)1)(1(1 ISSTIT FFF Deviation due to subpopulation differentiation

Overall deviation from H-W expectations

Deviation due to inbreeding within populations

F-Coefficients and IBD

View F-statistics as probability of Identity by Descent for different samples

)1)(1(1 ISSTIT FFF

Overall probability of IBD

Probability of IBD for 2 individuals in a subpopulation

Probability of IBD within an individual

F-Statistics Can Measure Departures from Expected Heterozygosity Due to Wahlund Effect

S

ISIS H

HHF

T

ITIT H

HHF

T

STST H

HHF

where

HT is the average expected heterozygosity in the total

population

HI is observed heterozygosity

within a subpopulation

HS is the average expected

heterozygosity in subpopulations

Calculating FST

Recessive allele for flower color

White: 10, Dark: 10

White: 2, Dark: 18

B2B2 = white; B1B1 and B1B2 = dark pink

Subpopulation 1:

F(white) = 10/20 = 0.5

F(B2)1 = q1= 0.5 = 0.707

p1=1-0.707 = 0.293

Subpopulation 2:

F(white)=2/20=0.1

F(B2)2 = q2 = 0.1 = 0.32

p2 = 1-0.32 = 0.68

Calculating FST

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

White: 2, Dark: 18

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

Bottom Line:

White: 10, Dark: 10

White: 2, Dark: 18

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)

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

T

STST H

DG

)1(1

1 1

2

m

i

n

jjS p

mH

STST HHD

Where pj is mean allele frequency of allele j over all subpopulation

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:

http://www2.unil.ch/popgen/softwares/fstat.htm

Goudet, J. (1995). "FSTAT (Version 1.2): A computer program to calculate F- statistics." Journal of Heredity 86(6): 485-486.

Often simply referred to as FST in the literature

Weir, B.S. and C.C. Cockerham. 1984. Estimating F-statistics for the analysis of population structure. Evolution 38:1358-1370.

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

Linanthus parryae population structure

Hartl and Clark 2007

R

SRSR H

HHF

T

RTRT H

HHF

T

STST H

HHF

FST as Variance Partitioning Think of FST as proportion of genetic variation

partitioned among populations

qp

qVFST

)(

where

V(q) is variance of q across subpopulations

Denominator is maximum amount of variance that could occur among subpopulations

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

Phi Statistics from AMOVA

http://www.bioss.ac.uk/smart/unix/mamova/slides/frames.htm

222

2

cba

aCT

Correlation of random pairs of

haplotypes drawn from a region relative to pairs drawn

from the whole population (FRT)

22

2

cb

bSC

Correlation of random pairs of

haplotypes drawn from an individual subpopulation relative to pairs drawn

from a region (FSR)

222

22

cba

baST

Correlation of random pairs of haplotypes drawn from an individual

subpopulation relative to pairs drawn from the whole population

(FST)

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)?

What’s a population anyway?

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:

http://pritch.bsd.uchicago.edu/structure.html

Londo and Schaal 2007 Mol Ecol 16:4523

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

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.

Taita thrush data1122334455

~0 ~0 ~0 ~0 0.9930.993 0.007 0.007 0.000050.00005

Assumed Assumed value of value of KK

Posterior Posterior probability of probability of KK

Another method for inference of K

The K method of Evanno et al. (2005, Mol. Ecol. 14: 2611-2620):

Eckert, Population Structure, 5-Aug-2008 46

Inferred population structure

Each individual is a thin vertical line that is partitioned into K colored segments according to its membership coefficients in K clusters.

Africans Europeans MidEast Cent/S Asia Asia Oceania America

Rosenberg et al. 2002 Science 298: 2381-2385

Inferred population structure – regions

Rosenberg et al. 2002 Science 298: 2381-2385