Transcript GLYPHOSATE RESISTANCE Background / Problem

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
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
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
F-Coefficients
Combine different sources of reduction in expected
heterozygosity into one equation:
1  FIT  (1  FST )(1  FIS )
Overall
deviation
from H-W
expectations
Deviation due
to
subpopulation
differentiation
Deviation due
to inbreeding
within
populations
F-Coefficients and IBD
 View F-statistics as probability of Identity by
Descent for different samples
1  FIT  (1  FST )(1  FIS )
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
where
HT  H S
FST 
HT
HT is the average expected
HS  HI
FIS 
HS
HS is the average
HT  H I
FIT 
HT
heterozygosity in the total
population
expected heterozygosity
in subpopulations
HI is observed
heterozygosity within
a subpopulation
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= 0.5 = 0.707
White: 10, Dark: 10
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
White: 2, Dark: 18
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
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
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 White: 10, Dark: 10
populations
AND
 Expected heterozygosity is increased
14% when subpopulations are merged
(Wahlund Effect)
White: 2, Dark: 18
Nei's Gene Diversity: GST
Nei's generalization of FST to multiple, multiallelic loci
GST
DST

HT
DST  HT  H S
Where HS is mean HE of m subpopulations, calculated for n alleles
with frequency of pj
m
n
1
2
HS   (1   p j )
m i 1
j 1
HT =1- å P
2
j
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
ö
1 30 æ
2
H S = åç1- å pim ÷
30 i=1 è m=1 ø
æ
ö
1 3
2
HR =
N r ç1- å prm ÷
å
å Nr r=1 è m=1 ø
r
æ
ö
2
H T = 2 ç1- å pm ÷
è m ø
H  HS
FSR  R
HR
0.1589 - 0.1424
FSR =
= 0.1036
0.1589
HT  H R
FRT 
HT
FRT =
0.2371- 0.1589
= 0.3299
0.2371
FST 
HT  H S
HT
FST =
0.2371- 0.1424
= 0.3993
0.2371
Hartl and Clark 2007
FST as Variance Partitioning
 Think of FST as proportion of genetic variation
partitioned among populations
V (q)
FST 
pq
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
CT

 2
 a     c2
2
a
2
b
 b2
SC  2
 b   c2
Correlation of random pairs of haplotypes
drawn from an individual subpopulation
relative to pairs drawn from a region (FSR)
 
ST  2
 a   b2   c2
2
a
Correlation of random pairs of
haplotypes drawn from a region
relative to pairs drawn from the
whole population (FRT)
2
b
Correlation of random pairs of haplotypes
drawn from an individual subpopulation
relative to pairs drawn from the whole
population (FST)
http://www.bioss.ac.uk/smart/unix/mamova/slides/frames.htm
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 MonteCarlo Markov Chain method to
explore parameter space
 Implemented in STRUCTURE
program:
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.
Assumed
value of K
Taita thrush data
1
2
3
4
5
Posterior
probability of K
~0
~0
0.993
0.007
0.00005
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
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. 2002 Science 298: 2381-2385
Inferred population structure – regions
Rosenberg et al. 2002 Science 298: 2381-2385