Lecture 14: Population structure and Population

AssignmentOctober 12, 2012

Lab 7 Update Corrected instructions for lab 7 will be posted

today

Problem 1: consider relative levels of F-statistics as well as significance from bootstrapping

Up to 3 points extra credit if problem 2 is done correctly

See lab open hours schedule on lab web page

Caveat: exams and class usage of lab

Other computers are available: see Hari or me

America

Africa

Eurasia

East Asia

Oceania

Population structure from worldwide human populationPopulation = subpopulation. Group = Regions

Lab 7 Revised Problem 1

Problem 1. File human_struc.xls contains data for 10 microsatellite loci used to genotype 41 human populations from a worldwide sample.

a.) Convert the file into Arlequin format and perform AMOVA based on this grouping of populations within regions using distance. How do you interpret these results? Report values of the phi-statistics and their statistical significance for each AMOVA you run.

b.) Do you think that any of these regions can justifiably be divided into subregions? Pick a region, form a hypothesis for what would be a reasonable grouping of populations into subregions, then run AMOVA only for the region you selected using distance measures. Was your hypothesis supported by the data?

c.) GRADUATE STUDENTS: Which of the 5 initially defined regions has the highest diversity in terms of effective number of alleles? What is your biological explanation for this?

Lab 7 Original Problem 2 (worth 8 points if you answer this). Use Structure to further test the hypotheses you developed in Problem 1.

a.) Calculate the posterior probabilities to test whether:i. All populations form a single genetically homogeneous group.ii. There are two genetically distinct groups within your selected regioniii. There are three genetically distinct groups within your selected region.

b.) Use the ΔK method to determine the most likely number of groups. How does this compare to the method based on posterior probabilities?

c.) How do the groupings of subpopulations compare to your expectations from Problem 1?

d.) Is there evidence of admixture among the groups? If so, include a table or figure showing the proportion of each subpopulation assigned to each group.

e.) GRADUATE STUDENTS: Provide a brief, literature-based explanation for the groupings you observe.

Last Time

Sample calculation of FST

Defining populations on genetic criteria: introduction to Structure

Today

Interpretation of F-statistics

More on the Structure program

Principal Components Analysis

Population assignment

FST: What does it tell us?

Degree of differentiation of subpopulations

Rules of thumb:

0.05 to 0.15 is weak to moderate

0.15 to 0.25 is strong differentiation

>0.25 is very strong differentiation

Related to the historical level of gene exchange between populations

May not represent current conditions

FST is related to life history

Seed DispersalGravity 0.446Explosive/capsule 0.262Winged/Plumose 0.079

(Loveless and Hamrick, 1984)

Successional StageEarly 0.411Middle 0.184Late 0.105

Life CycleAnnual 0.430Short-lived 0.262Long-lived 0.077

Structure Program

One of the most widely-used programs in population genetics (original paper cited >8,000 times since 2000)

Very flexible model can determine:

The most likely number of uniform groups (populations, K)

The genomic composition of each individual (admixture coefficients)

Possible population of origin

Individuals in our sample represent a mixture of K (unknown) ancestral populations.

Each population is characterized by (unknown) allele frequencies at each locus.

Within populations, markers are in Hardy-Weinberg and linkage equilibrium.

Roughly speaking, the model sorts individuals into K clusters so as to minimize departures from HWE and Linkage Equilibrium.

A simple model of population structure

Slide adapted from Jonathan Pritchard, 2007 presentation to Conservation Genetics meeting

More on the model...

Let A1, A2, …, AK represent the (unknown) allele frequencies in each subpopulation

Let Z1, Z2, … , Zm represent the (unknown) subpopulation of origin of the sampled individuals

Assuming Hardy-Weinberg and linkage equilibrium within subpopulations, the likelihood of an individual’s genotype in subpopulation k is given by the product of the relevant allele frequencies:

Where Pl is probability of observing genotype l at a particular locus in subpopulation k

Pr(Gi | Zi= k, Ak) = Pl loci

Slide adapted from Jonathan Pritchard, 2007 presentation to Conservation Genetics meeting

Probability of observing a genotype in a subpopulation

Probability of observing a genotype at locus l by chance in population is a function of allele frequencies:

for m loci

Homozygote Heterozygote

Assumes unlinked (independent loci) and Hardy-Weinberg equilibrium

If we knew the population allele frequencies in advance, then it would be easy to assign individuals.

If we knew the individual assignments, it would be easy to estimate frequencies.

In practice, we don’t know either of these, but the following MCMC algorithm converges to sensible joint estimates of both.

Slide adapted from Jonathan Pritchard, 2007 presentation to Conservation Genetics meeting

MCMC algorithm (for fixed K)

Start with random assignment of individuals to populations

Step 1: Gene frequencies in each population are estimated based on the individuals that are assigned to it.

Step 2: Individuals are assigned to populations based on gene frequencies in each population.

And this is repeated...

…Estimation of K performed separately.

Slide adapted from Jonathan Pritchard, 2007 presentation to Conservation Genetics meeting

Admixed individuals are mosaics of ancestry from the original

populations

AncestralAncestralPopulationsPopulations

Slide adapted from Jonathan Pritchard, 2007 presentation to Conservation Genetics meeting

The two basic ancestry models used by structure.

No Admixture: each individual is derived completely from a single subpopulation

Admixture: individuals may have mixed ancestry: some fraction qk of the genome of individual i is derived from subpopulation k.

The admixture model allows for hybrids, but it is more flexible and often provides a better fit for complicated structure. This is what we used in lab.

Slide adapted from Jonathan Pritchard, 2007 presentation to Conservation Genetics meeting

Notes on Estimating the Number of Subpopulations (k)

Likelihood-based method is the simplest, but likelihood often increases continuously with k

More variability at values of k beyond “natural” value

Evanno et al. (2005) method measures change in likelihood and discounts for variation

Use biological reasoning at arriving at final value

Priors based on population locations, other information

Often need to do hierarchical analyses: break into subregions and run Structure separately for each

Inferred human 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

Structure is Hierarchical: Groups reveal more substructure when examined separately

Rosenberg et al. 2002 Science 298: 2381-2385

Alternative clustering method: Principal Components Analysis

Structure is very computationally intensive

Often no clear best-supported K-value

Alternative is to use traditional multivariate statistics to find uniform groups

Principal Components Analysis is most commonly used algorithm

EIGENSOFT (PCA, Patterson et al., 2006; PloS Genetics 2:e190).

Eckert, Population Structure, 5-Aug-2008 49

Principal Components Analysis Efficient way to summarize multivariate data like

genotypes

Each axis passes through maximum variation in data, explains a component of the variation

http://www.mech.uq.edu.au/courses/mech4710/pca/s1.htm

How do we identify population of origin?

Human Population Assignment with SNP Assayed 500,000 SNP genotypes for 3,192 Europeans

Used Principal Components Analysis to ordinate samples in space

High correspondence betweeen sample ordination and geographic origin of samples

Individuals assigned to populations of origin with high accuracy

Novembre et al. 2008 Nature 456:98

Likelihood Approaches

Allow evaluation of alternative hypotheses by comparing their relative likelihoods given the evidence

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2

121 HEP

HEPEHHL

In a population assignment or forensic context, definition of the competing hypothesis is the most essential component

Population Assignment: Likelihood Assume you find skin cells and blood under

fingernails of a murder victim

Victim had major debts with the Sicilian mafia as well as the Chinese mafia

Can population assignment help to focus investigation?

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121 HGP

HGPLRGHHL

What is H1 and what is H2?

Population Assignment: Likelihood "Assignment Tests" based on allele

frequencies in source populations and genetic composition of individuals

Likelihood-Based Approaches

Calculate likelihood that individual genotype originated in particular population

Assume Hardy-Weinberg and linkage equilibria

Genotype frequencies corrected for presence of sampled individual

Usually reported as log10 likelihood for origin in given population relative to other population

Implemented in ‘GENECLASS’ program (http://www.montpellier.inra.fr/URLB/geneclass/geneclass.html)

for m loci

m

kkPP

1

2lilk pP

for homozygote AiAi in population l at locus k

ljlilk ppP 2for heterozygote AiAj in population l at locus k

Power of Population Assignment using Likelihood

Assignment success depends on:

Number of markers used Polymorphism of markers Number of possible source populations Differentiation of populations Accuracy of allele frequency estimations

Rules of Thumb (Cornuet et al. 1999) for 100% assignment success, for 10 reference populations need:

30 to 50 reference individuals per population 10 microsatellite loci HE > 0.6 FST > 0.1

Knowing what you know about human population genetics, is it worth the effort to assign our skin

sample to Asian or Sicilian populations?

Rules of Thumb (Cornuet et al. 1999) for 100% assignment success, for 10 reference populations need:

30 to 50 reference individuals per population 10 microsatellite loci HE > 0.6 FST > 0.1

Carmichael et al. 2001 Mol Ecol 10:2787

Population Assignment Example: Wolf Populations in Northwest Territories Wolf populations sampled on

island and mainland populations in Canadian Northwest Territories

Immigrants detected on mainland (black circles) from Banks Island (white circles)

Population Assignment Example:Fish Stories Fishing competition on

Lake Saimaa in Southeast Finland

Contestant allegedly caught a 5.5 kg salmon, much larger than usual for the lake

Compared fish from the lake to fish from local markets (originating from Norway and Baltic sea)

7 microsatellites

Based on likelihood analysis, fish was purchased rather than caught in lake

Lake Saimaa Market

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