Detection of domestication genes and other loci under selection

Bruce Walsh, jbwalsh@u.arizona.eduUniversity of Arizona

Depts. of Ecology & Evolutionary Biology,Molecular & Cellular Biology,

Plant Sciences,Animal Sciences,

Epidemology & Biostatistics

Search for Genes that experiencedartificial (and natural) selection

Akin in sprit to testing candidate genesfor association or using genome scans to find QTLs.

In linkage studies: Use molecular markersto look for marker-trait associations (phenotypes)

In tests for selection, use molecular markersto look for patterns of selection (patternsof within- and between-species variation)

Types of Genes that have experiencedselection in crop/animal species

Domestication genes: Alleles fixed in the courseof the initial domestication

Diversification/Improvement genes: Alleles fixed in the course of improvement following domestication.

Adaptation genes: Alleles in natural populationsresponding to natural selection on environmental conditions (candidates to transfer into elitegermplasms).

The general approaches for using sequencedata to search for signs of selection

• Tests based on pattern and amount of within-species polymorphism (departures from neutralpredictions). On-going or recent selection

• Tests based on polymorphism plus betweenspecies divergence. On-going or recent selection

• Tests based on phylogenetic comparisons betweenspecies. Historical selection (won’t discuss these further)

Key: Use of features of variation at a markerlocus to test for departures from strict neutrality

A quick review of the neutral theory(expected patterns of variation under drift)

• Drift and the coalescence process (its about time)

• Mutation-drift equilibrium (within-populationvariation). Function of population size andmutation rate. Expected variation = H = 4Ne

• Divergence between populations (between-population variation). Function of time and mutation rate (but not population size), d = 2t

Mutation-Drift Equilibrium (Single Loci)Drift removes variation, while mutationintroduces it. Thus, an equilibrium amountof genetic variance results

While alleles change over time, heterozygosity remains roughly constant.

A very powerful way of thinking about driftis the Coalescent Process

Instead of following alleles, think in termsof lineages.

As a consequence of drift, eventually allcurrent copies of alleles trace back to asingle ancestral lineage.

Hence, the current lineages coalesce asone moves back in time

From coalescent theory, the expectedtime back to the MRCA is 2N generations

Hence, for two randomly-chosen sequences,the expected number of mutations theydiffer by is just

2t = 2(2N) = 4N

If 4N>> 1, two random sequences will typically differ (and hence be heterozygotes)If 4N<< 1, two random sequences will typically differ (and hence be homozygotes)

Divergence Between Populations

Mutation and drift also generate a between-line variance, i.e., a population divergence

As lines separate, the initial heterozygosity israndomly partitioned, creating a between-linevariance.

More importantly, as new mutations arise in theseparated lines, some of these are fixed bydrift, and this drives a constant divergencebetween populations

One average, for a population of size N,2N mutations arise each generation

For any of these, their probability of fixationis just U(1/[2N]) = 1/(2N)

Hence, the rate at which new mutations arefixed within a line is just (# new per generation)*Pr(fixation)

2N1/(2N) =

Hence, divergence d(t) after t generations isjust d(t) = t

Independent of population size!

The major results from mutation-drift equilibrium

Within-population variation: 4Neu

Rate of divergence/generation: u

Between-population variation: 2tu

Logic behind polymorphism-based tests

Key: Time to MRCA relative to drift

If a locus is under positive selection, morerecent MRCA (shorter coalescent)

If a locus is under balancing selection, older MRCA relative to drift (deeper coalescent)

Shorter coalescent = lower levels of variation,longer blocks of disequilibrium

Deeper coalescent = higher levels of variation,shorter blocks of disequilibrium

Balancingselection

Selective Sweep

Neutral

Time

Present

Past

Longer timeback to MRCA

Shorter timeback to MRCA

Selection changes to coalescent times

Time to MRCAfor the individuals

sampled

Selective sweeps result in a local decreasein Ne around the selective site

This results in a shorter time to MRCA anda decrease in the amount of polymorphism

Note that this has no effect on the rateof divergence of neutral sites , as this is independent on Ne.

Conversely, balancing selection increasesthe effective population size, increasingthe amount of polymorphism

A scan of levels of polymorphism can thussuggest sites under selection

Directional selection(selective sweep)

Balancing selection

Local region withreduced mutation rate

Local region withelevated mutation rate

Map location

Map location

Vari

ati

on

Vari

ati

on

Example: maize domestication gene tb1

Major changes in plant architecture in transition from teosinte to maize

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

Doebley lab identified a gene, teosinite branched 1, tb1, involved in many of thesearchitectural changes

Wang et al. (1999) observed a significant decrease in genetic variation in the 5’ NTR region of tb1,suggesting a selective sweep influenced this region. The sweep did not influence the coding region.

Wang et al (1999) Nature 398: 236.

Clark et al (2004) examined the 5’ tb1 regionin more detail, finding evidence for asweep influencing a region of 60 - 90 kb

Clark et al (2004) PNAS 101: 700.

Wang et al. and Clark et al. controlled forthe reduction in neutral polymorphisms beingdue simply to reduced mutation rate byusing a close relative (teosinte) as a control.

The process of domestication itself is expectedto reduce variation genome-wide because ofthe population bottleneck that is typicallyinduced during domestication. In maize, thebackground level of polymorphism (genome wide)is only about 75% of that of teosinte.

Estimating strength of selectionfrom size of sweep region

Kaplan, Hudson, and Langley (1989) showed that thedistance d at which a neutral site can be influenced bya sweep is a function of the strength of selection s andthe recombination fraction c, with d ~ 0.01 s/c.For tb1, s -> 0.05.

Hence, s = 100 . d . c

With s in hand, one can also estimate the expectedtime for selection to fix the allele, which Wang et al.estimated at 300 to 1000 years, indicating a fairly longperiod of domestication.

“Sticky” (glutinous) rice results from low amylose levels, and are typical of temperate japonica varietygroups.

Example: Waxy gene in Rice (Olsen et al. 2006)

A number of groups showed this is due to a splice mutant in the Waxy gene. This is an example of animprovement (as opposed to domestication) gene

Olsen et al. observed a region 250kb in size aroundWaxy with a greatly reduced level of polymorphismcompared to control populations.

Using the Kaplan et al expression, this gives s = 4.6!

While the sweep around tb1 did not even influence the coding region of that gene, the Waxy sweep covers 39 rice genes!

One evolutionary consequence of a sweep is thatthe reduction in population size (that produces the signal of a sweep) also reduces the efficiency of selection on linked genes within the region (the Hill-Robertson effect)

Deleterious alleles have a higher probabilityof fixation

Favorable alleles have a reduced probabilityof fixation.

Accumulation of Deleterious mutations in domesticated rice genomes?

Lu et al (2006) compared the genomes of Oryza sativa ssp. indica and japonica with their ancestral relative O. rufipogon.

The Ka/Ks (ratio of the substitution rate of non-synonymous to synonymous changes) was much higher for indica vs. japonica (0.498) than for domesticated vs. wild rice (japonica vs. rufipogin, 0.259)

Lu et al suggest that roughly 25% of the amino acid differencesbetween indica and japonica are deleterious.

They suggest that excessive reductions in Ne due to selective-sweeps covering much of the genome during selection for domestication greatly reduced the efficiency of natural selectionin removing deleterious alleles.

Formal tests of selection• Tajima’s D. Requires: single-locus, within-population polymorphism data

• McDonald-Kreitman Test. Requires:coding region, data from 2 species (within-population variation, btw species divergence)

• Hudson-Kreitman-Aguade (HKA) test.Requires: at least two loci, data from 2 species (within-population variation, btw species divergence)

• Allele frequency vs. LD tests. Requires: densemarker scan around a single-locus usingwithin-population data

Tests based on Within-Population Variation

Two sequence evolution frameworks are typically used:infinite alleles vs. infinite sites.

These tend to compare different measures of variation (such as number of alleles vs. pair-wise distances among alleles)

Both assume each new mutation generates a new (unique)sequence. (such is not the case for STRs)

How do these frameworks differ?

A A G A C C

A A G G C C

A A G A C C

A A G G C C

A A G G C A

Consider the following five sequences

Infinite alleles: Treat eachdifferent haplotype as adifferent allele (look at rows)

Here, there are three alleles

1

1

2

2

3

Infinite sites model: Treat each site (baseposition) separately. How many polymorphicsites are there? (look over columns)

Here, 2 polymorphic sites

* *

Two typical classes of departures are seen with polymorphism data

2: An excess of intermediate frequency alleles, adeficiency of rare alleles (alleles older than expected)

1: An excess of rare alleles, a deficiency of intermediate frequency alleles (alleles younger than expected)

Pattern 1 expected under a selective sweep, whencoalescent times are shorter than expected

Pattern 2 expected under balancing selection, whencoalescent times are longer than expected

Summary Statistics for Infinite Sites Model

The key parameter is = 4Ne

• S, number of segregating sites. E(S) = an

• k, average number of pairwise differences . E(k) =

• , number of singletons. E() = n/(n-1)

Xan =

n °1

i=1

1i

bS =San

; bk = k; b¥ =n ° 1

n¥

These suggest the following three estimates for :

Tajima’s D test

One of the first, and most popular, polymorphismtests was Tajima’s D test (Tajima 1989)

D contrasts estimates of based on S vs. k

Idea: For S we simply count sites, independent oftheir frequencies. Hence, S rather sensitiveto changes in the frequency of rare alleles.

D =bk ° bS

pÆDS +ØDS2

On the other hand, k is a more frequency-weighted measure, and hence more sensitiveto changes in the frequency of intermediatealleles.

D < 0: too many rare alleles. Selective sweepor population expansion. MRCA more recentthan expected.

D > 0: too many intermediate-frequency alleles. Balancing selection or population subdivision. MRCA more ancient than expected.

D is a test whether the amount of polymorphism is consistent with the number of polymorphisms

Under selective sweeps/population expansion,heterozygosity should be significantly lessthan predicted from number of polymorphisms

Major Complication With Polymorphism-based tests

Demographic factors can also cause thesedepartures from neutral expectations!

Too many young alleles -> recent populationexpansion

Too many old alleles -> population substructure

Thus, there is a composite alternative hypothesis,so that rejection of the null does not imply selection.Rather, selection is just one option.

Can we overcome this problem?

It is an important one, as only polymorphism-based tests can indicate on-going selection

Solution: demographic events should leave aconstant signature across the genome

Essentially, all loci experience commondemographic factors

Genome scan approach: look at a large numberof markers. These generate null distribution(most not under selection), outliers = potentiallyselected loci (genome wide polymorphism tests)

Joint Polymorphism-Divergence tests

Under the neutral theory, heterozygosity is afunction of = 4Ne , while divergence isa function of t

Joint Polymorphism-Divergence tests use thesetwo different expectations to look for Concordance with neutral results.

For example, under neutrality, levels of Polymorphism and divergence should be positively correlated.

Under neutrality, the ratio of polymorphismto divergence at the i-th locus is just

Hence, for a series of neutral loci compared in the same populations, this ratio should be very similar.

H i

di=

4Neπi

2tπi=

2Ne

t

The very popular Hudson, Kreitman and Aguade (1987), or HKA test, is based on thisidea, with one using a series of controlled(neutral) loci to contrast with the locus ofinterest.

McDonald-Kreitman Test

dsyn

drep=

2tπsyn

2tπrep=

πsyn

πrep

Hsyn

Hrep=

4Neπsyn

4Neπrep=

πsyn

πrep

One of the most straight-forward tests of selection that jointly uses divergence and polymorphism data was proposed by McDonald and Kreitman (1991)

Consider the replacement & synonymous sitesat a single locus.

These ratios have the same expected value

Since these ratios have the same expectedvalue, the McDonald-Kreitman test proceedsvia a simple contingency table contrastingpolymorphism vs. divergence at replacementvs. synonymous sites.

Key feature: The McDonald-Kreitman testis NOT affected by demography

Fixed Polymorphic

Replacement 7 2

Synonymous 17 42

Example: McDonald & Kreitman looked at the ADH(Alcohol dehydrogease) loci in D. melanogaster &D. simulans.

24 fixed differences occur, 7 replacement, 17synonymous

44 polymorphisms, 2 replacement, 42 synonymous, giving

Fisher’s exact test gives p =0.0073

Linkage Disequilibrium (LD)

LD arises when allele frequencies alone cannotpredict gametic (i.e. chromosomal) frequencies,Freq(AB) = freq(A)*freq(B)

When a new mutation appears, it starts in complete LD with the haplotype within which it arose,

D = Freq(AB) - freq(A)*freq(B),D(t) = (1-c)t D(0)

Over time, recombination decays away much of thisblock of LD.

Starting haplotype

Under pure drift, high-frequency alleles should have short haplotypes

time

freq

Linkage Disequilibrium Decay

One feature of a selective sweep are derived allelesat high frequency. Under neutrality, older allelesare at higher frequencies.

Sabeti et al (2002) note that under a sweep such highfrequency young alleles should (because of their recentage) have much longer regions of LD than expected.

Wang et al (2006) proposed a Linkage Disequilibrium Decay, or LDD, test looks for excessive LD for high frequency alleles

Wang et. al used this approach with 1.6 million human SNPs, finding that 1.6% of the markers showed some signatures of positive selection.

Simulation studies by Wang et al. showed that theLDD test effectively distinguishes selection frompopulation bottlenecks and admixture.

All genome-based tests have an important caveat.

The large number of markers used are typicallygenerated by looking for polymorphisms in a verysmall, and often not very ethnically-diverse, sample

Results in a strong ascertainment bias, for example,an excess of intermediate-frequency markers

If such biases are not accounted for, they can skew test results.

Caveats and Unanswered Questions

• Even if they have experienced very strong selection, domestication genes may not leavea strong signal at linked neutral markers.

Must be sufficient background variation for the chance of a sweep being detected.

Hamblin et al. (2006) found that the genome-widebackground variation in Sorghum is too low to reliablydetect signatures of selection. Likely from extremebottleneck during domestication.

If the ancestral species itself had low variation, wouldalso be very difficult to detect selective sweeps.

• A more subtle complication results from the frequencyof favorable alleles at the start of the domesticationprocess

A typical adaptive selective sweep is generallythought to occur following the introduction of asingle favorable new mutation. Hence, only onefounding haplotype at the time of selection.

Selection on domestication alleles is akin to a suddenshift in the environment, with many of these allelespre-existing in the population before domestication

If the frequency of any such an allele is > 0.05, multiplehaplotypes are likely present, resulting in considerable variation around the selective site even after fixation,and hence a very weak (if any) signal.

Hence, there is the very real possibilitythan many important domestication geneswill not have left a detectable signature inthe pattern of linked neutral variation.

Optimal conditions for detecting selection

High levels of polymorphism at the start of selection

High effective levels of recombination givesa shorter window around the selective site

High levels of selfing reduces the effective recombination rate (eg. Maize vs. rice)

Signatures of sweeps persist for roughly Ne generations

Domestication vs. improvement genes

• Domestication genes will leave a signal in all lines,while improvement genes may leave a live-specificsignal

Unresolved question: Is selection strongeron domestication or improvement genes?

Maize: Domestication gene tb1: 90kb sweep, s = 0.05 Improvement gene Y1: 600kb sweep, s = 1.2

Summary

Linkage mapping vs. detection of selected loci

Linkage: Know the target phenotype

Selection: Don’t know the target phenotype

Both can suffer from low power and confoundingfrom demographic effects

Both can significantly benefit from high-densitygenomic scans, but these are also not without problems.

QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.

U of A Campus

Farewell from the “desert”

Searches for regions under selection complement standard linkage-based approaches for QTL detection (line-crosses, association mapping)

Using QTL approaches to find domestication genesrequires making crosses of wild progenitor x domesticated lines.

Localizing adaptation genes to a particular environment via a standard QTL cross very difficult, as one would miss potential pathways to adaptation by focusing only candidatephenotypes thought of by the investigator.

If Ne is the effective population size and the mutation rate, Crow & Kimura showedthe equilibrium heterozygosity is given by

H =4Neπ

4Neπ +1

Thus, H is simply a product of population sizeand mutation rate. The parameter 4Neisa fundamental one in molecular evolution andoften denoted by .

Genome-Wide Polymorphism TestsAs mentioned, general problem with polymorphismtests is that demographic signals can also give the samepattern as selection.

Cavalli-Sforza (1966) was among the first to note thatdemography effects all genomic locations (roughly)equally, while the effects of selection are unique toa particular locus

With the advent of very dense marker sets, we arenow seeing genome-wide scans over all markers.

Idea: Most are not under selection and hence reflectthe common demographic features. Outliers against thispattern suggest selection.

MRCA = most recentCommon ancestor

Coalescent theory provides an easy way to see why 4Ne appears.

For two randomsequences within a population, t =

2Ne

giving 2t = 4Ne

t mutations t mutationsExpected number of

mutations = 2t