Lecture 21: Tests for Departures from Neutrality November 9, 2012

uIntroduction to neutral theory uMolecular clock uExpectations for allele frequency distributions under neutral theory Last Time

Today uSequence data and quantification of variation  Infinite sites model  Nucleotide diversity (π) uSequence-based tests of neutrality  Ewens-Watterson Test  Tajima’s D  Hudson-Kreitman-Aguade  Synonymous versus Nonsynonymous substitutions  McDonald-Kreitman

Expected Heterozygosity with Mutation-Drift Equilibrium under IAM uAt equilibrium: uRemembering that H = 1-f: set 4Neμ = θ

Allele Frequency Distributions uNeutral theory allows a prediction of frequency distribution of alleles through process of birth and demise of alleles through time uComparison of observed to expected distribution provides evidence of departure from Infinite Alleles model uDepends on f, effective population size, and mutation rate Hartl and Clark 2007 Black: Predicted from Neutral Theory White: Observed (hypothetical)

Ewens Sampling Formula. Probability the i-th sampled allele is new given i alleles already sampled: Probability of sampling a new allele on the first sample: Probability of observing a new allele after sampling one allele: Probability of sampling a new allele on the third and fourth samples: Expected number of different alleles (k) in a sample of 2N alleles is: Example: Expected number of alleles in a sample of 4: Population mutation rate: index of variability of population:

Ewens Sampling Formula uPredicts number of different alleles that should be observed in a given sample size if neutrality prevails under Infinite Alleles Model  Small θ, E(n) approaches 1  Large θ, E(n) approaches 2N uθ can be predicted from number of observed alleles for given sample size uCan also predict expected homozygosity (f e ) under this model where E(n) is the expected number of different alleles in a sample of N diploid individuals, and  = 4N e .

Ewens-Watterson Test uCompares expected homozygosity under the neutral model to expected homozygosity under Hardy- Weinberg equilibrium using observed allele frequencies  Comparison of allele frequency distributions uf e comes from infinite allele model simulations and can be found in tables for given sample sizes and observed allele numbers

Ewens-Watterson Test Example uDrosophila pseudobscura collected from winery uXanthine dehydrogenase alleles u15 alleles observed in 89 chromosomes uf HW = uGenerated f e by simulation: mean fefe Hartl and Clark 2007 How would you interpret this result?

Most Loci Look Neutral According to Ewens-Watterson Test Expected Homozygosity f e Hartl and Clark 2007

DNA Sequence Polymorphisms uDNA sequence is ultimate view of standing genetic variation: no hidden alleles  Is this really true?  What about back mutation? uSignatures of past evolution are contained in DNA sequence uNeutral theory presents null model uDepartures due to:  Selection  Demographic events -Bottlenecks, founder effects -Population admixture

Sequence Alignment uNecessary first step for comparing sequences within and between species uMany different algorithms  Tradeoff of speed and accuracy

Quantifying Divergence of Sequences uNucleotide diversity (π) is average number of pairwise differences between sequences where N is number of sequences in sample, p i and p j are frequency of sequences i and j in the sample, and π ij is the proportion of sites that differ between sequences i and j

Sample Calculation of π A->B, 1 difference A->C, 1 difference B->C, 2 differences A B C On average, there are polymorphisms per kb between pairs of haplotypes in the population

Tajima’s D Statistic uInfinite Sites Model: each new mutation affects a new site in a sequence uExpected number of polymorphic sites in all sequences: where m is length of sequence, and where n is number of different sequences compared

Sample Calculation of θ S Two polymorphic sites S= A B C

Tajima’s D Statistic uTwo different ways of estimating same parameter: uDeviation of these two indicates deviation from neutral expectations where V(d) is variance of d

Tajima’s D Expectations uD=0: Neutrality uD>0  Balancing Selection: Divergence of alleles (π) increases OR  Bottleneck: S decreases uD<0  Purifying or Positive Selection: Divergence of alleles decreases OR  Population expansion: Many low frequency alleles cause low average divergence

Balancing Selection Balancing selection   ‘balanced’ mutation Neutral mutation Slide adapted from Yoav Gilad  Should increase nucleotide diversity (  )  Decreases polymorphic sites (S) initially.  D>0

Recent Bottleneck  Rare alleles are lost  Polymorphic sites (S) more severely affected than nucleotide nucleotide diversity (  )  D>0 Standard neutral model

Positive Selection and Purifying Selection sweep  S S Slide adapted from Yoav Gilad Advantageous mutation Neutral mutation  Should decrease both nucleotide diversity (  ) and polymorphic sites (S) initially.  S recovers due to mutation   recovers slowly: insensitive to rare alleles  D<0  s  s s Time recovery

Standard neutral model Often two main haplotypes, some rare alleles Rapid Population Growth will also result in an excess of rare alleles even for neutral loci Slide adapted from Yoav Gilad Time Rapid population size increase Most alleles are rare  Most alleles are rare  Nucleotide diversity (  ) depressed  Polymorphic sites (S) unchanged or even enhanced : 4N e μ is large  D<0

How do we distinguish these two forms of divergence (selection vs demography)?

Hudson-Kreitman-Aguade Test uDivergence between species should be of same magnitude as variation within species uProvides a correction factor for mutation rates at different sites uComplex goodness of fit test uPerform test for loci under selection and supposedly neutral loci

Polymorphism Divergence Neutral LocusTest Locus A /20 ≈ 3/8 Slide adapted from Yoav Gilad Hudson-Kreitman-Aguade (HKA) test Polymorphism: Variation within species Divergence: Variation between species

Polymorphism Divergence Neutral LocusTest Locus B /20 >> 3/19 Slide adapted from Yoav Gilad Hudson-Kreitman-Aguade (HKA) test Conclusion: polymorphism lower than expected in Test Locus B: Selective sweep?

Mauricio 2001; Nature Reviews Genetics 2, 376 TeosinteMaizeMaize w/TBR mutation

HKA Example: Teosinte Branched uLab exercise: test Teosinte-Branched Gene for signature of purifying selection in maize compared to Teosinte relative uCompare to patterns of polymorphism and diversity in Alchohol Dehydrogenase gene