Lecture 20 : Tests of Neutrality November 6, 2015

Last Time Mutation and selection Infinite alleles and stepwise mutation models Introduction to neutral theory

Today Sequence data and quantification of variation Infinite sites model Nucleotide diversity (π) Sequence-based tests of neutrality Ewens-Watterson Test Tajima’s D Hudson-Kreitman-Aguade Synonymous versus Nonsynonymous substitutions McDonald-Kreitman nov6_neutraltest

The main power of neutral theory is it provides a theoretical expectation for genetic variation in the absence of selection.

Equilibrium Heterozygosity under IAM Frequencies of individual alleles are constantly changing Balance between loss and gain is maintained 4Neμ>>1: mutation predominates, new mutants persist, H is high 4Neμ<<1: drift dominates: new mutants quickly eliminated, H is low

Effects of Population Size on Expected Heterozgyosity Under Infinite Alleles Model (μ=10-5) Rapid approach to equilibrium in small populations Higher heterozygosity with less drift

Fate of Alleles in Mutation-Drift Balance Generations from birth to fixation Time between fixation events Time to fixation of a new mutation is much longer than time to loss

Fate of Alleles in Mutation-Drift-Selection Balance Purifying Selection Which case will have the most alleles on average at any given time? Highest HE? What will this depend upon? Neutrality Balancing Selection/Overdominance

Number of Observations of Allele Assume you take a sample of 100 alleles from a large (but finite) population in mutation-drift equilibrium. What is the expected distribution of allele frequencies in your sample under neutrality and the Infinite Alleles Model? A. Number of Observations of Allele Number of Alleles 2 4 6 8 10 B. 2 4 6 8 10 C. 2 4 6 8 10

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

Ewens Sampling Formula Population mutation rate: index of variability of population: 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:

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

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

Ewens-Watterson Test Example Drosophila pseudobscura collected from winery Xanthine dehydrogenase alleles 15 alleles observed in 89 chromosomes fHW = 0.366 Generated fe by simulation: mean 0.168 fe Hartl and Clark 2007 How would you interpret this result?

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

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

Sequence Alignment Necessary first step for comparing sequences within and between species Many different algorithms Tradeoff of speed and accuracy

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

Sample Calculation of π 5 10 15 20 25 30 35 A B C A->B, 1 difference A->C, 1 difference B->C, 2 differences On average, there are 18.67 polymorphisms per kb between pairs of haplotypes in the population

Tajima’s D Statistic Infinite Sites Model: each new mutation affects a new site in a sequence Expected 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 S 5 10 15 20 25 30 35 A B C Two polymorphic sites S=2

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

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

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

Standard neutral model 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 recovery  S  s Time 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 Slide adapted from Yoav Gilad

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

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