Lecture 20 Introduction to Neutral Theory November 5

Lecture 20: Introduction to Neutral Theory November 5, 2012

Announcements Classes related to Population Genetics/Genomics next semester: BIOL 493 S SPTP: Next Generation Biology CRN 18190, 1 credit, Tues 13: 00 -13: 50 BIOL 321 Genomics 2 credits required, Total Science Experience Lab: Module, CRN 18084. W 13: 00 -15: 50 (capstone) (special permission limit 12 students)

Last Time u. Mutation introduction u. Mutation-reversion equilibrium u. Mutation and selection u. Mutation and drift

Today u. Introduction to neutral theory u. Molecular clock u. Expectations for allele frequency distributions under neutral theory

Classical-Balance u Fisher focused on the dynamics of allelic forms of genes, importance of selection in determining variation: argued that selection would quickly homogenize populations (Classical view) u Wright focused more on processes of genetic drift and gene flow, argued that diversity was likely to be quite high (Balance view) u Problem: no way to accurately assess level of genetic variation in populations! Morphological traits hide variation, or exaggerate it.

Molecular Markers u Emergence of enzyme electrophoresis in mid 1960’s revolutionized population genetics u Revealed unexpectedly high levels of genetic variation in natural populations u Classical school was wrong: purifying selection does not predominate u Initially tried to explain with Balancing Selection u Deleterious homozygotes create too much fitness burden for m loci

The rise of Neutral Theory u Abundant genetic variation exists, but perhaps not driven by balancing or diversifying selection: selectionists find a new foe: Neutralists! u Neutral Theory (1968): most genetic mutations are neutral with respect to each other u Deleterious mutations quickly eliminated u Advantageous mutations extremely rare u Most observed variation is selectively neutral u Drift predominates when s<1/(2 N)

Infinite Alleles Model (Crow and Kimura Model) u Each mutation creates a completely new allele u Alleles are lost by drift and gained by mutation: a balance occurs u Is this realistic? u Average human protein contains about 300 amino acids (900 nucleotides) u Number of possible mutant forms of a gene: If all mutations are equally probable, what is the chance of getting same mutation twice?

Infinite Alleles Model (IAM: Crow and Kimura Model) u Homozygosity will be a function of mutation and probability of fixation of new mutants Probability of sampling same allele sampling two alleles twice identical by descent due to inbreeding in ancestors Probability neither allele mutates

Expected Heterozygosity with Mutation-Drift Equilibrium under IAM u At equilibrium ft = ft-1=feq u Previous equation reduces to: Ignoring 2μ Ignoring μ 2 u Remembering that H=1 -f: 4 Neμ is called the population mutation rate, also referred to as θ

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

Equilibrium Heterozygosity under IAM u Frequencies of individual alleles are constantly changing u Balance between loss and gain is maintained u 4 Neμ>>1: mutation predominates, new mutants persist, H is high 2 Fraser et al. 2004 PNAS 102: 1968 u 4 Neμ<<1: drift dominates: new mutants quickly eliminated, H is low

Stepwise Mutation Model u Do all loci conform to Infinite Alleles Model? u Are mutations from one state to another equally probable? u Consider microsatellite loci: small insertions/deletions more likely than large ones? SMM: IAM:

Which should have higher produce He, the Infinite Alleles Model, or the Stepwise Mutation Model, given equal Ne and μ? SMM: IAM: Plug numbers into the equations to see how they behave. e. g, for Neμ = 1, He = 0. 66 for SMM and 0. 8 for IAM

Expected Heterozygosity Under Neutrality u Direct assessment of neutral theory based on expected heterozygosity if neutrality predominates (based on a given mutation model) u Allozymes show lower heterozygosity than expected under strict neutrality Observed u Why? Avise 2004

Neutral Expectations and Microsatellite Evolution u Comparison of Neμ (Θ) for 216 microsatellites on human X chromosome versus 5048 autosomal loci Ø Only 3 X chromosomes for every 4 autosomes in the population Why is Θ higher for Ø Ne of Xautosomes? expected to be 25% less than Ne of autosomes: θX/θA=0. 75 u Observed ratio of ΘX/ΘA was 0. 8 for Infinite Alleles Model and 0. 71 for Stepwise model Autosomes X X chromosome Correct model for microsatellite evolution is a combination of IAM and Stepwise

Sequence Evolution u DNA or protein sequences in different taxa trace back to a common ancestral sequence u Divergence of neutral loci is a function of the combination of mutation and fixation by genetic drift u Sequence differences are an index of time since divergence

Molecular Clock u If neutrality prevails, nucleotide divergence between two sequences should be a function entirely of mutation rate Probability of creation of new alleles Probability of fixation of new alleles u Time since divergence should therefore be the reciprocal of the estimated mutation rate Expected Time Until Fixation of a New Mutation: Since μ is number of substitutions per unit time

Variation in Molecular Clock u If neutrality prevails, nucleotide divergence between two sequences should be a function entirely of mutation rate u So why are rates of substitution so different for different classes of genes?

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

Fate of Alleles in Mutation-Drift Balance Generations from birth to fixation Time between fixation events u 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 Highest on H average at E? What will this depend upon? any given time? Neutrality Balancing Selection/Overdomina nce

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? Number of Alleles A. B. 10 C. 8 6 4 2 2 4 6 8 10 Number of Observations of Allele 2 4 6 8 10

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

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 2 N alleles is: Example: Expected number of alleles in a sample of 4: