1. Lecture 20: Introduction to Neutral Theory
November 5, 2012

2. Announcements
Classes related to Population Genetics/Genomics next semester:
BIOL 493S SPTP: Next Generation Biology CRN 18190, 1 credit, Tues 13:00-13:50
BIOL321 Total Science Experience Lab: Genomics Module, CRN W 13:00-15:50 2 credits (capstone) (special permission required, limit 12 students)

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

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

5. Classical-Balance
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)
Wright focused more on processes of genetic drift and gene flow, argued that diversity was likely to be quite high (Balance view)
Problem: no way to accurately assess level of genetic variation in populations! Morphological traits hide variation, or exaggerate it.

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

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

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

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

10. Expected Heterozygosity with Mutation-Drift Equilibrium under IAM
At equilibrium ft = ft-1=feq
Previous equation reduces to:
Ignoring 2μ
Ignoring μ2
Remembering that H=1-f:
4Neμ is called the population mutation rate,
also referred to as θ

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

12. 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 2
Fraser et al PNAS 102: 1968

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

14. Plug numbers into the equations to see how they behave.
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

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

16. Neutral Expectations and Microsatellite Evolution
Comparison of Neμ (Θ) for 216 microsatellites on human X chromosome versus 5048 autosomal loci
Only 3 X chromosomes for every 4 autosomes in the population
Ne of X expected to be 25% less than Ne of autosomes:
θX/θA=0.75
Autosomes X
Why is Θ higher for autosomes?
X chromosome
Correct model for microsatellite evolution is a combination of IAM and Stepwise
Observed ratio of ΘX/ΘA was 0.8 for Infinite Alleles Model and 0.71 for Stepwise model

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

18. Molecular Clock
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
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

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

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

21. 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

22. 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

23. 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

24. 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)

25. 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: