Lecture 21 : Introduction to Neutral Theory and Phylogenetics

1. Lecture 21 : Introduction to Neutral Theory and Phylogenetics March 31, 2014

2. Last Time • Mutation introduction • Mutation-reversion equilibrium • Mutation and selection • Mutation and drift

3. Today • Infinite alleles and stepwise mutation models • Introduction to neutral theory • Molecular clock • Introduction to phylogenetics • Exam

4. 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.

5. for m loci 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

6. 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)

7. 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?

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

9. Ignoring 2μ Ignoring μ2 Expected Heterozygosity with Mutation-Drift Equilibrium under IAM • At equilibrium ft = ft-1=feq • Previous equation reduces to: • Remembering that H=1-f: 4Neμ is called the population mutation rate 4Neμoften symbolized by Θ

10. 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

11. 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

12. 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:

13. Which should have higher produce He,the Infinite Alleles Model, or the Stepwise Mutation Model, given equal Ne and μ? 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 SMM: IAM:

14. Observed Avise 2004 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?

15. 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 Θhigher 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

16. 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

17. 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

18. 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?

19. Phylogenetics • Study of the evolutionary relationships among individuals, groups, or species • Relationships often represented as dichotomous branching tree • Extremely common approach for detecting and displaying relationships among genotypes • Important in evolution, systematics, and ecology (phylogeography)

20. O G P C Q H A R S I D J T U K E V L W B X M Y F Z N Ç Evolution Slide adapted from Marta Riutart

21. O P Q R S T U V W X Y Z Ç Whatis a phylogeny? • Homology: similarity that is the result of inheritance from a common ancestor Slide adapted from Marta Riutart

22. Group, cluster, clade Leaves, Operational Taxonomic Units (OTUs) terminal branches node interior branches Phylogenetic Tree Terms A B C D E F G H I J ROOT Slide adapted from Marta Riutart

23. Bacteria 1 Bacteria 2 Bacteria 3 Eukaryote 1 Eukaryote 2 Eukaryote 3 Eukaryote 4 Bacteria 1 Bacteria 2 Bacteria 3 Eukaryote 1 Eukaryote 2 Eukaryote 3 Eukaryote 4 Tree Topology (Bacteria1,(Bacteria2,Bacteria3),(Eukaryote1,((Eukaryote2,Eukaryote3),Eukaryote4))) Slide adapted from Marta Riutart

24. Are these trees different? How about these? http://helix.biology.mcmaster.ca

25. eukaryote eukaryote eukaryote eukaryote Rooted versus Unrooted Trees archaea archaea Unrooted tree archaea Rooted by outgroup bacteria outgroup archaea Monophyletic group archaea archaea eukaryote Monophyletic group eukaryote root eukaryote eukaryote Slide adapted from Marta Riutart

26. Rooting with D as outgroup A B D A C B C G E F D G F E Slide adapted from Marta Riutart

27. A B D A C G B E C F G D E A F B C D Now with C as outgroup G F E

28. Baum et al. Which of these four trees is different?