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

Last Time uMutation introduction uMutation-reversion equilibrium uMutation and selection uMutation and drift

Today uInfinite alleles and stepwise mutation models uIntroduction to neutral theory uMolecular clock uIntroduction to phylogenetics uExam

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

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

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

Infinite Alleles Model (Crow and Kimura Model) uEach mutation creates a completely new allele uAlleles are lost by drift and gained by mutation: a balance occurs uIs this realistic? uAverage human protein contains about 300 amino acids (900 nucleotides) uNumber 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) uHomozygosity will be a function of mutation and probability of fixation of new mutants Probability of sampling same allele twice Probability of sampling two alleles identical by descent due to inbreeding in ancestors Probability neither allele mutates

Expected Heterozygosity with Mutation- Drift Equilibrium under IAM uAt equilibrium f t = f t-1 =f eq uPrevious equation reduces to: Ignoring μ 2 uRemembering that H=1-f: 4N e μ is called the population mutation rate Ignoring 2μ 4N e μ often symbolized by Θ

Equilibrium Heterozygosity under IAM uFrequencies of individual alleles are constantly changing uBalance between loss and gain is maintained u4N e μ>>1: mutation predominates, new mutants persist, H is high u4N e μ<<1: drift dominates: new mutants quickly eliminated, H is low

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

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

Which should have higher produce H e,the Infinite Alleles Model, or the Stepwise Mutation Model, given equal N e and μ? IAM:SMM: Plug numbers into the equations to see how they behave. e.g, for N e μ = 1, H e = 0.66 for SMM and 0.8 for IAM

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

Neutral Expectations and Microsatellite Evolution Comparison of N e μ (Θ) for 216 microsatellites on human X chromosome versus 5048 autosomal loci – Only 3 X chromosomes for every 4 autosomes in the population – N e of X expected to be 25% less than N e of autosomes: θ X /θ A =0.75 Autosomes X X chromosome Correct model for microsatellite evolution is a combination of IAM and Stepwise Why is Θ higher for autosomes? uObserved ratio of Θ X /Θ A was 0.8 for Infinite Alleles Model and 0.71 for Stepwise model

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

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

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

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)

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

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

Phylogenetic Tree Terms ABCDEFGHIJ ROOT interior branches node terminal branches Leaves, Operational Taxonomic Units (OTUs) Slide adapted from Marta Riutart Group, cluster, clade

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

How about these? Are these trees different?

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

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

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

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