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Lecture 19 : Mutation, Selection, and Neutral Theory November 2, 2015 Last Time Mutation introduction Mutation-reversion equilibrium Mutation and drift Today Mutation and selection Introduction to neutral theory Exam Mutation-Selection Balance Equilibrium occurs when creation of mutant allele is balanced by selection against that allele For a recessive mutation: 2 sq p qs 1 sq 2 At equilibrium: 2 qmu qs 0 q eq 2 s qmu p qeq sq p p 2 1 sq s assuming: 1-sq21 What is the equilibrium allele frequency of a recessive lethal with no mutation in a large (but finite) population? What happens with increased forward mutation rate from wild-type allele? How about reduced selection? qeq s Balance Between Mutation and Selection Recessive lethal allele with s=0.2 and μ=10-5 Muller’s Ratchet Deleterious mutations accumulate in haploid or asexual lineages Driving force for evolution of recombination and sex Question: Do most mutations cause reduced fitness? Why or why not? Relative Abundance of Mutation Types Most mutations are neutral or ‘Nearly Neutral’ A smaller fraction are lethal or slightly deleterious (reducing fitness) A small minority are advantageous Types of Mutations (Polymorphisms) Synonymous versus Nonsynonymous SNP First and second position SNP often changes amino acid UCA, UCU, UCG, and UCC all code for Serine Third position SNP often synonymous Majority of positions are nonsynonymous Not all amino acid changes affect fitness: allozymes Nuclear Genome Size Size of nuclear genomes varies tremendously among organisms Weak association with organismal complexity, especially within kingdoms Arabidopsis thaliana Poplar Rice Maize Barley Hexaploid wheat Fritillaria (lilly family) 120 Mbp 460 Mbp 450 Mbp 2,500 Mbp 5,000 Mbp 16,000 Mbp >87,000 Mbp Genic Fraction (%) Noncoding DNA accounts for majority of genome in many eukaryotes Genome Size (x109 bp) What is the probability of a mutation hitting a coding region in humans? Assumptions? Composition of the Human Genome Lynch (2007) Origins of Genome Architecture 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. 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 i 1 s1 p s2 q 2 2 i m for m loci 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) 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: n4 900 7.14 x10 542 If all mutations are equally probable, what is the chance of getting same mutation twice? Infinite Alleles Model (IAM: Crow and Kimura Model) Homozygosity will be a function of mutation and probability of fixation of new mutants 1 1 ft (1 ) f t 1 (1 ) 2 2Ne 2Ne Probability of sampling Probability of sampling same allele twice two alleles identical by descent due to inbreeding in ancestors Probability neither allele mutates Expected Heterozygosity with Mutation-Drift Equilibrium under IAM 1 1 ft (1 ) f t 1 (1 ) 2 2Ne 2Ne At equilibrium ft = ft-1=feq Previous equation reduces to: Ignoring μ2 1 2 f eq 4 N e 1 2 Ignoring 2μ 1 f eq 4Ne 1 Remembering that H=1-f: 4Ne He 4Ne 1 4Neμ is called the population mutation rate 4Neμ often symbolized by Θ Equilibrium Heterozygosity under IAM 4N em q He = = 4N em +1 q +1 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 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: 1 He 1 (8 N e 1) IAM: 4Ne He 4Ne 1 Which should have higher produce He,the Infinite Alleles Model, or the Stepwise Mutation Model, given equal Ne and μ? SMM: 1 He 1 (8 N e 1) IAM: 4Ne He 4Ne 1 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 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 Observed Why? He 1 Avise 2004 Neutral Expectations and Microsatellite Evolution Comparison of Neμ (Θ) for 216 microsatellites on human X chromosome versus 5048 autosomal loci Autosomes X 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 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 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 1 k = 2N m =m 2N 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: t 1 Since μ is number of substitutions per unit time 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? Exam 2 Results: 86.8% Avg, 9.8% Std Dev.