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Lecture 19 : Mutation November 2, 2012 Last Time Human origins Human population structure Signatures of selection in human populations Neanderthals, Denisovans and Homo sapiens Today Mutation introduction Mutation-reversion equilibrium Mutation and selection What Controls Genetic Diversity Within Populations? 4 major evolutionary forces Mutation Drift + - Diversity +/Selection + Migration Mutation Primary driver of genetic diversity Main source of new variants within a reproductively isolated species Mutation often ignored because rates assumed to be extremely low relative to magnitude of other effects Accumulation of mutations in population primarily a function of drift and selection PLUS rate of back-mutation Mutation rates are tough to estimate! Spontaneous mutation rates Schlager and Dickie (1967) tracked spontaneous mutation at 5 loci controlling coat color in 7.5 million house mice Forward > Backward mutation http://jaxmice.jax.org http://www.gsc.riken.go.jp Mutation Rates can Vary Tremendously Among Loci Length mutations occur much more frequently than point mutations in repetitive regions Microsatellite mutation rates as high as 10-2 Source: SilkSatDB Question: Do most mutations cause reduced fitness? 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 Noncoding DNA accounts for majority of genome in many eukaryotes Intergenic space is larger Transposable element insertions (Alu in humans) Genic Fraction (%) Noncoding DNA accounts for majority of genome in many eukaryotes Genome Size (x109 bp) Intron Size Partly Accounts for Genome Size Differences log(number of introns) Aparicio et al. 2002, Science 297:1301 Human: 3500 Mbp Fugu: 365 Mbp Intron Size (bp) Composition of the Human Genome Lynch (2007) Origins of Genome Architecture What is the probability of a mutation hitting a coding region? Reverse Mutations Most mutations are “reversible” such that original allele can be reconstituted Probability of reversion is generally lower than probability of mutation to a new state Possible States for Second Mutation at a Locus Thr Tyr Leu Leu ACC TAT TTG CTG Reversion A C ACC TCT TTG CTG Thr Ser Leu Leu C T ACC TTT TTG CTG Thr Cys Leu Leu ACC TGT TTG CTG C G Thr Phe Leu Leu Allele Frequency Change Through Time With no back-mutation: p1 p0 p0 (1 ) p0 pt (1 ) p0 t How long would it take to reduce A1 allele frequency by 50% if μ=10-5? Two-Allele System with Forward and Reverse Mutation A1 µ ν A2 where μ is forward mutation rate, and ν is reverse mutation rate Expected change in mutant allele: q p q Allele Frequency Change Driven By Mutation q p q q q( ) Equilibrium between forward and reverse mutations: qe ( ) pe ( ) Allele Frequency Change Through Time with Reverse mutation Allele Frequency (p) Reverse Mutation (ν) Forward Mutation (µ) Mutant Alleles (q) Equilibrium Occurs between Forward and Reverse Mutation Is this equilibrium stable or unstable? μ=10-5 qe ( ) Forward mutation 10-5 Lower rate of reverse mutation means higher qeq Mutation-Reversion Equilibrium pe ( ) where µ=forward mutation rate (0.00001) and ν is reverse mutation rate (0.000005) 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: qmu qs 0 q eq 2 s qeq qmu p 2 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 Mutation-Selection Balance with Dominance Dominance exposes alleles to selection, and therefore acts to decrease equilibrium allele frequencies qeq for h>>0 hs Complete Dominance of A2: qeq s Recessive Case: qeq s Which qeq is larger? Why? Effect of dominance and selection on allele frequency in mutation-selection balance (μ=10-5) Drastic effect of dominance on equilibrium frequencies of deleterious alleles Exposure to selection in heterozygotes recessive case What if the population is not infinite? Fate of Alleles in Mutation-Drift Balance p=frequency of new mutant allele in small population Time to fixation of a new mutation is much longer than time to loss 1 u ( p) 2N An equilibrium occurs between creation of new mutants, and loss by drift 1 u (q) 1 2N u(p) is probability of fixation u(q) is probability of loss 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 2 Ne 2Ne Probability of 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 1 1 ft (1 ) f t 1 (1 ) 2 2 Ne 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 Equilibrium Heterozygosity under IAM 4Ne He 4Ne 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
