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Chapter 8 – Molecular Evolution Molecular Population Genetics

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Chapter 8 – Molecular Evolution Molecular Population Genetics 4/26/13 Chapter 8 – Molecular Evolution Neutral/Nearly Neutral Theory Measuring Divergence & Polymorphism The Molecular “Clock” Variation in Molecular Rates Tests for Deviation from Neutral Expectations Molecular Evolution at Linked Loci/Sites Molecular Population Genetics v increasing complexity of genetic data ² “Aa” to allozymes to RFLPs to DNA sequences v the same evolutionary processes (mutation, drift, selection, gene flow) considered in the “Modern Synthesis” are responsible for the patterns of variation observed in DNA sequences v theory developed for two alleles at a locus is generally applicable to DNA sequence data, although the additional information contained in sequences provides added information… 1 4/26/13 The Neutral Theory v Kimura (1968) - most polymorphism at the molecular level is selectively neutral ² ideas developed during the allozyme era, but even more relevant for DNA sequences v strongly deleterious or advantageous mutations are expected to be eliminated or fixed quickly and therefore not contribute much to segregating polymorphism ² mutation rate µ is effectively the rate of neutral mutation Neutral Expectations… v ...with constant population size and mutation nucleotide diversity E Π =θ = 4Nµ ( ) # segregating sites " 1 1 1 1 % E (S) =θ $1+ + + +... + ' # 2 3 4 k −1& homozygosity 1 Fˆ = 1+ 4Nµ # unique alleles θ θ θ E(k) =1+ + + ...+ allele frequency distribution θ +1 θ + 2 θ + n −1 € n! n θ aj Pr a ,..., a = { 1 n } ∏ aj θ (θ +1) ... (θ + n −1) j=1 j a j ! € 2 4/26/13 Time to Coalescence 4000 3500 3000 # 1& t = 4N%1 − ( 2500 $ k ' 2000 1500 1000 500 € Number of Generations to MRCA 0 0 5 10 15 20 25 # alleles sampled, k MRCA = most recent common ancestor, N = 1,000 3 4/26/13 Basic Neutral Theory Principles v at mutation/drift equlibrium (gain and loss of alleles due to mutation and drift are equal), expected homozygosity is: 1 1 = (4Neµ +1) θ +1 v and expected heterozygosity is: 1 θ 1− = θ +1 θ +1 v so larger populations€ should have greater genetic diversity € Mutation vs. Fixation/Substitution 4 4/26/13 Fixation/Substitution v average time to fixation (for alleles that eventually become fixed) is 4Ne generations v average time to loss of new mutations is 35 30 2N 25 e ln 2N = 2ln 2N ( ) ( ) 20 N 15 generations 10 5 Time to Loss (# Generations) 0 1 100 10,000 1,000,000 € Population Size Time to Coalescence 4000 3500 3000 # 1& t = 4N%1 − ( 2500 $ k ' 2000 1500 1000 500 € Number of Generations to MRCA 0 0 5 10 15 20 25 # alleles sampled, k MRCA = most recent common ancestor, N = 1,000 5 4/26/13 Probability of Fixation & Rate of Evolution v new mutations have a frequency of 1/(2N) and therefore have a probability of fixation of 1/(2N) v new mutations become fixed at a rate equal to µ (see next slide) ² mutation rate equals “substitution” rate ² neutral rate is independent of population size! v average time interval between fixation of new mutations is 1/µ Neutral Expectations… v the rate of neutral evolution is independent of population size ² substitution rate (k) equals mutation rate 1 k = 2Nµ × = µ 2N 6 4/26/13 Average time to fixation/substitution Directional Fate of Selection New Mutations Neutral Drift Balancing Selection 7 4/26/13 Nearly Neutral Theory v what happens in small populations when selection is weak? ² changes in allele frequency due to drift and selection are approximately equal 2Ns ≈1 v probability of fixation for a new, “nearly neutral” allele: 2s Pr(A fixed) = −4 Ns € 1− e wAA =1+ s, wAa =1+ s/2, waa =1 € € 0.06 s = -0.01 0.05 s = -0.001 s = -0.0001 0.04 0.03 0.02 Probability of Fixation 0.01 0 10 100 1000 10000 Population Size 2s Pr(A fixed) = 1− e−4 Ns € 8 4/26/13 What qualifies as nearly neutral? v Hamilton: 2s = 1/2Ne or 4Nes = 1 ² value at which “the processes of genetic drift and selection are equal” v Hartl & Clark: |2Ns| ≈ 1 v Hedrick: s < 1/(2N) or 2Ns < 1 v Ohta & Gillespie (1996): s ≈ 1/N or Ns ≈ 1 1− e−4 Nesp Pr(A fixed) = 4 Ns 1− e− if p =1/ 2N 1− e−2s 2s = ≈ 1− e−4 Ns 1− e−4 Ns N = 500 s = -0.004 4Nes = -1 4Nes = 1 s = 0.004 9 4/26/13 Nearly Neutral Theory - Summary v the rate of neutral evolution is independent of 1 population size 2Nµ × = µ ² substitution rate equals mutation rate 2N v in contrast, the fate of nearly neutral mutations depends on population size ² when N is small, the effect of genetic drift can be 2Ns ≈1 comparable to that of selection,€ making slightly deleterious mutations “effectively neutral” v thus, lineages experiencing small population size should accumulate both neutral and nearly neutral mutations, leading to a faster € rate of sequence evolution Woolfit & Bromham 2003 Increased rates of sequence evolution in endosymbiotic bacteria and fungi with small effective population sizes. MBE 20:1545-1555. § higher rate in endosymbiotic bacteria interpreted as a consequence of nearly neutral evolution 10 .
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