Balancing and disruptive selection The HKA test

Transcription

1 Natural selection The time-scale of evolution Deleterious mutations Mutation selection balance Mutation load Selection that promotes variation Balancing and disruptive selection The HKA test Adaptation The fate of selected mutations The MK test Genetic hitch-hiking The relationship between recombination and variation The nearly neutral theory of molecular evolution Copyright: Gilean McVean, 200

2 The time-scale of evolution First life Human-chimp split Extinction of dinosaurs Land Multicellular eukaryotes vertebrates 3500 MBP 250,000 generations Chimp Human 4N e generations Copyright: Gilean McVean, 200 2

3 The effect of natural selection on allele frequency N 0 N N 2 N 3 N t ASK What is the expected change in allele frequency due to the action of natural selection? Genotype AA Aa aa Frequency ( - x) 2 2x( - x) x 2 Viability w AA w Aa w aa Relative fitness - h s - s w = average fitness of population = 2x( x) hs ( x) 2 s Copyright: Gilean McVean, 200 3

4 The rate of change in allele frequency x( x) E S [ x] = 2w dw dx Rate fastest when allele frequency is intermediate Allele frequency increases if it increases population fitness Fisher s Fundamental theorem k V A Rate of evolution of character Additive genetic variance in character Copyright: Gilean McVean, 200 4

5 Deleterious mutations in populations 2 nd Chromosome of D. melanogaster Proportion Homozygous Outcrossed Greenberg and Crow (960) Viability Inbreeding in humans Incidence of disease, physical or mental defect Outcrossed 4% First-cousin marriages 6% Suggests each genome carries at least 5 severe recessive mutations Copyright: Gilean McVean, 200 5

6 Mutation - selection balance Dominant disease Genotype AA Aa aa Fitness - s - s E s [ x] sx( x) E u [ x] = ( x) u Selection Mutation ~ x = u s Recessive disease Genotype AA Aa aa Fitness - s E s [ x] sx 2 ( E u [ x] = ( x) u x) Selection Mutation ~ x = u s u = 0-6, s = 2% Dominant = in 20,000 Recessive = in 40 Copyright: Gilean McVean, 200 6

7 Mutation load arguments Fraction that does not reproduce Load = Prevalence Effect Dominant 2 Recessive = u s s u s = 2u 2 s = u Total genetic load if multiplicative [ ] L = exp U rec + 2U dom In humans: U del > Will the human population inevitably accumulate deleterious mutations? Copyright: Gilean McVean, 200 7

8 Selection that promotes genetic variation Balancing selection Heterozygote advantage Genotype AA Aa aa Fitness - t - s.00 Frequency ~ x = t t + s time Haemoglobin S and sickle-cell anaemia Genotype AA AS SS Fitness in malarial areas Expected frequency S = 0. Observed 0.09 Copyright: Gilean McVean, 200 8

9 The effect of balancing selection on gene genealogies r r High diversity Positive Tajima D statistic Decay away from balanced locus Copyright: Gilean McVean, 200 9

10 Testing the standard neutral model versus testing the neutral theory The standard neutral model Mutations segregating in a sample are neutral and have been generated by a Fisher-Wright population process The neutral theory The vast majority of mutations segregating within a species and different between species are of no selective importance Testing Data Neutrality Within species Neutral theory Within versus between Example tests Ewens homozygosity test Tajima D Fu and Li D* HKA test MK test Relative rate test Copyright: Gilean McVean, 200 0

11 The Hudson, Kreitman and Aguadé test Gene E[ S ] = θa n E[ d] = τθ Gene 2 T a n n = i= i E [ S ] = θ 2 2a n E[ d2] = τθ 2 Copyright: Gilean McVean, 200

12 Application to empirical data Adh in Drosophila D. sechellia (n = ) 5 flanking Adh 20 diffs 8 diffs D. melanogaster (n = 8) S = 9 S = 8 Solving the simultaneous equations τ ˆ = 3.4 θˆ θˆ χ 2 2 N e = 2.7 = 0.7 = 6.09 generations P = 0.06 Fast / slow polymorphism in exon 4 leads to a twofold difference in enzyme activity Cline in polymorphism: Fast more common in northern America and at higher altitudes Copyright: Gilean McVean, 200 2

13 Trans-specific polymorphism Species A Species B Species A Species B Self-incompatibility systems in plants Pollen Stigma HLA loci in mammals Many human-chimp shared alleles Some date back as far as 65 million years Data suggest heterozygote advantage (also known as overdominance) Copyright: Gilean McVean, 200 3

14 Adaptation and directional selection Direction selection Genotype AA Aa aa Fitness + h s + s Frequency time Examples of genetic adaptations Different types of haemoglobin Lysozyme of ruminants and green monkeys Colour vision in primates Drug resistance in HIV Copyright: Gilean McVean, 200 4

15 The fixation probability of selected alleles Branching process argument (Haldane 927) Pr{Ultimate extinction} E E 2 E 3 E 4 E 5 Pr{Extinction} P PE P E 2 P E 3 = PE i If independent reproduction Pr{Extinction} = e = e (+ s)( E) P i = e (+ s) ( + i! s) 2 2 (+ s) ( + s) E ( + + ( + s) E + 2! Pr{Fixation} = - Pr{Extinction} 2s i s) i! i E i i Copyright: Gilean McVean, 200 5

16 Diffusion theory treatment Kimura (964) Backward Kolmogorov equation Pr{ fixation} 2s e Ne N 4N e s Fixation probability Kimura s formula 2s approximation -2-0 N 2 e s Rate of evolution = Rate of mutation Rate of fixation Ne 2Nu 2s N = 4N su e Copyright: Gilean McVean, 200 6

17 Synonymous and nonsynonymous mutations Directional selection will fix mutations faster than under neutrality The rate of synonymous mutation can be used as in indicator of the neutral mutation rate Nonsynonymous Arg Gln Val AGA CAA GTA Synonymous Arg Gln Val AGA CAA GTA A G Mutation CAG CGA GTA Arg Arg Val AGA CAG GTA Arg Gln Val Copyright: Gilean McVean, 200 7

18 The McDonald-Kretiman test Nonsynonymous Synonymous Fixed Polymorphic Deleterious mutations Neutral mutations Advantageous mutations Copyright: Gilean McVean, 200 8

19 The difference in patterns of replacement variability between mtdna and nuclear loci Number of studies mtdna Nuclear loci Polymorphism > Divergence 25 5 Divergence > Polymorphism 6 24 Weinreich and Rand (2000) Suggests purifying selection in mtdna but adaptive evolution in nuclear loci Differences in Selective constraint? Recombination environment? Copyright: Gilean McVean, 200 9

20 The hitch-hiking effect of beneficial mutations.00 Frequency time Genetic distance for swept locus Low variability rare variants Strong haplotype structure Copyright: Gilean McVean,

21 The relationship between recombination rate and polymorphism θˆ W D. melanogaster Recombination rate ( 0 5 ) Also in humans and Lycopersicon Background selection Removal of deleterious mutations Copyright: Gilean McVean, 200 2

22 The nearly-neutral theory of molecular evolution The generation time effect is stronger for synonymous mutations than nonsynonymous ones u u u u u u u u u k = u u u year gen T t year gen u If most amino acid mutations are slightly deleterious, the rate of substitution depends on the population size k Mildly deleterious Neutral Advantageous 0 Population size Species with longer generation times have smaller population sizes Ohta (995) Copyright: Gilean McVean,