The evolutionary significance of structure. Detecting and describing structure. Implications for genetic variability

Transcription

1 Population structure The evolutionary significance of structure Detecting and describing structure Wright s F statistics Implications for genetic variability Inbreeding effects of structure The Wahlund effect Drift and founder effects Island models of population structure Identity by descent Diffusion methods The coalescent with structure Selection in subdivided populations Location adaptation Clines Wright s Shifting-Balance theory Copyright: Gilean McVean,

2 Population structure Distribution of surname Hannah Non-random location Non-random mating Goodacre and Sykes Genetic and phenotypic divergence due to Chance Selection Selection plus chance Copyright: Gilean McVean,

3 Detecting and describing genetic structure Wright s F ST statistic Heterozygosity over all populations = HT H H T S Average heterozygosity within subpopulations Testing by permutation Copyright: Gilean McVean,

4 The hierarchical nature of F statistics F statistics can be used to contrast structure at different levels e.g. F IS = H S H H measure of inbreeding S I Average withinindividual heterozygosity H < H < H < H < Individual Subpopulation Population Region H Total Copyright: Gilean McVean,

5 F ST in natural populations Allozymes Organism H T H S F ST Human (major races) Human (Yanomama) House mouse Jumping rodent Nei (1975) SNPs Organism H T H S F ST Human (major races) Drosophila melanogaster a a Based on pairwise diversity Copyright: Gilean McVean,

6 The inbreeding effect of population structure Differences in allele frequency between populations lead to an excess of homozygotes HWeqm Combined samples Expected homozygosity p q1 p Observed homozygosity + q + σ + σ p q Heterozygosity = 1- Homozygosity F ST = 2 2 S FT p q = 2 1 FT 1 p q F σ + σ 2 Copyright: Gilean McVean,

7 The Wahlund effect Increase in heterozyogisty following mixing of isolated populations Combine Random mating Medical implications for disease incidence in admixed populations Recessive disease reduced by mixing Disease Cystic fibrosis Albinism Tay-Sachs disease High risk population Caucasians Hopi Ashkenazi Jews Disease allele frequency Copyright: Gilean McVean,

8 Differences between allozymes and DNA? American oysters (Crassostrea virginica) 1 Allozymes MA SC GA FL FL FL FL FL LA DNA mtdna MA SC GA GFL FL FL FL FL LA Avise (1994) Copyright: Gilean McVean,

9 Differences between allozymes? Locus pgm pgi got ak bdh α-gpdh to hk F ST Checkersport butterfly Euphydryas editha McKechnie et al Unusually high differentiation Problems with F ST Arbitrary a priori choice of structure to test High sampling variance when polymorphism low Throws away much information Copyright: Gilean McVean,

10 Population genetics models of structure Quantify relationship between genetic drift, selection and population differentiation Island model n-island model Assumptions Infinite mainland population (island) Equal population size (n-island) Constant population size Proportion m of population replaced migrants each generation Symmetric migration (n-island) Copyright: Gilean McVean,

11 Identity by descent in the island model Event Same parent Different parents Migration Identity 1 f t-1 0 Probability 1/ 2N 1 1/ 2N e 2m 2m e At equilibrium f = N e m 4 N e m = 2 Number of migrants per generation Only a few migrants each generation are required to prevent a build up of identity within the island population Copyright: Gilean McVean,

12 Relationship between F ST and migration rate E[ F ST ] N e m Can estimate scaled migration rate from estimated F ST (assuming equilibrium, etc.) N e m F ST 0.01 E.g. in humans, F ST N e m 3.5 NB: This is NOT a good estimator do not trust the answer! Copyright: Gilean McVean,

13 Wright s diffusion model for allele frequencies with migration Mainland frequency = x m Island frequency = x Deterministic M V δx δx = = Drift m( x m x(1 x) 2N e x) Wright (1951) Probability density 4 N e m =10 Allele frequency on mainland = N e m = allele frequency on island Copyright: Gilean McVean,

14 Example: SNP frequencies in African Americans Goddard et al. (2000) 114 SNPs in 33 genes 190 African Americans sampled African American frequency Worldwide frequency Likelihood estimation of N e m from sample assume independence between SNPs 0 Ln(L) N e m N e m = Copyright: Gilean McVean,

15 The coalescent in structured populations Two-island model Population 1 Population 2 Pr{coalescence} = Pr{migration} = ni ( ni 1) 4N m n i e Copyright: Gilean McVean,

16 The time to coalescence for two sequences sampled from the same population Pr{1 st event is a coalescence} 1/ 2Ne 1/ 2N + 2m e = N e m Pr{1 st event is a migration} 2m 4Nem = 1/ 2Ne + 2m 1+ 4Nem Expected time to coalescence = 4Ne For expected pairwise diversity (within population) N e N e 2N e BUT Subdivided: 4N e m = 0.2 Single population Variance affected by population structure Average pairwise differences Copyright: Gilean McVean,

17 Effect on allele frequency spectrum Mutation at high frequency Slow coalescence between populations Rapid coalescence within population Subdivided: 4N e m = 0.1 Single population Frequency of derived allele Copyright: Gilean McVean,

18 Effect on neutrality statistics within populations Tajima s D statistic Subdivided: 4N e m = 0.2 Single population Fu and Li D statistic Single population Subdivided: 4N e m = Main effect is to increase the variance Other statistics (e.g. Fay and Wu, 2000) more sensitive Copyright: Gilean McVean,

19 Effect on polymorphism between populations Tajima s D statistic Single population Subdivided: 4N e m = Frequency distribution Single population Subdivided: 4N e m = Copyright: Gilean McVean,

20 Effect on linkage disequilibrium Linkage disequilibrium measures correlations between alleles at different loci D = AB Population structure increases linkage disequilibrium between linked loci f f A f B 4 N e r =1 Single population Subdivided: 4N e m = r 2 f A Population structure creates linkage disequilibrium between unlinked loci in different populations = 0.2, f D = 0 f A = 0.8, f D = 0 B B = 0.8 = 0.2 Naive analysis D = 0.09 Admixture Copyright: Gilean McVean,

21 Admixture dynamics Combination of two previously separated populations f 1 A f 2 A = δ A f 1 B f 2 B = δ B Over time random mating returns population to equilibrium D 0 = 4 1 δ A δ B D = D (1 r) Disequilibrium between unlinked loci can persist for several generations, while Hardy-Weinberg equilibrium is achieved instantly t 0 t D t / D 0 1cM distance unlinked generation Copyright: Gilean McVean,

22 Selection in a subdivided population Maruyama (1970) The fixation probability of an unconditionally beneficial mutation is unaffected by population structure (P fix 2s) Levene (1953) Environmental heterogeneity can maintain genetic polymorphism favoured on favoured on BUT If migration high, selection has to be strong and finely balanced to habitat frequencies to maintain polymorphism Low migration rates can promote local adaptation Heavy metal tolerance in plants Melanism in the peppered moth Milk tolerance in humans Copyright: Gilean McVean,

23 Selection at different scales Evidence for local adaptation from gradients in allele frequency : clines Continental clines in Adh activity and allozyme variation in Drosophila Frequency F/S 1 Driven by scale of environmental heterogeneity Clines in genetic and morphological characters in the toad Bombina Latitude Berry & Kreitman (1993) Frequency B. variegata morphological 1 0 Genetic Distance ( km) Balance between selection against hybrids and migration, following secondary contact Szymura & Barton (1991) Copyright: Gilean McVean,

24 Indirect evidence for local adaptation? Local hitch-hiking? Microsatellite diversity India Zimbabwe China Antilles Locus Schlötterer et al. (1997) But the structured coalescent also leads to variation in coalescence times Copyright: Gilean McVean,

25 The interaction between selection, gene flow and genetic drift Wright s Shifting Balance theory Epistasis between alleles at different loci Locus 2 BB Bb bb AA Aa aa Locus 1 least fit most fit The adaptive landscape Epistasis creates adaptive valleys between peaks of fitness Population fitness Adaptive valley Starting point of population Frequency allele A Frequency allele B Copyright: Gilean McVean,

26 The Shifting Balance theory Drift allows population to cross adaptive valley due to stochastic processes in finite populations Subpopulations are natural experiments, allowing species to evolve across complex adaptive landscapes Evidence for widespread epistasis? F2 hybrid breakdown Coadapted gene complexes Theoretical issues Very difficult for a population that has crossed a valley to spread throughout rest of population The interaction between epistatic selection and genetic drift may be important in reproductive isolation e.g. recessive epistatic interactions important in Haldane s rule of unisexual hybrid sterility Copyright: Gilean McVean,

27 Future directions Theoretical and statistical issues Methods for discriminating between local adaptation and chance effects of coalescence in a structured population The relationship between population structure and linkage disequilibrium Selection on polygenic traits in subdivided populations Empirical challenges Describing patterns of gene diversity at many loci across genomes (from an wellchosen sample) Comparing differentiation for different types of mutation (e.g. silent v replacement) Mapping genetic variation to phenotypic variation Copyright: Gilean McVean,