21 March, 2016: Population genetics I

Transcription

1 21 March, 2016: Population genetics I

2 Background reading This book is OK primer to pop.gen. in genomics era focus on coalescent theory and SNP data unfortunately it contains lots of typos

3 Population genetics Definition studies distributions & changes of allele frequencies in populations over time effects considered: natural selection, genetic drift, mutation and gene flow recombination, population subdivision and population structure allows inferring past events as well as predicting future History fundamental work by Haldane, Wright and Fisher on first half of 20th century recent development: coalescent theory by Kingman in 1980 s suitable for SNPs data computationally highly efficient

4 Population genetics basics (1) Allele one of alternative forms of a gene or same genetic locus used to be visible gene product (e.g. blond vs. red hair) now typically SNP (e.g. rs (c) vs. rs (t))

5 Population genetics basics (1) Allele one of alternative forms of a gene or same genetic locus used to be visible gene product (e.g. blond vs. red hair) now typically SNP (e.g. rs (c) vs. rs (t))

6 Population genetics basics (1) Allele one of alternative forms of a gene or same genetic locus used to be visible gene product (e.g. blond vs. red hair) now typically SNP (e.g. rs (c) vs. rs (t))

7 Population genetics basics (1) Allele one of alternative forms of a gene or same genetic locus used to be visible gene product (e.g. blond vs. red hair) now typically SNP (e.g. rs (c) vs. rs (t)) Alleles in a genetic locus do not need to be functional in many studies we are interested in neutral variation: we can then exclude natural selection and focus on genetic drift and gene flow, and e.g. infer historical events of populations rs associated e.g. with Skin sensitivity to sun, Hair color, Nonmelanoma skin cancer, Freckles : it may not be entirely neutral Genome provides millions of variable loci, majority of those neutral Inferring presence of function for a locus/allele is of special interest

8 Population genetics basics (2) Population model Theoretical models assume a simplified population model Most commonly used model is WrightFisher model. It assumes: haploid population no sex constant population size WrightFisher model (WFM) can be generalised: diploid population panmictic, random mating variable population size WFM gives a good approximation for more complex populations

9 Population genetics basics (2) WrightFisher model Evolution of an idealised population: generation 1

10 Population genetics basics (2) WrightFisher model Evolution of an idealised population: generation 2

11 Population genetics basics (2) WrightFisher model Evolution of an idealised population: generation 2

12 Population genetics basics (2) WrightFisher model Evolution of an idealised population: generation 3

13 Population genetics basics (2) WrightFisher model Evolution of an idealised population: generation 10

14 Population genetics basics (2) WrightFisher model Evolution of an idealised population: generation 10

15 Population genetics basics (3) Population size One central parameter in population genetics is population size Abbreviated as N Population size defines how quickly variation is lost (forwards) how much frequencies change per generation (now) how quickly sample coalesces to MRCA (backwards) Population size is measured in units of WFM population known as effective population size, Ne can be very different from census population size some violations of WFM can be corrected for

16 Population genetics basics (3) loss of variation change of allele frequencies Known as genetic drift

17 Population genetics basics (3) loss of variation change of allele frequencies Known as genetic drift, affects small populations more heavily

18 Population genetics basics (4) Genetic drift At every locus, variation is eventually lost and one allele becomes fixed in nonneutral loci, selection affects chances of fixation variation is lost much more rapidly in small populations in small populations genetic drift prevails selection and even harmful alleles may get fixed Variation once lost is lost forever population bottleneck reduces variation and population recovery cannot bring it back new variation is created by mutations

19 Population genetics basics (4) Genetic drift gingers conquering a population in ten generations!

20 Population genetics basics (3) Coalescence time small populations coalesce faster, more recent MRCA conversely: Ne defined by coalescence time

21 Population genetics basics (5) Effective population size Some violations of WFM that can be corrected for variation in population size: 10, 100, 50, 80, 20, 500 Ne = 30.8 nonequal sex ratio: = 100 Ne = 64 variation in reproductive success selffertilisation

22 Population genetics basics (5) Effective population size There are roughly 8 million Holstein cattle in the USA theoretical Ne is approximately 80 and declining

23 Coalescence theory Problems of classical population genetics theory no analytical solutions for practical problems typical questions about large populations over many generations typically, data are simulated under different assumptions parameter values producing results similar to observed data considered good forward simulations of full populations time consuming sample only a tiny subset of total coalescence models only consider what happens for the sample

24 Coalescence theory Simulation of full population (N=100) vs. sample (n=5) only