Population genetic structure Bengt Hansson
Conservation: Greater prairie chicken Population structure? Geographical isolation? Dispersal? Effective population size?
Phylogeography: Chorthippus parallelus Population structure? Signs of population expansion? Barriers to gene flow?
Selection: e.g. Ischnura damselflies Differentiation at colour locus vs. differentiation at neutral loci > directional selection = genetic drift < balancing selection Fst Heterozygosity
Causes of genetic differentiation between populations: Genetic drift 0.45 0.45 0.4 0.4 0.35 0.35 Pop. A Frequency 0.3 0.25 0.2 0.15 Frequency 0.3 0.25 0.2 0.15 Allele loss! 0.1 0.1 0.05 0.05 0 1 2 3 4 5 6 0 1 2 3 4 5 6 Allleles Allleles 0.45 0.45 0.4 0.35 0.4 0.35 Pop. B Frequency 0.3 0.25 0.2 0.15 Frequency 0.3 0.25 0.2 0.15 0.1 0.05 0.1 0.05 0 1 2 3 4 5 6 0 1 2 3 4 5 6 Allleles Allleles t = 0 t = 1
Causes of genetic differentiation between populations: Mutations 0.45 0.4 0.45 0.4 Pop. A Frequency 0.35 0.3 0.25 0.2 0.15 0.1 Frequency 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 1 2 3 4 5 6 0.05 0 1 2 3 4 5 6 Allleles Allleles Pop. B Frequency 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 1 2 3 4 5 6 Frequency 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 1 2 3 4 5 6 Allleles Allleles t = 0 t = 1
Causes of genetic differentiation between populations: Selection 0.45 0.45 0.4 0.4 0.35 0.35 Pop. A Frequency 0.3 0.25 0.2 0.15 Frequency 0.3 0.25 0.2 0.15 0.1 0.1 0.05 0.05 0 1 2 3 4 5 6 0 1 2 3 4 5 6 Allleles Allleles Pop. B Frequency 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 1 2 3 4 5 6 Frequency 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 1 2 3 4 5 6 Allleles Allleles t = 0 t = 1
How to describe this difference in allele frequencies between populations? Wright s F-statistics: F ST Fixation index
F ST = Ht Hs Ht
Ht = Expected heterozygosity in the Total population Hs = Expected heterozygosity in the Sub-population
Hobs = 0.5 Hs = 0.49 Hobs = 0.17 Hs = 0.3 Hobs = 0 Hs = 0
Hardy-Weinberg theorem Allele frequencies: A = 50% and B = 50% Random mating Selfing (inbreeding) Null alleles B- A- A- A- A- B- HW: Yes No No H S : 0.5 0.5 (0.67) H O : 0.5 0.17 0.17 F IS : 0 0.66 0.75 F IS = Hs Ho Hs
Hobs = 0.5 Hs = 0.49 Hobs = 0.17 Hs = 0.3 F ST = Ht Hs Ht Hobs = 0 Hs = 0 Ht = 0.5 Mean Hs = 0.26
Two island populations (one locus; two alleles R and B) Fst = 0
Two island populations (one locus; two alleles R and B) Fst = 1
Two island populations (one locus; two alleles R and B) Fst = 0-1
Two island populations (one locus; two alleles R and B) Fst = 0-1; isolation-by-distance
Two island populations (one locus; two alleles R and B) What is Fst? How to calculate Fst? Fst = is the degree of Fixation in the Subpopulation relative to the Total population; or the heterozygosity deficiency due to substructure. F ST = H T H T H S
Two island populations (one locus; two alleles R and B) HT HS 0.5 0 F = = = 1 ST H 0.5 T
Two island populations (one locus; two alleles R and B) HT HS 0.5 0.5 F = = = ST H 0.5 T 0
Global: pr = 75% pb = 25% Two island populations (one locus; two alleles R and B) pr = 100% Fst =? pr = 50%, pb = 50% HT HS 0.375 0.25 F = = = ST H 0.375 T 0.333
Estimates of F ST There are several estimates of F ST Nei 1986, 1987 measure that uses genotype frequencies (sensitive to sample size differences between pops); G ST Weir and Cockerham 1984 uses allele frequencies (corrects for sample size differences between populations); Θ Slatkin 1995 F ST defined for markers undergoing stepwise mutation (e.g. microsatellites); R ST
Problem with Fst when highly variable loci are used CC CC DD CD CD CD DD CD CC CD DD CD Hs = 0.5 Ht = 1 (Expected Homozygosity) = 1-(4*0.25^2) = 0.75 Fst = (0.75-0.5)/075 = 0.25/0.75 = 0.33
Problem with Fst when highly variable loci are used: fixation but not differentiation # of alleles Alleles in 2 pops Ht Hs Fst D 1+1 A vs B 0.5 0 1 1 2+2 vs CD 0.75 0.5 0.33 1 4+4 CD vs EFGH 0.875 0.75 0.14 1 10+10 A-J vs K-T 0.95 0.9 0.05 1 D est = [(Ht-Hs)/(1-Hs)] * [n/(n-1)], where n is the number of populations Jost (2008) Molecular Ecology 17, 4015 4026 doi: 10.1111/j.1365-294X.2008.03887.x Use both Fst and Dest
Randomisation test Test whether the observed Fst (or the Fis) is significantly different from what would be expected if there was no population structure (or random mating) The randomisation procedure uses population specific sample sizes and global allele frequencies
Two island populations (one locus; two alleles R and B) Our calculated Fst = 1 based on data from 12 inds pr = 100% pb = 100% Global: pr = 50% pb = 50%
Two island populations (one locus; two alleles R and B) Randomisation 1: Fst = 0 Global: pr = 50% pb = 50%
Two island populations (one locus; two alleles R and B) Randomisation 2: Fst = 0.5 Global: pr = 50% pb = 50%
Two island populations (one locus; two alleles R and B) Randomisation 3: Fst = 0.1 Global: pr = 50% pb = 50%
Two island populations (one locus; two alleles R and B) Randomisation 756: Fst = 1 Global: pr = 50% pb = 50%
Two island populations (one locus; two alleles R and B) Randomisation 1000: Fst = 0.1 Global: pr = 50% pb = 50%
Distribution of randomised Fst values Count Observed Fst 0 1 Fst
Distribution of randomised Fst values Observed Fst Count 0 1 Fst
Non-a priori identification of populations Structure analyses