Lecture 13: Variation Among Populations and Gene Flow Oct 2, 2006
Questions about exam?
Last Time Variation within populations: genetic identity and spatial autocorrelation
Today Variation among populations: genetic distance to F-statistics Indirect estimates of gene flow
Expected Heterozygosity Expected Heterozygosity (H E ): a measure of the diversity of a population, assuming H-W 2pq for 2-allele, 1 locus system OR 1-(p 2 + q 2 ) or 1-Σ(expected homozygosity) more general: what s left over after calculating expected homozygosity
Partitioning of Diversity H E depends on how you define populations Separate Subpopulations: H E = 2pq = 2(1)(0) = 0 Merged Subpopulations: H E = 2pq = 2(0.5)(0.5) = 0.5 H E ALWAYS increases when randomlymating subpopulations are merged: Wahlund Effect This effect is quantified by the Fixation Index (F ST )
Calculating F ST First, get allele frequencies, using your old friends Hardy-Weinberg B 2 B 2 = light pink; B 1 B 1 and B 1 B 2 = dark pink Subpopulation 1: F(light pink) = 10/20 = 0.5 F(B 2 ) = q 1 = 0.5 = 0.707 p 1 =1-0.707 = 0.293 Light: 10, Dark: 10 Subpopulation 2: F(light pink)=2/20=0.1 F(B2) = q 2 = 0.1 = 0.32 p 2 = 1-0.32 = 0.68 Light: 2, Dark: 18
Calculating F ST Calculate Average H E of Subpopulations (H S ) For 2 subpopulations: H S = Σ2p i q i /2 = (2(0.707)(0.293) + 2(0.32)(0.68))/2 H S = 0.425 Calculate Average H E for Merged Subpopulations (H T ): F(light pink) = 12/40 = 0.3 q = 0.3 = 0.55; p=0.45 Light: 10, Dark: 10 H T = 2pq = 2(0.55)(0.45) H T = 0.495 Light: 2, Dark: 18
Bottom Line: F ST = (H T -H S )/H T = (0.495-0.425)/ 0.495 = 0.14 14% of the total variation in flower color alleles is due to variation among populations Light: 10, Dark: 10 AND Expected heterozygosity is increased 14% when subpopulations are merged Light: 2, Dark: 18
Other Estimates of F ST Nei's Gene Diversity: G ST Nei's generalization to multiple, multiallelic loci G ST = D ST /H T D ST =H T -H S Where H S is mean H E of m subpopulations, calculated for i alleles with frequency of p i H S = 1 m m (1 n i= 1 j= 1 p 2 i ) H = p T 1 i 2 where p i ismeanallele frequencyin totalpopulation
F ST as Variance Partitioning Think of FST as proportion of genetic variation partitioned among populations 2 Θ = σ a AMOVA: Analysis of Molecular Variance: partition variance at any level of population structure σ Method of choice for dominant markers 2
Unbiased Estimate of F ST Weir and Cockerham's (1984) Theta Compensates for sampling error, which can cause large biases in F ST or G ST (e.g., if sample represents different proportions of populations) Calculated in terms of variance: Calculated by FSTAT software: http://www2.unil.ch/popgen/softwares/fstat.htm Goudet, J. (1995). "FSTAT (Version 1.2): A computer program to calculate F- statistics." Journal of Heredity 86(6): 485-486. 2 Θ = σ a σ 2 Often simply referred to as F ST in the literature Weir, B.S. and C.C. Cockerham. 1984. Estimating F-statistics for the analysis of population structure. Evolution 38:1358-1370.
F ST for Microsatellites: R ST Remember genetic distance measure for microsatellites: This is a variance if you compare to population average: S = n i= 1 ( i n a i) 2 where S bar is overall variance and Sw is variance within subpopulations
F ST : What does it tell us? Degree of differentiation of subpopulations: 0.05 to 0.15 is weak to moderate 0.15 to 0.25 is strong differentiation >0.25 is very strong differentiation Most Importantly, F ST can be directly related to the migration rate: Nm = (1-F ST )/(4F ST ) Assumes island model of population structure, and an equilibrium with three other evolutionary forces: drift, mutation, selection
F ST is related to life history Seed Dispersal Gravity 0.446 Explosive/capsule 0.262 Winged/Plumose 0.079 Successional Stage Early 0.411 Middle 0.184 Late 0.105 Life Cycle Annual 0.430 Short-lived 0.262 Long-lived 0.077 (Loveless and Hamrick, 1984)
Polar Bear Population Structure Need accurate measures of population connectedness for setting sustainable native hunting limits Sampled 19 populations from throughout range Differentiation exceedingly low: pairwise F ST =0.004 to 0.10; Nm as high as 89 (but probably wrong)! Island populations more isolated (Paetkau et al., 1999)
Salamander Population Structure Gyranophilus porphyriticus Stream salamanders almost exclusively aquatic, move mostly upstream Hypothesized that steepness of stream inhibits migration between populations Pairwise genetic differentiation of sites was negatively correlated with stream steepness Lowe et al. 2006
Aspen Population Structure Aspen is most broadly distributed tree in North America: boreal forests to Mexico Wind-dispersed seed and pollen Very long gene flow distances, so low differentiation expected Lowe et al. 2006
Aspen Population Structure Jelinski and Cheliak (1992) studied 6 subpopulations near Glacier National Park: F ST = 0.03 Stevens et al. (1999) studied 23 subpopulations in Yellowstone: F ST = 0.34 Jelinski and Cheliak studied adult trees, Stevens et al. studied isolated stands of seedlings, possibly from just a few mother trees 1998 Yellowstone Fires
Limitations of F ST F ST is a long, integrated look into the evolutionary/ecological history of a population: may not represent status quo Assumptions of the model frequently violated: Island model unrealistic Selection is often an important factor Mutation may not be negligible Sampling error!
Alternatives to F ST Direct measurements of movement: mark-recapture Genetic structure of paternal and maternal gametes only Chloroplast and mitochondrial DNA Pollen gametes Parentage analysis: direct determination of the parents of particular offspring through DNA fingerprinting Next time!
Next Time Direct measures of gene flow: parentage analysis