What causes geographic populations to become differentiated? Natural Selection? Genetic Drift? (limited gene flow) http://anthro.palomar.edu/adapt/images/skin_color_range.jpg http://alex.roedlach.at/Kottak/Map%2009.jpg

What hold species together? Migration and gene flow Leopard frogs from different populations Banding pattern variation in water snakes http://www.snakesandfrogs.com/scra/snakes/images/brnwtre.jpg

Continent-Island model of gene flow Island, pI Continent, pC m = proportion of Island that comes from Continent (1-m) = proportion of Island the DOESN”T come from continent Want to know: pIsland,t+1 = pIsland,t • (1-m) + pcontinent,t • (m) How “purple” is the island after “blue” genes enter “red” pool Dp = pt+1 - pt DpIsland = [pIsland,t • (1-m) + pContinent,t • (m)] - pIsland,t DpIsland = m(pContinent - pIsland) = -m(pIsland – pContinent)

pIsland,t = pIsland,0 • (1-m)t + pcontinent,0 • [1-(1-m)t] http://www.sanfranciscosentinel.com/wp-content/uploads/2011/01/atlas-slave-trade.jpg

Continent – Island model General (island) model

Migration matrix: from subpopulation j into subpopulation i

Wahlund effect Little Italy Chinatown AA Aa aa .81 .18 .01 AA Aa aa .81 .18 .01 AA Aa aa .01 .18 .81 http://www.nyctourist.com/images/maps/map_hoods4.gif p = 0.9, q=0.1 p = 0.1, q=0.9 What if we sampled here?

Population structure The distribution of genetic variation within and among populations Heterozygosity in the total assemblage of populations, relative to the heterozygosity in an AVERAGE sub-population Fst = Vq/q(1-q) = Qbar-qbar2/pq Gst estimates Fst = (Htotal – averageHsub) / Htotal Inbreeding coefficient F = (Hexpected - Hobserved) / HExpected

Population structure: variation within vs. between population Two separate populations One ‘pooled’ population Two separate populations One ‘pooled’ population vs. vs. p1 = 0.0, p2 = 1.0 H1 = 0.0, H2 = 0.0 H=2pq Average of each: pbar = 0.5 Hbar = 0.0 (‘bar’ = average) If populations were pooled: pbar = qbar = 0.5 Ht = 2pbarqbar = 2(.5)(.5) = 0.5 Fst = (Ht - Hbar)/Ht = (0.5 – 0.0) / 0.5 = 1.0 100% of variation lies BETWEEN sub-populations 0% of variation lies WITHIN the average sub-population p1 = 0.5, p2 = 0.5 H1 = 0.5, H2 = 0.5 H=2pq Average of each: pbar = 0.5 Hbar = 0.5 (‘bar’ = average) If populations were pooled: pbar = qbar = 0.5 Ht = 2pbarqbar = 2(.5)(.5) = 0.5 Fst = (Ht - Hbar)/Ht = (0.5 – 0.5) / 0.5 = 0.0 0% of variation lies BETWEEN Sub-populations 100% of variation lies WITHIN average sub-population

Changing levels of consanguinity in France Decrease in levels of inbreeding in one generation Due to better roads? Higher migration? WWII? 1926-1930 1956-1958

Loss of heterozygosity (H) H = heterozygosity = 2pq (from p2, 2pq, q2) = proportion of heterozygotes in population = (1 - sum of all homozygotes) = 1 - Sxi2, where xi = frequency of ith allele if there were 1, 2, 3, …i alleles in popln. H decays due to drift (and inbreeding) Ht+1 = Ht [1 - 1/(2Ne)] Inbreeding coefficient = F = Hexpected - Hobserved Hexpected

Fst = (Htotal - averageHsub)/Htotal Inbreeding coefficient Drift and Inbreeding Individual Subpopulation Total set of subpopulations AA AA Aa Aa aa AA AA AA Aa Aa aa Aa AA Aa Aa Aa aa aa Population structure Fst = (Htotal - averageHsub)/Htotal Inbreeding coefficient Fis = (Hsub - averageHindividual)/Hsub F = (Hexpected - Hobserved)/Hexpected Fit = (Htotal - averageHindividual)/Htotal F = (2pq – f(Aa)observed)/2pq

Gst = (HT – Hsub)/HT = 1-Hsub/HT < 1-Hsub Since 1-Hsub = average homozygosity What happens to Gst for highly variable markers?

Migration – drift equilibrium Fst = 1/[4Nem +1] Nem = 1/4 [1/Fst – 1] Variance in allele freq. among populations = pq / [4Nem + 1] Large, unknown Small, unknown

Mutation – drift equilibrium Mutation (u) introduces variation within populations, drift (determined by Ne) eliminates it Heterozygosity = H = 4Ne u /[4Ne u + 1] Per nucleotide heterozygosity = q ~= 4Neu Large, unknown Small, unknown

Gene flow and drift affect all loci Selection acts on individual loci Fst outlier analyses Gene flow and drift affect all loci Selection acts on individual loci ‘Outlier’ loci may be targets of selection Wilding et al. 2001, J. Evol. Biol

Distribution of Fst values in humans Figure 7.8

Clinal Variation: change in frequency across a geographic transect A balance between selection and migration?

Gene flow vs. selection Start s = 0.9 m = 0.1 200 Low Gens. migration AA favored at this end aa favored at this end Gene flow vs. selection Start s = 0.9 m = 0.1 Low migration 200 Gens. later s = 0.9 m = 0.5 High migration

Gene flow among demes in a metapopulation Ne = N•D[1 + 1/(4Nem)]