Drift Inflates Variance among Populations. Geographic Population Structure. Variance among groups increases across generations (Buri 1956)

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1 Geographic Population Structure Alan R Rogers December 4, 205 / 26 Drift Inflates Variance among Populations 2 / 26 Variance among groups increases across generations Buri 956) 3 / 26 Gene flow migration) reduces population differences 0 p m = 0: No gene flow 0 p m = 0: strong gene flow 4 / 26 PC map of European genetic distances Mormon US England Denmark Germany Sweden Finland Norway Iceland France Italy Spain Switzerland Poland Netherlands McLellan et al 984) 5 / 26 Genetic and geographic distance Genetic Distance Europe N America S America Genetic Distance Geographic Distance ) World Australia and Pacific;, Americas 6 / 26

2 Long shared segments recent common ancestry Sharing with French-speaking Swiss and UK Each dot an individual Color shows country of origin Those who share ancestry with Swiss also share ancestry with UK Presumably reflects immigration from ancestors of Swiss and British 7 / 26 Sharing with Irish and Germans 8 / 26 Geographic decay of recent relatedness Each dot an individual Pink, Germans; Green, British; Blue, Irish Brits with lots of German ancestry have little Irish ancestry British population is a mixture of Celts and Germans If we focused on shorter IBD blocks, we d be studying a different time scale, and the pattern might be different Genetic similarity versus geographic distance Small dots are pairs of individuals E, Eastern Europe; W, Western Europe; N, Northern Europe; I, Italy & Iberia; TC, Turkey & Cyprus Ralph & Coop 203) 9 / 26 0 / 26 / 26 2 / 26 Genetic map of Britain Colors indicate genetically similar groups

3 3 / 26 4 / 26 Variance among groups increases across generations Buri 956) 5 / 26 6 / 26 Wahlund principle: subdivision reduces heterozygosity A A A A A 2 A 2 A 2 Pop 4/6 /6 6/6 9/6 Pop 2 2/6 9/6 6/6 /6 Species 8/6 5/6 6/6 5/6 Hardy-Weinberg 8/6 4/6 8/6 4/6 Amount of reduction: 2/6 p i p p i p) 2 Pop 4/6 /6 Pop 2 4/6 /6 Variance: /6 Wahlund showed that heterozygosity is reduced by group differences in allele frequencies Buri s experiment illustrates that Drift reduces heterozygosity Drift increases group differences We need a theory to connect these facts Let us build one on top of what we have already H S = H T 2V Wahlund 928) 7 / 26 8 / 26

4 What we already know about heterozygosity E[H t p t ] = 2p t q t Hardy-Weinberg) E[H t p 0 ] = 2p 0 q 0 ) t Ch 2) How can these both be true? It must be true that E[p t q t p 0 ] = p 0 q 0 On the other hand, it is also true that ) t E[p t q t p 0 ] = p 0 q 0 V t Wahlund) Rearranging gives the variance among groups V = p 0 q 0 [ ) t ] We usually normalize this expression by dividing both sides by p 0 q 0 The result is called F ST : F ST = V = ) t p 0 q 0 In data analysis, we take p 0 p, the current population mean where V t is the variance of p t about p 0 9 / / 26 Data from Buri 956) Data from Buri 956) Series I Series II theory 05 data 00 Series I 005 Series II / / 26 Application to differences among human races Theory assumes no migration Seems unlikely, but let s see where it leads For major human populations, F ST 0 Two major hypotheses about the age human races Replacement model: about 50,000 years 2000 generations) Multiregional model: at least,000,000 years 40,000 generations) Plug these into and solve for N e F ST = ) t e What do these imply about N e of major continental populations? Replacement: N e 0, 000 Multiregional: N e 200, 000 The first figure is more plausible: agrees with genetic diversity within populations If human races had been separated for a million years without gene flow, race differences should be larger But what about gene flow? 23 / / 26

5 The role of migration Summary Drift increases group differences Migration m) reduces them Eventually, an equilibrium is reached F ST = 4N e m + Depends only on N e m Small if N e m > Human value /9) implies N e m 2 Drift increases variance among groups and reduces that within them Wahlund s principle: H S = H T 2V F ST measures between-group variance relative to total variance By distinguishing between long and short IBD blocks, we can examine geographic population structure on different time scales 25 / / 26