1. What causes geographic populations to become differentiated?
Natural Selection?
Genetic Drift?
(limited gene flow)

2. What hold species together? Migration and gene flow
Leopard frogs
from
different
populations
Banding pattern
variation in
water snakes

3. 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)

4. pIsland,t = pIsland,0 • (1-m)t + pcontinent,0 • [1-(1-m)t]

6. Continent – Island model
General (island) model

7. Migration matrix: from subpopulation j into subpopulation i

8. Wahlund effect Little Italy Chinatown AA Aa aa .81 .18 .01 AA Aa aa
AA Aa aa
p = 0.9, q=0.1
p = 0.1, q=0.9
What if we sampled here?

10. 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

11. 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 = (‘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 = (‘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

12. Changing levels of consanguinity in France
Decrease in levels of inbreeding in one generation
Due to better roads? Higher migration? WWII?

13. 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

14. 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

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

17. 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

18. 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

19. 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

20. Distribution of Fst values in humans
Figure 7.8

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

22. 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

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