1. Evolutionary Biology Advanced Course
Kyushu University
Hidenori Tachida

2. Genetic variation1: two alleles（indel）
indel polymorphisms at CCR5 in human populations（Samson et al. 1998）
alleles: ＋、Δ
p+ : frequency of +
P++
PDD
P+D
“Evolutionary Analysis”

3. Genetic variation ２：Microsatellite
microsatellite polymorphism in cichlids of Lake Victoria（Maeda et al. 2008）
CACACACACACACACA （8 repeats）
CACACACACACACACACACA （10 repeats）
alleles: 134,136,140,170,182,196
Expected: H-W eq.

4. Genetic variation 3: nucleotide sequence
DNA polymorphism at GBSSI in Japanese prickly ash（Kamiya et al. 2008)
HR： Hirado
IK： Ikutsuki
MT： Motooka
OZ： Ozasa
SB： Shiiba

5. Genetic variation 4: Quantitative Traits

6. Summary statistics of genetic variation
gene frequency
heterozygosity
linkage disequilibrium
F-statistics (fixation index etc)
neutrality test statistics
Frequency spectrum
Variance and covariance
population genetics
genealogy theory
Past population events (history)
population structure (size, migration etc.)
natural selection

7. Heterozygosity 2 alleles, A, a． pA : A frequency pa : a frequency
Heterozygosity (Gene diversity )
= Prob[two genes sampled are different alleles ]
= pA pa+pa pA
= 2pA pa = H
different?
: individual
Problem 1
Compute pA and heterozygosity in the population shown on the left. A a

8. Fixation index FST HS HT HT HS subpopulations
HT = Prob[two genes sampled from the same subpopulation are different]
HS = Prob[two genes sampled from different subpopulations are different ] HT HS
(a measure of population differentiation)

9. Linkage disequilibrium
A locus
B locus
locus
allele
frequency A pA a pa B qB b qb
gamete AB Ab aB ab
frequency
gAB
gAb
gaB
gab
Do genes at different loci randomly associated?
gAB = pA qB ?
D = gAB - pA qB

10. Contents One locus Hardy-Weinberg equilibrium Inbreeding
Natural selection
Mutation
Migration
Genetic drift
Two locus (linkage disequilibrium)
Gene genealogy
Quantitative genetics
Books
S. Freeman and J. C. Herron (2014) "Evolutionary Analysis", 5th ed.
J．Ｆ．クロー著・安田訳「基礎集団遺伝学」、培風館
J. Gillespie (2004) "Population Genetics: a concise guide" 2nd ed. Sinauer.
D. L. Hartl (2000) "A Primer of Population Genetics" 3rd ed. Sinauer.
D. L. Hartl and A. Clark (2007) "Principles of Population Genetics" 4th ed. Sinauer.
Hudson, R. R. (1990) Gene genealogy and coalescent process. Oxford Surveys Evol. Biol. 7: 1-44.
R. Nielsen and M. Slatkin “An Introduction to Population Genetics: Theory and Applications”, Sinauer
D. S. Falconer and T. F. C. Mackay (1996) ''Introduction to Quantitative Genetics'' 4th edition. Longman Sci. and Tech.

11. Genotype and gene frequencies （Hardy-Weinberg Eq.）
Random mating　→　Mating does not depend on genotypes
Mother
Alleles: A, a
Father
A frequency in the next generation A a A a pA pA
PAA = pA2
PAa = pA pa+ pA pa = 2 pA pa
Paa = pa2
HW equilibrium
Reasons for not attaining HW equilibrium
non-random mating (inbreeding, assortative mating, geographical structure), natural selection, mutation, migration, differences in allele frequencies in male and females.

12. k alleles Mother Father Allele frequency in the next generation A1 A2 Ak
Frequencies
pA1
pA2
pAk
Mother
Father
Allele frequency in the next generation A1 A2 A1 A2
pA1
pA1
PA1A1 = pA12
PAiAi = pAi2
PAiAj = pAi pAj+ pAj pAi = 2 pAi pAj
H-W eq
Problem 2 The frequencies of A, B, and AB blood types were 0.24, 0.39 and Estimate A, B, O frequencies assuming H-W eq.

13. Test of H-W equilibrium (c2 test)
2 alleles: A (pA), a (pa) pA + pa =1
Expected values at H-W equilibrium AA Aa
Sum
Expected freq.
pA2
2 pA pa
pa2 1
Expected number
npA2
n2pA pa
n pa2 n
Estimate the frequencies and compute the following statistic
(approximately distributed as χ２ with d. f. 1)

14. Example (MN blood type)
MN blood type (New York African)
Genotype MM MN NN Total
Counts (Obs)
Frequency
Expected
pM= =0.480 pN=0.520
c2=( )2/ = < 3.86 (df=1)
Problem 3 Test H-W equilibrium in the following,
Genotype ST/ST ST/CH CH/CH Total
Counts (Obs)

15. Inbreeding Inbreeding
Mating in which two genes in the offspring are identical by descent (ibd) (descent from a common ancestral gene).
Ex. 1　selfing Ex. 2 brother-sister mating

16. Coefficient of inbreeding
F : coefficient of inbreeding
F = Prob[two genes in the individual are identical by descent（ibd）]
ex. selefing a b
F = Prob[two genes are from a」
＋Prob[two genes are from b」
= =0.5

17. Coefficient of inbreeding and genotype frequencies
PAA : AA frequency
PAa : Aa frequency
case 1（ibd, F）
case 2（not ibd, 1-F）
case 2 （not ibd, 1-F）
same A A A A A a pA pA pA pA 1 pa AA AA Aa pA
pA2
2pA(1-pA)
PAA = (1-F)pA2+FpA
PAa = 2(1-F)pA(1-pA)

18. Computation of F (1) a b a b m n I I

19. Computation of F (2) A is also inbred
FA > 0 （FA : Coefficient of inbreeding of A） FA A a b
In the general case (m and n individuals on each descent as in case (1)) I

20. Computation of F (3) Ex. Full-sib mating A1, FA1 Ai, FAi
Multiple common ancestors
Sum over all ancestors I
Ex. Full-sib mating I

21. Inbreeding depression
genotype AA Aa aa
value 1 1-hs 1-s
allele A a
frequency p q
WF ：Average value with coefficient of inbreeding, F
Inbreeding depression

22. Inbreeding depression in human populations
Infant mortality rate of 1000 offspring by unrelated and first-cousin mating in various countries
”Evolutionary Analysis”より