1. Hudson Kreitman Aguadé 1987
Multilocus approach:
Jody Hey’s web page
Maximum Likelihood aaproach
Wright & Charlesworth (2004)
Demography affects entire genome
Selection acts on single (few) loci

2. HKA Test The “footprint” of balancing selection at Adh in Drosophila
Kreitman and Hudson (1991) Genetics 127:565-82
polymorphism
Adh locus
Adh-dup
Fast/Slow
polymorphism
HKA Test
Adjacent silent sites
in linkage disequilibrium
Fast F
Fast F
Adh
Adh-dup 16 20
Fast F
Fast F
Slow S 50 13
Slow S
Slow S
Slow S
Distant sites in Linkage Equilibrium
P < 0.02

3. The effect of recombination on levels of polymorphism
Marker loci # • • • • • • • * • • • • • •
0.012
0.010
0.008
0.006
0.004
0.002
0.000 • • • # •
Rate of
re-
combi-
nation
DNA polymorphism • • • • • • • • •
Aquadro, Begun
& Kindahl, 1994 *
Physical position along 3rd chromosome
0.1
0.05
0.000 • * • •
DNA
divergence # •
Locus 1 33 1 • • • 26 6
Begun & Aquadro 1992
P < 0.05
Rate of recombination

4. * = beneficial mutation
Reduced polymorphism due to selective sweeps (adaptive mutations and hitchhiking) *
* = beneficial mutation *
No recombination:Polymorphism removed *
Free recombination: Locally reduced variation
Reduced polymorphism due to background selection eliminating deleterious mutations X
X = deleterious mutation
“mutation-free” chromosomes {
No recombination:Polymorphism removed
Free recombination: little effect

5. Testing for selection in mtDNA
The genetic code and DNA “phenotypes”

6. Polymorphism in mtDNA and the MK test
N S
Population or family
Sister species
or unrelated
strain B.
dN/dS
‘within’
‘between’
Polymorphism and divergence of mutations
Allele frequency
Time
Type Polymorphic Fixed
of within between
mutation populations? species?
Neutral Yes Yes
Beneficial No Yes
Deleterious Yes No
Balanced Yes Yes & No
dN/dS
‘within’
‘between’
= Neutrality Index (NI)
NI < 1.0 implies positive selection
NI > 1.0 implies negative selection
(opposite of simple dN/dS)
Rand & Kann (1996) MBE
Rand (2008) PLoS Biology

7. McDonald Kreitman Test

8. Silent Replacement MK test S R F P S R F P F P S R 100 10 20 2 100 10
Fixed
Poly
morphic
MK test N S
N S
Population or family
Sister species
or unrelated
strain
dN/dS
‘within’
100 10 20 2
dN/dS
‘within’
‘between’
= Neutrality = 1.0
Index (NI) S R
F P
This based on the McDonald Kreitman test, which should be familiar to every one
I will review some salient points, as I plan to bludgeon you with several of the figures later on:
Sequence eityhin and between, count silent and replacement changes, classify as fixed or polymorphic
MK data can be represented as an Odds Ratio, what I have called the neutrality index, as a ratio of ratios
Three examples: table portrayed as a histogram:
Left (BLUE) axis is silent differences fixed or polymorphic, Right (RED) axis is replacement differences – NOTE different scale.
Negative selection will lead to an excess of amino acid polymorphism (NI > 1), Positive selection to a deficiency of amino acid polymorphism (NI < 1)
NOTE different scales, so in this case the departure appears in the polymorphism column if the explanation is extra fixation. S R
F P
F P S R
NI>1
negative
NI=1
neutral
NI<1
positive

9. Polymorphism and Divergence at Silent and Replacement Sites
Rand&Kann 1996
MBE 13:
=> mildly deleterious => advantageous

10. N.I. is very sensitive to selection
Sawyer&Hartl (1992)
Akashi (1995)
Nachman (1998)
Weinreich & Rand (2000)
Kimura (1983)
Negative Neutral Positive

11. Nuclear and mtDNA genes have distinct N.I. distributions
Arabidopsis nuclear genes are like mtDNA
Weinreich and Rand (2000)
P < 0.005
Data include:
• 31 mtDNA data sets
• 37 Drosophila nuclear data sets
• 6 Arabidopsis nuclear data sets
• About 1000bp per data set
• About 20 alleles per data set
• About 1.5 million base pairs
• About 1.5 liters of Taq polymerase
All
data
sets
P <
Significant
data
sets
Gerber et al. 2001
Ann. Rev. Genet.
41 animal mtDNAs
Same result
Adaptive evolution:
Excess amino acid
fixed differences
Mildly deleterious evolution:
Excess amino acid
polymorphism

12. Low recombination, Muller’s ratchet effects:
Accumulation of weakly deleterious mutations
Occasional beneficial mutations cannot out-compete load of deleterious mutations
Selective sweeps reduce effective population size, and weaken selection
15 vs. 3
High recombination, faster evolution:
Chromosome segments can respond to “local” fitness differences
Beneficial mutations fix, deleterious mutations remain at low frequency
2 vs. 1
can go to fixation

13. Recombination rate Supports hitchhiking model (weakly)
419 genes, 24 alleles per gene
DNA polymorphism
Tajima’s D
Recombination rate
Supports hitchhiking
model (weakly)
DNA divergence
Recombination rate

15. Fay & Wu (2002): A frequency twist to the MK test
The distribution of site frequencies is important
Type of mutation Rare? Intermediate? Common?
Yes Yes yes
No More likely
Yes No No
No Yes No

16. Allele (Site) frequency distribution
Excess of low frequency alleles
Excess of intermediate frequency alleles
Neutral (Ewens) frequency spectrum
Chimp
Human N S
Outgroup needed
to distinguish “derived”
Alleles (18,19 vs 1,2)
Nielsen (2005) Ann. Rev. Genet. 39:197
Sequence 20 alleles, record frequency of each SNP

17. 419 genes, 24 alleles sequenced/gene, compared to D. simulans

18. (Fixed A) / (Fixed S) Fixation Index = (Poly A) / (Poly S)
(Poly A) / (Fixed A)
(Poly S) / (Fixed S)
NI =

19. Noncoding DNA is more constrained than silent sites

20. How do you perform an MK test on non-coding DNA?
Need to define functional classes

21. Proportion of positively selected fixations
= 1 - (Ds•Px) / (Dx•Ps)
Where: s = silent, x = other class
Smith & Eyre-Walker (2002) Nature 415:
• Silent sites are neutral
• Assumes polymorphism is neutral
• Excluding singletons increases estimate of positive selection

22. Estimating selection coefficients from MK data
Excluding singletons increases estimate
Mildly deleterious polymorphisms at low frequency

23. Measuring DNA Evolution
Align sequences between species
Determine length of sequences, L
Count number of differences
Divergence = proportion of differences
D = p-distance = (number of differences) / (length of sequence)
Rate of divergence
 = (sequence divergence) / (age of common ancestor)
 = D / time
Rate of substitution
 = D / 2 x time
time
Example: 5 differences in 100
D = 0.05, t = 6 million years
Divergence = 0.05/6x106
Divergence = 8.3 x 10-9

24. Jukes Cantor One parameter model
= rate of substitution
PA(t) = ¼ + ¾ e-4at = probability that A remains A at time t
PNN = ¼ + ¾ e-8at = probability that two sequences have the same nucleotide at N
D = proportion of different nucleotides = 1 - PNN
Dhat = 3/4(1-e-8t)
K = - ¾ ln (1-4/3p)
where p = proportion of nucleotide differences (# diffs./total bp)

25. Kimura two-parameter modelb
a = rate of transition substitution
b = rate of transversion substitution
PAA(t) = ¼ + ¾ e-4bt + ½ e-2(a+b)t
= probability that A remains A at time t
K = ½ ln(1/[1- 2P-Q]) + ¼ ln(1/[1-2Q])
where P = proportion of transitional differences
Q = proportion of transversional differences

26. P-distance
Jukes Cantor
Kimura 2-parameter
Tamura-Nei
Etc…

27. Molecular clocks
Approximately constant
Divergence of proteins
K = •f0
Rate of substitution =
Mutation rate x proportion of
neutral mutations
“Saturation” due to multiple
Hits in DNA evolution

29. 100%
Synonymous
site
33%
Synonymous AND 66% nonsynonymous
site: T->C silent; T->A or G nonsynonymous

30. dN and dS
dS = number of synonymous differences PER
synonymous site (not per all sites)
dN = number of nonsynonymous differences PER
nonsynonymous site (not per all sites)
More nonsynonymous sites than synonymous

31. DNA test of neutrality Antigen binding sites: dN/dS > 1
“positive” selection
Neutral prediction:
amino acid (nonsynonymous) substitution rate (dN) should be lower than silent (synonymous) substitution rate (dS)
True for most genes
Follows from functional constraint argument
Different for Major Histocompatibility Complec (MHC) loci
Antigen recognition sequence shows dN > dS
Rest of molecule shows dN > dS, as expected
Amino acid mutations are favored in antigen recognition region
Promotes diversity, better recognition of foreign peptides
Rest of molecule: dN/dS < 1
Negative (purifying) selection

35. MK vs HCY tests Human Chimp N S dN dN FR PR dS dS FS PS (dN/dS)within
Fixed
Poly
Fixed
Poly dN
between dN
within
Non
synonymous
Replacement FR PR dS
between dS
within
Silent FS PS
synonymous
(dN/dS)within
Niw =
(dN/dS)between
NI = (PR/FR) / (PS/FS)
w = (dN/dS);
McDonald-Kreitman test
2x2 G-test
Or FET
Hasegawa, Cao, Yang test
Likelihood of tree with 1 w
vs.
Likelihood of tree with 2 w
Chimp
Human N S

36. HCY test is more powerful than MK test w ratio is better than NI* ** NI
or w ratio NI
NIw NI
or NIw
Variation among genes in NeS
NI values larger with HCY
HCY NIw leads to larger estimate of negative selection
HCY becomes more powerful as species divergence increases

37. Anatomy of a phylogenetic tree
Terminal (external) nodes
Taxa =
OTUs =
Operational
taxonomic units
Taxon1
Taxon2
Taxon3
Taxon4
Taxon5
Taxon6
Polytomy
Non-dichotomous
splitting
External branch
Internal branch
Internal nodes
Root

38. Relative rate test KAC = KBC KOC is shared Tajima test
(m1-m2)2 / (m1+m2)
Chi square, df=1
Species O m1 m2
Species A
Species B
Species C