12/5/14 Migration/Selection Equilibrium
v what level of migration is sufficient to
counter the effects of selection?
² “divergence with gene flow”
Hemoglobin
1 12/5/14 Waterfowl Hemoglobin
v waterfowl adapted to high-altitude
² Bar-headed goose: Pro-119-alpha --> Ala
² Andean goose: Leu-55-beta --> Ser
Waterfowl Hemoglobin
2 12/5/14 Dendrocygna
Thalassornis
Nettapus
Oxyura
Nomonyx
Heteronetta
Stictonetta
Branta
Anser
Cygnus
Coscoroba
Cereopsis
Malacorhynchus
Biziura
Chenonetta
Anas cyanoptera
A. sibilatrix
A. waigiuensis
A. formosa
Tachyeres
Lophonetta
Speculanas
Amazonetta
Hymenolaimus
Sarkidiornis
Cyanochen
Pteronetta
Marmaronetta
Asarcornis
Aythya
Rhodonessa
Netta
Calonetta
Tadorna
Alopochen
Aix
Cairina
Somateria
Polysticta
Merganetta
Chloephaga
Neochen
Clangula
Plectropterus
Melanitta
Histrionicus
Bucephala
Mergellus
Mergus
Lophodytes
Bar-headed Goose: Anser indicus
Andean Goose: Chloephaga melanoptera
Jessen et al. 1991 Adaptation of bird hemoglobins to high
altitudes - demonstration of molecular mechanism by protein
engineering. PNAS 88 (15): 6519-6522.
v bar-headed goose: Pro-119-alpha --> Ala
v Andean goose: Leu-55-beta --> Ser
v both mutations destabilize the deoxygenated
state of hemoglobin
v site-directed mutagenesis to engineer Ser-55beta into human hemoglobin
v increases affinity of molecule for oxygen
v crystal structure of engineered molecule
identical to human hemoglobin except for the
2-carbon gap left by the replacement of
methionine with serine
3 12/5/14 McCraken et al. 2010
Mol. Phylog. Evol.
Hemoglobin in
Andean Waterfowl
4 12/5/14 Hemoglobin in
Andean Waterfowl
Yellow-billed
pintail (Anas
georgica)
McCracken et al.
2009 Mol. Biol. Evol.
5 12/5/14 MIGRATE
(LAMARC)
assumptions:
v  system at
mutation/drift
equilibrium
v  constant
population sizes
and migration
rates through time
v  no selection
N1
m15,m51
m12, m21
m25, m52
N5
m14, m41 m13, m31
m45,
m54
N4
m35, m24,
m53 m42
m34,
m43
N2
m23,
m32
N3
Migrate Results
McCracken et al. 2009 Mol. Biol. Evol.
6 12/5/14 Migration/Selection Equilibrium
v what level of migration is sufficient to counter
the effects of selection?
m>s
²  “divergence with gene flow”
Migration/Selection Equilibrium
v suppose an allele (a) is disadvantageous in one
population but not another
v fitness of genotypes
² AA: 1, Aa: 1-hs, aa: 1-s
v q*: frequency of a in incoming migrants
v mi, mo: incoming and outgoing migration rates
Δq =
−spq #$q + h ( p − q )%&
1− sq ( 2hp + q )
+ mi q * −mo q
7 12/5/14 Pocket mice
v  Hoekstra et al. 2004 Evolution 58:
1329-1341
v  light and dark coloration
produced by alternative alleles
of MC1R gene
Estimating Selection in Pocket Mice
v mi, mo from MIGRATE analysis of mtDNA
v p, q, q* from DNA sequencing
v h from phenotype/genotype comparison
v selection against the Mc1r d allele on dark
substrate was 0.013 to 0.126
² depending on estimate of Ne
v stronger than selection against dark mice on
light substrate
Δq =
−spq[q + h ( p − q)]
1− sq(2hp + q)
+ miq * −moq
Hoekstra et al. 2004
Evolution 58: 1329-1341
€
8 12/5/14 h = 0.5, q* = 0.9
0.8
0.01,
miim
m ==o0.001
0.01
= 0.01,
=0
ss==s0.01,
m
==m
i =oom
Allele Frequency (a)
0.7
0.6
0.5
0.4
0.3
0.2
1
7
13
19
25
31
37
43
49
55
61
67
73
79
85
91
97
Generations
Migration rate vs. Number of migrants
v migration rates yielding Nm = 1
² Ne = 100, m = 0.01
² Ne = 1,000, m = 0.001
² Ne = 10,000, m = 0.0001
² Ne = 100,000, m = 0.00001
9 12/5/14 Migration rate vs. Number of migrants
v number of migrants equivalent to m > s
for s = 0.01
² Ne = 100, Nm > 1
² Ne = 1,000, Nm > 10
² Ne = 10,000, Nm > 100
² Ne = 100,000, Nm > 1,000
Migration rate vs. Number of migrants
v migration rate yielding Nm = 1
²  Ne = 10,000, m = 0.0001 = 0.01%
v number of migrants equivalent to
m>s
²  Ne = 10,000, s = 0.01, Nm > 100
v the level of migration needed to prevent
adaptive divergence is generally much greater
than the level needed to prevent neutral
divergence
v populations can diverge due to selection
despite ongoing gene flow!
10 12/5/14 Genome scan
v compare FST at multiple loci to look for
outliers that may be under selection
11 12/5/14 Yellow-billed
pintail (Anas
georgica)
McCracken et al.
2009 Mol. Biol. Evol.
12 12/5/14 Conservation Genetics and Contrasting
Results for Different Loci
v basic question: are populations genetically
differentiated?
²  if so, should we try to maintain genetic diversity
by managing populations separately?
v analyses almost always focus on “neutral” loci
²  errors possible in both directions:
²  “undifferentiated” populations may differ in
important adaptive traits
²  “differentiated” (historically isolated)
populations may be essentially identical in
functional traits
13 12/5/14 Equlibrium vs. Non-equlibrium Models
v estimation of Nm from FST requires migration/
drift equilibrium assumption
v inherent in island model used by MIGRATE
(LAMARC)
v also possible to estimate gene flow under a
non-equilibrium model
²  e.g., IM, IMa software
IM: nonequilibrium
model
FST ~ 0
FST > 0
14 12/5/14 mtDNA gene tree for big
brown bats (Eptesicus fuscus)
Turmelle et al. 2011 Mol. Ecol. nuclear gene trees for big brown bats (Eptesicus fuscus)
eastern NA
Caribbean
Colorado
"southwest"
S. AZ, Sonora
Inyo Co., CA
S. Mexico; VZ
S. California
N. California
Pacific NW
outgroups
4
nCR
4
Enol
4
26
15
EPFR
14
18
EPDI
42
EPBR
8
9
3 bp
indel
7
25
5
5
15
8
EPDI
4
EPFR
EPBR
6
Turmelle et al. 2011 Mol. Ecol.
15 12/5/14 Pavlova et al. (2013) Perched at the mito-nuclear crossroads: divergent
mitochondrial lineages correlate with environment in the face of ongoing
nuclear gene flow in an Australian bird. Evolution 67, 3412-3428.
mtDNA
nDNA (microsatellites)
eastern yellow robin
Eopsaltria australis
16 12/5/14 Pavlova et al. (2013) Perched at the mito-nuclear crossroads: divergent
mitochondrial lineages correlate with environment in the face of ongoing
nuclear gene flow in an Australian bird. Evolution 67, 3412-3428.
mtDNA
eastern yellow robin
Eopsaltria australis
nDNA
(microsatellites)
Pavlova et al. (2013) Perched at the mito-nuclear crossroads: divergent
mitochondrial lineages correlate with environment in the face of ongoing
nuclear gene flow in an Australian bird. Evolution 67, 3412-3428.
mtDNA
nDNA (sequenced loci)
eastern yellow robin
Eopsaltria australis
17 12/5/14 Pavlova et al. (2013) Perched at the mito-nuclear crossroads: divergent
mitochondrial lineages correlate with environment in the face of ongoing
nuclear gene flow in an Australian bird. Evolution 67, 3412-3428.
Mutation, Selection & Drift
µ a→A
v mutation (infinite N,
fˆA =
µ a→A + µ A→a
no selection)
v single-locus
vAA f A2 + vAa f A
selection (infinite N,
f A! =
no mutation)
v
v genetic drift (no
Pr { j alleles of type A}
selection, no
! 2N $
mutation)
j 2 N− j
= ##
"
j
&& f A fa
%
18 12/5/14 Mutation, Selection & Drift
v combining mutation, selection & drift
into a single model
² the diffusion approximation can be used to
predict the equilibrium distribution of allele
frequencies (Wright 1931)
φ ( x ) = Ce 4 N e sx x 4 N e v−1 (1− x) 4 N e u−1
²  where x is the frequency of allele A, s is the selection
coefficient, u and v are mutation rates (A to a and a to A),
and C is a constant set to make the integral 1
€
Mutation, Selection & Drift
Hartl & Clark
φ ( x ) = Ce 4 Nesx x 4 Neν −1 (1− x)4 Neµ −1
wAA = 1+2s, wAa = 1+s, waa = 1
² where x is the frequency of allele A, s is the
selection coefficient, µ and v are mutation
rates (A to a and a to A), and C is a constant
set to make the integral 1
Hamilton
φ ( p) = Cp 4 Neµ −1q 4 Neν −1e 4 Nespq
wAA = waa = 1-s, wAa = 1
² where u and v are the forward and
backward mutation rates (??)
19