Transcript Evolution Along Selective Lines of Least

EVOLUTION ALONG
SELECTIVE LINES OF
LEAST RESISTANCE*
Stevan J. Arnold
Oregon State University
*ppt available on Arnold’s website
Overview
• A visualization of the selection surface tell us more than
directional selection gradients can.
• Selection surfaces and inheritance matrices have
major axes (leading eigenvectors).
• Peak movement along these axes could account for
adaptive radiation.
• We can test for different varieties of peak movement
using MIPoD, a software package.
• A test case using MIPoD:
the evolution of vertebral numbers in garter snakes.
• Conclusions
Directional selection gradients
and what they tell us
1. Suppose you have data on the fitness (w) of each individual
in a sample and measurements of values for two traits (z1
and z2) .
2. You can fit a planar selection surface to the data, which has two
regression slopes, β1 and β2:
w    1z1  2 z2  
3. The two slopes are called directional selection gradients. They
measure the force of directional selection and can be used to predict
the change in the trait means from one generation to the next: e.g.,
z1  G111  G122
Lande & Arnold 1983
Stabilizing selection gradients
and what they tell us
1. You can fit a curved (quadratic) selection surface to the data using
a slightly more complicated model:
w    1 z1  2 z2   z   22 z2   12 z1 z2  
1
2
2.
2
11 1
1
2
2
γ11 and γ22 measure the force of stabilizing (disruptive) selection and
are called stabilizing selection gradients.
3.
γ12 measures the force of correlational selection and is called a
correlational selection gradient.
4. The two kinds of selection gradients can be used to predict how much
the inheritance matrix, G, is changed by selection (within a generation):
 s G  G (   T )G
Lande & Arnold 1983
Selection surfaces and adaptive
landscapes have a major axis, ωmax
0 
 .020
r  0
49 0 

 0 49

Value of trait 1
(b)
50 0 

 0 50
P
Average value of trait 1
(c)
Value of trait 2
 .020
 
 0
Average value of trait 2
Average value of trait 2
Value of trait 2
(a)
 .020  .023
 

  .023  .020
r  0.9
49 44

44 49

Individual
selection
surfaces
Value of trait 1
ωmax
(d)
Adaptive
landscapes
50 44

44 50
P
Average value of trait 1
Arnold et al. 2008
The G-matrix also has a major axis, gmax
gmax
Arnold et al. 2008
Average value of trait 2
Peak movement along ωmax could account for
correlated evolution: how can we test for it?
Average value of trait 1
Arnold et al. 2008
MIPoD:
Microevolutionary Inference from
Patterns of Divergence
P. A. Hohenlohe & S. J. Arnold
American Naturalist March 2008
Software available online
MIPoD: what you can get
Input: neutral process model
• phylogeny
• trait values
• selection surface (≥1)
• G-matrix (≥1)
• Ne
Output:
• Test for adaptive,
correlated evolution
• Tests for diversifying and
stabilizing selection
• Tests for evolution along
genetic lines of least
resistance
• Tests for evolution along
selective lines of least
resistance
A test case using MIPoD
The evolution of vertebral numbers in
garter snakes: a little background
Phylogeny of garter snake species based on four mitochondrial
genes; vertebral counts on museum specimens
body tail vertebral counts
190K generations
4.5 Mya ≈ 900,000 generations ago
de Queiroz et al. 2002
Observe correlated evolution of body and
tail vertebral numbers in garter snakes
110
tail vertebrae
100
90
80
70
60
50
120
130
140
150
160
170
180
body vertebrae
Hohenlohe & Arnold 2008
Correlated evolution: described with a 95%
confidence ellipse with a major axis, dmax
110
tail vertebrae
100
90
80
dmax
70
60
50
120
130
140
150
160
170
180
body vertebrae
Hohenlohe & Arnold 2008
An adaptive landscape vision of the
radiation: a population close to its adaptive
peak
110
ωmax
tail vertebrae
100
90
80
70
60
50
120
130
140
150
160
body vertebrae
170
180
An adaptive landscape vision of the radiation:
peak movement principally along a selective line of
least resistance
110
ωmax
tail vertebrae
100
90
80
70
60
50
120
130
140
150
160
body vertebrae
170
180
Arnold et al. 2001
Vertebral numbers may be an adaptation to
vegetation density
Jayne 1988, Kelley et al. 1994
MIPoD
Input:
•
•
•
•
•
phylogeny of garter snake species
mean numbers of body and tail vertebrae
selection surfaces (2)
G-matrices (3)
Ne estimates
Output: uses a neutral model to assess the
importance and kind of selection
Hohenlohe & Arnold 2008
-2σ
tail vertebrae
-1σ
0
+1σ +2σ
Field growth rate as a function of vertebral numbers
-2σ
selective line of least resistance
ωmax
-1σ
0
+1σ +2σ
body vertebrae
Arnold 1988
tail vertebrae
-1σ
0
+1σ +2σ
Crawling speed as a function of vertebral numbers
selective line of
least resistance
-2σ
ωmax
-2σ
-1σ
0
+1σ +2σ
body vertebrae
Arnold & Bennett 1988
Similar G-matrices in three poplations, two species
tail vertebrae
95
T. sirtalis
85
75
65
Lassen T. elegans
Humboldt T. elegans
155
165
175
body vertebrae
Dohm & Garland 1993, Phillips & Arnold 1999
Similar G-matrices in three poplations, two species
Schluter’s conjecture: population differentiation occurs
along a genetic line of least resistance, gmax
tail vertebrae
95
T. sirtalis
85
gmax
75
65
Lassen T. elegans
Humboldt T. elegans
155
165
175
body vertebrae
Dohm & Garland 1993, Phillips & Arnold 1999
Estimates of Ne for two species from
microsatellite data: average Ne ≈ 500
T. elegans
T. sirtalis
Manier & Arnold 2005
Neutral model for a single trait: specifies the
distribution of the trait means as replicate lineages
diverge
• Trait means normally distributed with variance proportional to
elapsed time, t, and genetic variance, G, and
• inversely proportional to Ne
Probability
t=200
h2 = 0.4
Ne = 1000
t=1,000
t=5,000
t=20,000 generations
mean body vertebrae
Lande 1976
Neutral model for two traits: as replicate populations
diverge, the cloud of trait means is bivariate normal
tail vertebrae
• Size: proportional to elapsed time and the size of the average
G-matrix , inversely proportional to Ne
• Shape: same as the average G-matrix
• Orientation: same as the average G-matrix, dmax = gmax
t=5,000 generations
t=1,000
t=200
body vertebrae
Lande 1979
Neutral model: equation format
• One trait, replicate
lineages
• D(t) = G(t/Ne )
• Multiple traits,
replicate lineages
• D(t) = G(t/Ne )
• Multiple traits,
lineages on a
phylogeny
• A(t) = G(T/Ne )
Neutral model: specifies a trait
distribution at time t
• Trait means are normally distributed with mean μ
and variance-covariance A
P ( ) 
exp[ (1 / 2)(   )T A1 (   )]
(2 ) mxn A
• Using that probability, we can write a likelihood
expression
• Using that expression, we can test hypotheses
with likelihood ratio tests
Neutral model: specifies a trait
distribution at time t
• Trait means are normally distributed with mean μ
and variance-covariance GT/Ne
P( ) 
exp[ (1 / 2)(   )T (GT / N e ) 1 (   )]
(2 ) mxn (GT / N e
• Using that probability, we can write a likelihood
expression
• Using that expression, we can test hypotheses
with likelihood ratio tests
Hypothesis testing in the MIPoD
maximum likelihood framework
bold = parameters estimated by maximum likelihood (95% confidence interval)
Size: we observe too little divergence
6
tail vertebrae
4
2
0
P < 0.0001
-2
-4
-6
-6
-4
-2
0
2
4
6
body vertebrae
Implication: some force (e.g., stabilizing
selection) has constrained divergence
Hohenlohe & Arnold 2008
Shape:divergence is more elliptical than
we expect
1
tail vertebrae
0.5
0
P = 0.0122
-0.5
-1
-1
-0.5
0
0.5
1
body vertebrae
Implication: the restraining force acts more
strongly along PCII than along PCI
Hohenlohe & Arnold 2008
tail vertebrae
Orientation: the main axis of divergence
is tilted down more than we expect
P = 0.0001
body vertebrae
Implication: the main axis of divergence is
not a genetic line of least resistance
Hohenlohe & Arnold 2008
Divergence occurs along a selective line
of least resistance
No, P = 0.0003
1
tail vertebrae
0.5
Yes, P = 0.2638
0
-0.5
-1
-1
-0.5
0
0.5
1
body vertebrae
Implication: adaptive peaks predominantly
move along a selective line of least resistance
Hohenlohe & Arnold 2008
-2σ
tail vertebrae
-1σ
0
+1σ +2σ
Field growth rate as a function of vertebral numbers
-2σ
ωmax
coincides
with dmax
-1σ
0
+1σ +2σ
body vertebrae
Arnold 1988
An adaptive landscape vision of the radiation:
peaks move along a selective line of least
resistance in the garter snake case
110
tail vertebrae
100
90
80
70
60
50
120
130
140
150
160
170
180
body vertebrae
Hohenlohe & Arnold 2008
General conclusions
• Using estimates of the selection surface, the G-matrix,
Ne , and a phylogeny enables us to visualize the adaptive
landscape and to assess the role that it plays in adaptive
radiation.
• Need empirical tests for homogeneity of selection
surfaces.
• Need a ML hypothesis testing framework that explicitly
incorporates a model of peak movement.
Acknowledgements
Lynne Houck (Oregon State Univ.)
Russell Lande (Imperial College)
Albert Bennett (UC, Irvine)
Charles Peterson (Idaho State Univ.)
Patrick Phillips (Univ. Oregon)
Katherine Kelly (Ohio Univ.)
Jean Gladstone (Univ. Chicago)
John Avise (UC, Irvine)
Michael Alfaro (UCLA)
Michael Pfrender (Univ. Notre Dame)
Mollie Manier (Syracuse Univ.)
Anne Bronikowski (Iowa State Univ.)
Brittany Barker (Univ. New Mexico)
Adam Jones (Texas A&M Univ.)
Reinhard Bürger (Univ. Vienna)
Suzanne Estes (Portland State Univ.)
Paul Hohenlohe (Oregon State Univ.)
Beverly Ajie (UC, Davis)
Josef Uyeda (Oregon State Univ.)
References*
• Lande & Arnold 1983 Evolution 37: 1210-1226.
• Arnold et al. 2008 Evolution 62: 2451-2461.
• Hohenlohe & Arnold 2008 Am Nat 171: 366-385.
• de Queiroz et al. 2002 Mol Phylo Evol 22:315-329.
• Estes & Arnold 2007 Am Nat 169: 227-244.
• Arnold et al. 2001 Genetica 112-113:9-32.
• Jayne 1988
• Kelley et al. 1994 Func Ecol 11:189-198.
• Arnold 1988 in Proc. 2nd Internat Conf Quant Genetics
• Arnold & Bennett 1988 Biol J Linn Soc 34:175-190.
• Phillips & Arnold 1999 Evolution 43:1209-1222.
• Dohm & Garland 1993 Copeia 1993: 987-1002.
• Manier et al. 2007 J Evol Biol 20:1705-1719.
• Lande 1976 Evolution 30:314-334.
• Lande 1979 Evolution 33: 402-416.
•Arnold & Phillips 1999 Evolution 43: 1223__________________________________________________
* Many are available as pdfs on Arnold’s website