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Adaptive Landscapes
E3: Lecture 10
Adaptation
• Linnen et al. 2009 find
that a single amino acid
deletion in Agouti may be
responsible for adaptive
color change in deer mice.
Catherine
Linnen
• Schluter and colleagues
(e.g., Barrett et al. 2008)
have found that an allele
shift at Ectodysplasin
underlies adaptive shifts in
stickleback armor.
• Bradshaw & Schemske
(2003) found that change at
YUP can account for shifts
in pollinator visitation in
monkeyflowers.
Dolph
Schluter
How do these findings jibe with the
orthodox view of Darwinian
evolution?
Toby Bradshaw
Hopi
Hoekstra
Adaptive Landscapes
Lecture Outline
• Fisher’s Geometric Model
• Wright’s Adaptive Landscape
• Bottom-Up Approach
• Top-Down Approach
• Summary
Adaptive Landscapes
Lecture Outline
• Fisher’s Geometric Model
• Wright’s Adaptive Landscape
• Bottom-Up Approach
• Top-Down Approach
• Summary
Fisher’s Geometric Model
• One of the first models to address the topic of adaptation
focused on phenotypic adaptation: Fisher’s geometric model.
• Imagine that different traits of an organism are laid out on
Cartesian axes, with the optimal combination on the origin.
• Now imagine a change in the environment that
generates a new optimal phenotype (e.g., a
predator arrives selecting for longer, deeper fish)
• The organism currently exists some distance
from the new optimum; any point in phenotype
space the same distance from this new optimum
was assumed equally fit.
R. A. Fisher
body
depth
• Evolutionary movement in phenotype space
requires mutation, represented as a vector.
• Fisher assumed that mutations:
- were random, not directed.
- exhibited pleiotropy (affecting multiple traits).
- could differ in the size of their effect.
body length
equally probable
Baby Steps or Giant Leaps?
• Now given that mutation size could vary, Fisher
pondered the optimal size of the phenotypic effect
of mutations: would these be small or large?
• Given that a larger fraction of the mutations would
be beneficial if the effect size were small, Fisher
reasoned that most adaptive evolution occurred by
mutations with small effect.
Talk to folks around you for 2 minutes about:
1) What do you think of Fisher’s proposition?
2) Are there any reasons to think that
adaptation proceeds through mutations of
larger effect?
• Motoo Kimura reasoned that while smaller steps
are more likely to be beneficial, larger steps are
more likely to be fixed– thus, intermediate sized
steps might be favored.
• Current versions of this model suggest step size
should decrease as the optimum is approached.
Motoo
Kimura
Adaptive Landscapes
Lecture Outline
• Fisher’s Geometric Model
• Wright’s Adaptive Landscape
• Bottom-Up Approach
• Top-Down Approach
• Summary
Picking the Wright Metaphor
In 1932, Sewall Wright was invited to give a nontechnical talk on his view of evolution at the sixth
International Congress of Genetics.
•
Wright (1932) started with a very simple idea: a
functional map from genotype to fitness, where
“the entire field of possible gene combinations
[could] be graded with respect to adaptive value.”
•
Thus, a genotype-to-fitness (G→F) map and
specification of how genotypes are connected
defines an adaptive landscape.
Fisher
Wright
Haldane
Fitness
•
Figure 2 from Wright (1932)
Evolution in the Balance
•
Wright envisioned populations (of genotypes) as
“clouds” on the landscape.
•
The movement of these clouds determines the course
of evolution.
•
Wright felt that the landscape was likely very rugged;
the problem that occupied him was how a population
could mover from a lower peak to a higher peak
•
His shifting balance theory rests on two assumptions:
1.
2.
•
Genotype Space
Epistasis leading to distinct “peaks” (rugged landscape)
The population is structured (as semi-isolated sparsely
populated demes)
Physical Space
Wright’s shifting balance invokes several processes
(mutation, selection, drift, and migration):
Phase 1:
Phase 2:
Phase 3:
Demes drift over the adaptive landscape
Selection drives demes to new peaks
Competition between demes where the most
fit pulls the metapopulation to its adaptive peak
deme 2
deme 3
deme 1
deme 4
The Expansive Landscape
•
The landscape metaphor has been a very
successful one, sometimes taking different
forms from Wright’s original formulation:
–
–
•
Mapping gene frequency to fitness
Mapping phenotype to fitness
In many of these cases, evolution is
center-stage, but issues arise when
considering “movement” in the landscape.
–
–
•
Genetic linkage
Genetic underpinnings of phenotype
The G→F map that Wright envisioned
might be decomposed into two maps:
–
–
•
Genotype to phenotype (G→P)
Phenotype to fitness (P→F)
Thus, Wright’s metaphor touches on a set
of issues important to biology:
–
–
–
Development (G→P)
Ecology (P→F)
Evolution (movement in the landscape)
Benkman,
2003
The Shifting Landscape
Fitness
Climber
analogy
STATIC
EXOGENEOUSLY
CHANGING
ENDOGENEOUSLY
CHANGING
Take 5 minutes to talk about the following:
1) In what (biological) cases do these different conceptions of the landscape apply?
2) How does one approach the importance of changing landscapes experimentally?
3) Are there reasons this might be important?
The Basic Question
•
F6
Overall, we would like to know
about “the” topography of an
adaptive landscape and how this
influences evolutionary paths.
 13383 nucleotides
 Gene P13 has
421610130 alleles.
100 nm
•
Basic problems
–
–
–
•
The space of genotypes is BIG
Our intuitions from three
dimensional worlds may be illequipped to deal with ultra-high
dimensional worlds.
The landscape may not be static;
indeed, movement on the landscape
may change the landscape!
There have been two approaches
employed up to this point:
–
–
Bottom-up
Top-down
 RNA virus
H. Ackerman
 Volume of virion:
7.9510-5 mm3
Survey Question: Visible universe
 Its size is:
80
3
Suppose you wanted 3.5610
a F6 virusm
 Its age
is: allele;
particle with each unique
P13
10 yrs
you would need to fill 1.3710
the following
Hubble
Ultra Deep Field
with
viruses:
If
filled the
entire
A)you
A gallon
sized
milkvisible
jug universe
with
F6 virions,
each
with
a of
distinct
B) Three
stadiums
the
size
Husky
allele
at
P13
and
updated
the
entire
C) The volume of planet Earth
set
every
nanosecond
from the
D) The
volume
of our sun
beginning
of time,
you would
cover
E) The visible
universe
10 times
over
less than 20% of the P13 genotypes!
Adaptive Landscapes
Lecture Outline
• Fisher’s Geometric Model
• Wright’s Adaptive Landscape
• Bottom-Up Approach
• Top-Down Approach
• Summary
The Bottom-Up Approach
•
One way to approach the basic question is to start with two genotypes
characterized by a set amount of differences (a certain distance apart in the set of
possibilities).
•
Along the shortest paths between these two genotypes, the fitness of
“intermediate” genotypes can be assessed.
•
By fully characterizing this “sliver” of genotype space, the probability of different
mutational paths can be determined and the context-dependence of a given
mutation can be assessed.
A Test System
•
The antibiotic
cefotaxime is a
3rd generation
cephalosporin
with broad
antimicrobial
activity.
cefotaxime
•
Cefotaxime interferes with the
synthesis of the bacterial cell wall.
•
The enzyme b-lactamase hydrolyses
the b-lactam ring, conferring resistance.
•
Different bacterial alleles of blactamase do not break down into fully
sensitive or fully resistant states…
•
For each allele, a minimum inhibitory
concentration (MIC: the drug
concentration that inhibits growth) can
be determined (a fitness proxy).
Bash
TEM b-lactamase
growth
no growth
increasing drug concentration
MIC
A Landscape from the Bottom Up
+----
Dan Weinreich
-----
-+---
--+--
TEMwt
---+-
+++++
TEM*
----+
++---
+++--
+-+--
++-+-
+--+-
++--+
+---+
+-++-
-++--
+-+-+
-+-+-
+--++
-+--+
-+++-
--++-
-++-+
--+-+
-+-++
---++
--+++
++++-
+++-+
++-++
+++++
TEM*
+-+++
-++++
•
Weinreich et al. considered two TEM alleles (TEMwt & TEM*) differing at 5 sites.
•
There are 1+5+10+10+5+1=32 alleles, counting intermediates.
•
The MIC for each of the 32 alleles can be measured (Table 1).
•
There are 5!=120 trajectories between TEMwt and TEM*
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
Probability of Traversing Trajectories
---
•
+--
++-
-+-
+-+
--+
-++
+++
0.1
Consider only three mutations at the
TEM locus with MICs given to the right.
•
Weinreich et al. assume:
–
–
•
The probability of following a trajectory in
which a single step is downward is zero.
The probability of following a trajectory is
diluted by the number of times that an
evolving population could take another
accessible trajectory.
1
9
1
0.1
0.05
7
20
inaccessible paths
9
1
Sign epistasis occurs when the sign
1 effect of a9given mutation
of the fitness
0.1
1
0.1
20
depends on genetic background
0.1
---
1
0.05
--+
0.1
7
0.1
20
0.05
0.05
1
decrease
fitness
7
-1+ +
1
0.1
9
Weinreich et al. find:
–
–
–
Only 18 of 120 trajectories are accessible!
Only a handful of these are probable.
Rampant sign epistasis.
-0.1
+-
7
20
increase fitness
0.05
7
Pleiotropy and Epistasis
•
Weinreich et al. suggested that pleiotropy played a role in generating sign
epistasis.
•
For instance, one mutation improved hydrolytic activity of the enzyme, but also led
to higher aggregation, while another mutation did the opposite.
•
However, both mutations together gave the best of both worlds…
Worsen hydrolysis
Lessen aggregation
[Lowest MIC]
We ought to have
a child together–
think of it…with
my looks and
your brain…
-+
++
--
Improve hydrolysis
Lessen aggregation
[High MIC]
[Very Low MIC]
+-
Improve hydrolysis
Increase aggregation
[Low MIC]
Ah… but what
if it had my
looks and your
brain…
Adaptive Landscapes
Lecture Outline
• Fisher’s Geometric Model
• Wright’s Adaptive Landscape
• Bottom-Up Approach
• Top-Down Approach
• Summary
The Top-Down Approach
•
One way to approach the basic question is to start with (or evolve) several
different genotypes (distributed points in the space of possibilities).
•
These “starting” genotypes may differ in fitness.
•
Genetic neighbors can be generated (via mutagenesis, mutation accumulation
experiments, or selection experiments) and their fitness assessed.
•
From statistical properties of these neighborhoods (e.g., deviations in fitness
between the starting genotypes and the mutants), landscape properties can be
explored in a local sense.
A Top-Down Experiment
• Christina Burch and Lin Chao used a topdown approach to study the landscape
topography of phage F6 (a viral parasite of
the bacterium Pseudomonas syringae).
• Using the same ancestor possessing a
deleterious mutation, two separate phage
populations, A and B, were propagated.
Christina Burch
A
• They found that population A improved in
fitness while population B stayed fairly
constant.
ancestor
phage
B
• The authors considered two hypotheses:
1. Both populations were climbing the same
slope in the landscape, but at different rates.
2. Each population was climbing separate
slopes to separate peaks.
A
A
B
Hypothesis 1
B
Hypothesis 2
Lin Chao
Phage F6
Evolution Redux
• Burch and Chao took a single isolate from
generation 50 of the A and B propagation lines.
• Five replicates of the A replay tended to increase in
fitness (as expected).
• Five replicates of the B replay decreased in fitness!
• The authors took this data as support for
hypothesis 2. Their sampled isolate from A was
below average in fitness and their sampled isolate
from B was above average.
Hypothesis 1
A
Hypothesis 2
A
B
B
A
B
isolate isolate
Adaptive Landscapes
Lecture Outline
• Fisher’s Geometric Model
• Wright’s Adaptive Landscape
• Bottom-Up Approach
• Top-Down Approach
• Summary
Summary
• One of the principle aims of evolutionary biology is to determine how
the process of adaptation occurs.
• Visual metaphors have been employed in thinking about this problem.
• Fisher’s geometric model considers the phenotypic effect of a
mutation as vector of a specific size in phenotype space, which places
the mutant closer or further from a phenotypic optimum.
-Fisher reasoned that small mutations would predominate
-Kimura countered that larger mutations would be more likely to fix
• Wright introduced the adaptive landscape metaphor; a map from
genotype to fitness. He focused on the problem of moving from lower to
higher peaks (invoking mutation, drift, migration and selection).
• Landscape spaces are HUGE. However, bottom-up and top-down
approaches have started to reveal features:
-Limited paths from one genotype to another
-Potential ruggedness (multiple peaks)