This document discusses evolution in changing environments using adaptive landscape metaphors. It describes Darwin's concept of natural selection acting on variations, Wright's shifting balance theory involving semi-isolated populations on a rugged adaptive landscape, and how environmental changes can move populations between peaks. Network representations of selectively accessible paths are introduced as alternatives to landscapes. The document explores applying these approaches to microbial evolution under changing drugs and coevolution, suggesting networked models could represent accessible evolutionary paths. It raises issues for further discussion around experimental directions, visualization techniques, broader applications, and intersections with optimization problems.

1. Adaptive Landscapes
in Changing Environments
Sandbox Session
BEACON Congress 2013
Ben Kerr (UW)

2. fitness
“It may metaphorically be said that natural selection is daily and
hourly scrutinising, throughout the world, the slightest variations;
rejecting those that are bad, preserving and adding up all that are
good; silently and insensibly working, whenever and wherever
opportunity offers, at the improvement of each organic being in
relation to its organic and inorganic conditions of life.”
Darwin, The Origin of Species
beak depth
aB ab AB Ab
aB
ab
AB
Ab
• Darwin’s “opportunity”
depends on the variants
present in the
population.
• The genotype to
phenotype (G→P) map
carves out the possible.
• The genotype to phenotype to fitness (G→P→F)
map gives information on evolutionary
accessibility and evolutionary constraints.
Mapping out Adaptation
beak depthaB ab AB Ab

3. Picking the Wright Metaphor
Wright
• In 1932, Sewall Wright was invited to give a non-
technical talk on his view of evolution at the sixth
International Congress of Genetics.
• Wright (1932) started with a simple idea: a 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.
Figure 2 from Wright (1932)
Fitness

4. Evolution in the Balance
Genotype Space
Physical Space
deme 1
deme 2
deme 3
deme 4
• Wright felt that the landscape was likely rugged; the
problem that occupied him was how a population
could move from a lower peak to a higher peak
• His shifting balance theory rests on two assumptions:
1. Epistasis leading to distinct “peaks” (rugged landscape)
2. The population is structured (as semi-isolated sparsely
populated demes)
• Wright’s shifting balance invokes several processes
(mutation, selection, drift, and migration):
Phase 1: Demes drift over the adaptive landscape
Phase 2: Selection drives demes to new peaks
Phase 3: Competition between demes where the most
fit pulls the metapopulation to its peak
• Despite the importance of Wright’s shifting balance
to evolution in natural populations, the
accompanying metaphor has been very popular.

5. Selectively Accessible Paths (to SSWiM Upstream)
• Maynard Smith imagined mutations as
steps on a walk through sequence space.
• Think of a game in which one word is
changed to another via single letter
changes and intermediates are words.
• A path (multiple mutational steps) is
selectively accessible if each step increases
fitness (takes you uphill).
• Epistasis occurs when the effect of a
mutation changes given different
background contexts in either:
– Magnitude
– Sign
• Simple walks along selectively accessible
paths occur when:
- Selection is strong
- Mutation is weak
• In “SSWM” conditions, the population can
be thought of as a point moving through a
directed network, where the topology is
dictated by the adaptive landscape.
OPA
OPO
OVA
EPA
OVO
EPO
EVA
EVO
WORD  WORE  GORE  GONE  GENE
AT
IT
ASAT AS
ISIS
WERD
WEIRDWED
 WERE
 WIRED
A T
SI
wordfreq.
genotype space
fitness
Gavrilet’s (1997)
“holey” landscape
(necessary for ruggedness)
fitness
low
high
TS
TS
WORDS FROM BEACON PROPOSALS
OE
Neg.
OE
Pos.
Burch Chao Weinreich

6. Changing Environments: Changing Metaphors?
• The standard incarnation of the metaphor does not emphasize the role of the
environment and the role of the evolving organism on the environment.
• Partly in response to Wright’s shifting
balance process, Fisher argued that
environmental change could lead to
movement from a former peak.
• Wright also acknowledged that
environmental change could move
populations in genotype space
fitness
low
high
OPA
OPO
OVA
EPA
OVO
EPO
EVA
EVO
WORDS FROM
BEACON PROPOSALS
OPA
OPO
OVA
EPA
OVO
EPO
EVA
EVO
WORDS FROM
1950’s NEW ZEALAND
OPA
OPO
OVA
EPA
OVO
EPO
EVA
EVO
WORDS FROM
ENVIRONMENTAL LIT

7. Evolution in Changing and Changed Environments
• When the landscape is
rugged (e.g., due to
genetic epistasis), the
population can become
trapped on a sub-optimal
peak.
• A changing environment
can move a population to
a new peak (perhaps a
higher one).
• An environment changed
by organisms can also
move a population to
new places.
• Coevolution or niche
construction can have a
diversifying or
concentrating effect.
reference
environment
alternate
environment
reference
environment
reference
environment
altered
environment
reference
environment

8. Adapting the Adaptive Landscape
ab
Ab
aB
AB
environment
ab
Ab
aB
AB
environment
ab
Ab
aB
AB
environment
ab AbaB ABAB
• How might we visualize evolution under SSWM
conditions, but where the environment changes
exogenously?
• The landscapes
can be simplified
to directed
networks.
• The networks
can be stacked
in an ordered
way.
• Evolution can be
understood as
movement
down the wall.
• Also, epistasis
can be read off
the wall:
– Genetic
– Environmental

9. Network Approach: Application to Multi-Drug Resistance
• Let’s consider microbial
evolution under
changing drugs.
• When drugs
change, selectively
accessible paths can
change.
• Cycles are thus
selectively feasible.
- Cycles have been found
(Goulart et al. 2013).
Miriam
Barlow
• Possible “evolutionary flow” under
multiple drugs is given by connections
among the strongly connected clusters in
the union of the separate networks.
- In the b-lactam data, many (but not all)
“sink” clusters are single genotypes.
• Accessible paths between two genotypes
under multiple drugs can be enumerated.
- Certain combinations of drugs exposure may
make multi-drug resistance more likely.
000
100
010
001
110
101
011
111
sink
connector
connector
source
Number of Accessible Paths
Distribution of Sink Sizes
size
frequency

10. 00 10
01 11
Network Approach: Application to Coevolution
• One of the most important
components of “the
environment” involves
interacting species.
• How might we represent
“the landscape” for a
coevolving pair of species?
• One approach could
involve consideration of an
“expanded genotype”–
simply the concatenation
of genotypes into a single
“super-genotype”
• Under SSWM
assumptions, coevolution
involves movement in
different dimensions and
epistasis (intra- and inter-)
can be gauged. 00 10
01 11
0000
0001
0010
0011
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0101
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11. ISSUES TO DISCUSS
1. RESEARCH DIRECTIONS: What are the most exciting experimental directions to pursue in
exploring evolution in changing environments? Are there obvious evolution experiments
(with microbes, Avidians, etc.) that would contribute to deeper understanding? What are
the most pressing theoretical issues to address? What computational/engineering
contributions would have the highest impact? Does the form of environmental change
(exogenous/endogenous) matter?
2. VISUALIZATION: What are the best ways to visualize evolution in changing environments?
Can/should the landscape metaphor be salvaged? Are network approaches valuable (and
should we be focusing on static topology or dynamic movement on networks)? How should
environments be visually represented? Does it matter if the environment is abiotic/biotic or
exogenous/endogenous? Does the best way to visualize adaptation in changing worlds
depend on assumptions (e.g., SSWM) of the evolutionary process, and how might it change
with different assumptions?
3. BROADER APPLICATIONS: What are the most pressing applications of these topics? Climate
change? Antibiotic resistance? Are landscape metaphors (or network approaches) helpful
in addressing these issues? What is currently most necessary for understanding evolution in
changing environments in a way that has relevance for these broader applications?
4. WRITE-IN: Intersection between evolution and multi-modal optimization problems…