• ２nd Talk: Phenotypic Evolution• Evolutionary Fluctuation-Response Relation• Evolution of Robustness, GenotypePhenotype Relation• Sympatric Speciation as a result of phenotype
differentiation• Evolution of Development• Spontaneous Adaptation by Noise• Summary+Discussion

GFP abundances

Motivation 1:Phenotypic Fluctuation Æevolution？
• Even in isogenic indiviudals(clones) there is large phenotypicfluctuation
Recognized now extensively
Exp + Model+Theory
Cell size• Relevance of thisfluctuation to evolution?
Positive role of noise?

• Phenotypic Fluctuation Æ Relationship to Evolution?
＊Standard evolutionary genetics;(0) selection is based on phenotype（activity, size, protein abundances, fluorescence,…),Fitness(phenotype)(i)gene a Æ phenotype x
Æif this mapping is uniquely determinedÆ
Fitness(Genotype) instead(ii) only genotype is transferred the offspring
Change of distribution P(geneotype) Æ evolution
But gene—``development ‘’ Æ Phenotype
Is not necessarily unique
Phenotypic fluctuation of isogenic organisms
ÆP(x; a) x—phenotype, a – geneMotivation2:Evolution of Robustness• Robustness ----- Insensitivity of Fitness (Phenotype)to system’s change
Å due to environmental changeÅ against noise during ‘developmental processÅ against parameter change by mutation*Question :relationship among these robustness
condition for evolution of robustness
Background(1) relationship between development and evolution,(2) robustness increases through evolution? --Schmalhausen’s stabilizing selection: Waddington’s canalization(3)Landscape in Geno-pheno coupling (,Ancel-Fontana.Wagner,.,)Motivation 1 and2, combined:• (A)Plasticity, Potency, Flexibility, (Robustness),
Evolvability …. Traditional concepts
Ambiguous Concepts; Often Explained only Verbally but
probably important biologically (as an organism level)* (B) Quantitative Biological studies on dynamics andfluctuations: Progresses rapidly recently• Still Large Gap between (A) and (B);
• Especially when (A) concerns with macroscopic
biological characteristics

Need to fill the gap(cf: stat mechanics is constructed after establishment of thermodynamics to be consistent)

Plasticity Measure--- changeability (response against externalchange)--- related with
degree of fluctuation ?
(negatively correlated with) robustness

So-called fluctuation-dissipation theorem in physics:
Force to change a variable x;
response ratio = (shift of x ) / force
fluctuation of x (without force)
response ratio proportional to fluctuation
originated by Einstein’s paper a century ago…
Generalization::(mathematical formulation)
response ratio of some variable x against the changeof parameter a versus fluctuation of xP(x;a) x variable, a: control parameterchange of the parameter a Æpeak of P(x;a) ( i.e.,<x>average ) shifts< x > a +Δa − < x > a∝< (δ x) 2 > a =< ( x − < x >) 2 >ΔaFluctuation-response relationship (generalized form)
Gaussian distribution of x; under the parameter a
at a=a0
Change the parameter from a0 to a

Approximate

formula；trivialbyNon-trivial point： representation
ｘ：phenotype a；enviroment etc

itselfbyP(x;a)

• General Viewpoint:
x: phenotype (variable)
a: genotype (parameter)parameterÆ variable:
condition （１）a： scalar continuous parameter showing
gene (say, number of matched sequences etc.)
for given direction of specific function,
ｘ is distributed even if gene (a) is specified
consider P(x;a) under given environment ｈ
Environment h change to select ‘a’ value
selection Æ change in P(x;a)

Artificial selection experiment with bacteria
for enzyme with higher catalytic activity
for some protein with higher function
Change in gene (parameter; a) ⇒``Response’’ ------ change of phenotype <x>(e.g.,fluorescence intensity)
per generation per (synonymous) mutation rate
Fluctuation ---- Variance of phenotype x of clone
Fluctuation in the phenotype x of clone⇔ speed of evolution to increase <x>(proportional or correlated)Artificial selection experiment with bacteria
Selection to increase the fluorescence of protein in bacteria

Schematic drawing of selection process～2,000 clones
Eyes

Mutagenesis

1st screening

・・・・・ ～30 clones
Spectrofluorometer5～8 clones

2nd screening

Spectrofluorometer
The highest clone

FACS analysis

Ito,Yomo,..

RP-334Log.LMD
900
800
700

Log[FS]

600
500
400
300
200

400

600

Log[Fluorescence]

800

1000

I10-6Log.LMD
Slope=1
X-intercept= Log[Fluorescence]FS=1

900
800
700

Log[FS]

600
500
400
300
200

400

600

Log[Fluorescence]

800

1000

Sato,Ito,
Yomo,KKPNAS(2003)

Fluctuation ---- Variance of phenotype of clone
Organisms with larger phenotypic fluctuation higher evolution
speed;- change of phenotype per generation per mutation -``Response against mutation+selection’’ResponseÅÆ FluctuationNaïve expectation:
Just propt to mutation rate

Fluctuation-response relation
Phenotype fluct. × mutation rate

(Evolution Speed per generation)
Sato,Ito,Yomo,KK, PNAS 2003

Cofirmation by model:
Ｔｏｙ Cell Model with Catalytic Reaction Network
C.Furusawa & KK⚦⢩

ｋ species of chemicals 、Xo…Xｋ－１
number ---n０ 、n１ … nｋ－１

:（resource）

random catalytic reaction networkwith the path rate pfor the reaction
Ｘi＋Ｘj－＞Ｘk+Xj
some chemicals are penetrable
through the membrane with the
diffusion coefficient D
resource chemicals are thustransformed into impenetrable
chemicals, leading to the growth in
Ｎ＝Σni, when it exceeds Nmax
the cell divides into twocellreaction

:

:
:

:
:
diffusion

catalyze:・・・

K >>1 species

mediummodel• Confirmation by numerical evolution experimentby the reaction-net cell model
Mutate the network (‘gene’) with mutation rate μ, (rewire the pathof the network with the rate) and select such network
having highest concentration ｃ of a specific chemical
1. Prepare initial mother cells.
2. From each parent cell, mutant cells
are generated by randomly replacing
reaction paths,
with mutation
rate μ3. reaction dynamics of all mutants are
simulated to determine phenotype x
phenotype x = log (ns)

4. Top 5% cells with regard tophenotype x are selected as parent
cells of next generation

Fluctuation of Phenotype x
Change of distribution ofphenotype x through evolution

Prepare 105 clonal cells(having an identical network)

difference of
average value

Distributions of phenotype x
are plotted.

Confirmation of Fluctuation Dissipation
Theorem by reaction-network cell modelFluctuation of x=log c

μ=0.01
0.03.0.05

Increase in average x

Furusawa,KK 2005

（１）the use of log(fluorescence), because
log x is close to Gaussian distribution inexperiments(２) New mystery？ phenotype fluctuation ofclone vs evolution speed in contrast to
evolution speed ∝ phenotypic fluctuation by
genetic variation（Vg): (fundamental theorem ofnatural selection; established)pheno fluct of clone Vp∝ pheno fluct by gene variation Vg？
（fluct by noise ∝ variation in ‘equation’)Follow the spirit of Einstein；micro-macro consistencyÆBrownian motionVip ∝ evolution speed ( exp (?), model)
Vg ∝ evolution speed (Fisher) a simple derivation(?)

distribution

Change of distribution
through evolution
Distribution of phenotype
x of a clone
Æ Vp

Log(concentration)

Distribution of phenotype
x over mutants (genetic
variation)
Æ Vg

Phenotype fluct. (Vp) vs Gene Fluct. (Vg) in the evolution of
toy cell model
Vp: fluct. for given network, Vg: fluct. by network variation
μ

Vg

～μmax

μ

Viｐ=VgVp
Phenotype fluctuation of clone

variance of log(x),x is the concentration of the molecule
Beyond Darwin with the spirit of Einstein!

Consider 2-variable distrb
P(x=phenotype,a=genotype) =exp(-V(x,a))
Keep a single-peak (stability condition).
KK,Furusawa, 2006 JTB

Hessian condition

Up to this point pheno(x) and geno (a) aretreated in the same way.
Then given a, the peak(average) phenotype isx0(a)--function of a --

Phenomenological Theory for these experimental
observations?
Consider P(phenotype,genotype) distribution P(x,a)
or P(x,a)=exp(-V(x,a))
Condition to keep single peak(evolutionary stability) .

KK,Furusawa, 2006 JTB＝

Ave over all populations

From Stability condition -Æ Vip> Vig is derived

Vg increases with the mutation rate
if the increase continues, there is critical mutation rate
μｃ at which Vip ~Vig
Error catastrophe Æ evolution stops
Here, Vig ≠ Vg
Vig for distribution for a given phenotype
Vg for all population

OR def Vp as average of Vip,
Then Vp ≧ Vg

consistent(i) Vip ≧ Vg （from stability condition) ( **)(ii)error catastrophe at Vip ~ Vg(**)
(where the evolution does not progress)(iii) Vg~(μ/μmax)Vip∝μVip（∝evolution speed)
at least for small μ＊＊Consistent with the experiments, but,,,,,
Existence of P(x,a) assumption ??;;+ Robust Evolution assumption ?? +Why isogenetic phenotypic fluctuation leads torobust evolution?
(**) to be precisely Vig, variance those from agiven phentype x: but Vig ~Vg if μ is small•• ??? to the theory• P(x,a) rather than conditional probability (TRICK)‘’Genetic-Phenotyic correpondence’’what phenotype can vary ÅÆ
what gene can change
fluctuation of variable (micro) vsvariation of equation (genetic evolution)(cf Waddington’s genetic assimilation)
Q: Why error catastrophe when Vg>Vip?
Robust evolution is possible only under noise-counterintuitive ;it says phenotype noise isimportantÆ gene-net model

Gene expression dynamics model::Relevance of Noise to evolution?
Simple Model:Gene-net(dynamics ofstochastic gene expression ) Æon/off state
Xi – expression of gene i :on off
Activation
Repression
Jij=1,-1,0

i

i

j

δij

Gaussian white

M;total number of genes, ｋ: output genes
Noise strength σ• Fitness:
Starting from off of all genes, after
development genes xi i=1、2、‥・・、k should be on（Target Gene Pattern)
Fitness F= －（Number of off x_i）

Genetic Algorithm
Mutate networks and Select those with higher <F>
Choose top n networks among total N,
and mutate with rate μto keep N networks

Low noise case:
top reaches the fittest
but low-fitness
mutants remain
Generation

High Noise case:
top-lowest
All reach the fittest

Result of evolution
Top:reaches the fittest
Lowest;cannot evolvefor low noise(σ)σ＜σｃFitness Distribution
σ＜σｃ --low fitness mutants distributed
σ＞σｃ －
eliminatedthrough evolution

Existence of critical noise level σcbelow which low-fitness mutants accumulate(error catastrophe)generation

(1) Vip≧Vg forσ≧σcVg(2)Vg→Vipas σ→σcσcVp=Vg(3) evolution progresses
only for Vip ≧Vg
Vp(4) Vip∝Vgthrough evolution
courseTheory confirmed
KK,PLosOne,2007

Why?; difference in basin structureσ＞σc Æ large basin for target attractor(robust, Δ（distance to basin boudary) ↑σ＜σｃ Æ only tiny basin around target orbit
Δ remains small
Basin Volume for
Each fitnessÆGlobal constraint to potential landscape(funnel?)why threshold?
choose paths to avoid turning
pts within σ (noise)Δ

Mutation→ touches turning
points within range of μΔsmall σ －＞an orbit with small Δ
can reach the target
Δ
Δ

Deviation of basinboundary (turning points)
by Noise －＞δpby Mutation -> δｇ
Vg ~ (δｇ/ Δ）^2
Vip ~（δｐ/Δ)^2
Δ increases
ーー＞robustness
increases
if δｇ＞δｐ,
Δ~distance to turning points
mutation destroys(basin boundary)
the history
ÆVip>Vg necessaryfor evolution of robustness

• Genetic robustness isincreased for network
evolved under higher
noise• Increase in genetic
robustness tomutation
fraction of fitted
state for n-mutants

F=-c(σ）ｍ；
C(σ)>0 if σ<σc
C(σc）=0m

Discussion:Evolution of Robustness• Robustness ----- Insensitivity of Fitness (Phenotype)to system’s changeÅ against noise during ‘developmental processÅ against parameter change by mutation• Developmental Robustness to noise ---- Vip• Robustness to mutation in evolution ----Vg
For σ>σc, both decrease, i.e., robustness
Noise is necessary for evolution of robustnessVip ∝ Vg ÆDevelopmental robustness and genetic(evolutionary) robustness are linked(or embedded)
WADDINGTON genetic assimilation(cf. Ancel-Fontana J ExpZoolB 2000
A Wagner et al, PLoS Comp Biol 2007)

Formation of smooth dynamics；how？
Consolidation of non-target gene expressions
X(i)

Vip(i)

Black---target

Generation

Expression of many non-target gene expressions are
fixed successively:-- variance of many gene expressions i - genetic Vg(i) &epigenetic Vip(i) decrease successively ;Further Surprise; Universal relationship over all genes?
Vg(i)Evolutionary course of (Vip(i),Vg(i))
plot for several genes I(color –different gene i)
Approaches proportionality
relationship
Vip(i)

Snapshot plot of all gene
expression variances ;(color different generation)Vg(i)Approach a unique line
for all genes(?!)
Vip(i)

KK,Chaos２００８Vip(i)-Vg(i) relationship over genes; snapshot at
200th generation

σ=.03

σ=.1

Histogram of Vg(i)/Vip(i)As noise increases, evolved
dynamics are more robust,
to lose plasticity
Plasticity ~ Vg(i)/Vip(i)Fraction of plastic gene
expression decreases as σσ
1

Log Scale‘universal line is approached ‘over genes’ and ‘over generations’High-dim instability
Plasticity decreases
(log)
Vg

Vg=VipRecent experiment(Landry etal,
Vg=CVip
Science07)
suggests suchcorrelation over genes(KK.Lehner, in prep)-but scatteredLow-dim limit

Vip
(log)

Universal proportion coefficient over genes akin to fluctuationdissipation relation ----- result of consistency of each gene
expression dynamics and fitness as collective state (cf Einstein)Through directed evolution; fluctuations
decrease(**Model, experiments, theory, i.e.,
increase of robustness through evolution.)
Then, evolution slows down..
ÅÆHow Evolution continues?
Why Large Fluctuations exist?
?? Is there regain of fluctuations????
• Experimentally Observed: Appearance ofmutants with large fluctuations at further
evolution. (Å interference with otherprocesses) (Ito,Toyota,KK,Yomo, submitted)• Æ Restoration of Plasticity

In fixed environment/fitness, plasticity decreases.
When environmental condition is switched in the modelÆ fluctuation once increases to regain plasticity( evolvability ) and then decreases
generation

Variances of fitness

Start after 100 generationof evolution under
given fitness; switch++++++++Æ++++---On -> Off for someTarget genes

In a fluctuating environment, fluctuation (plasticity) Is sustained(Increase of fluctuation in bacterial evolution; Ito-Toyota-KK-Yomo)

Vg(i)

Vip(i)

increase
instabilty toapproach Vg~Vip
Vg

Vip

Vip/VgWorks asa measureofbiologicalplasticity
Generation after switch• Generality of our result; For a system
satisfying:(1) fitness is determined after developmental
dynamics（2）developmental dynamics is complex(catastrophic pts leading to error are distributed)(3) effective equivalence between mutations andnoise with regards to the consequence tofitness(Æ genetic assimilation by Waddington)

Symbiotic Sympatric Speciation

Kk,Yomo2000
ProcRoySoc• So far, ‘fluctuation’ – single-peaked distribution• Speciation Æ change to double peaked distribution** Allopatric vs Sympatric ( S fundamental? Difficult?)• Our scenario for sympatric speciation (confirmed byseveral models):(1) Isologous divesification ( interaction-induced
phenotype differentiation);
homogeneous state is destabilized by the interaction
e.g., by the increase in resources(2) Amplification of the difference through geno-pheno
relation
Two groups form symbiotic relationship, and coevolve(3) Genetic Fixation and Isolation of Differentiated Group
consolidated to genotypes

Isologous Diversification:internal dynamics and interaction : development

phenotypeinstability
distinct phenotypes
interaction-induceddx m= f m ( x1 , x 2 ,.., x k )dt

Example: chemical reaction network
specialize in the use of some path

Study of coupled dynamical systems (globally coupled map) etc.,
differentiation??

ÆWith the increase of the number

Distinct types are formed through instability in ‘developmental
dynamics’ and interaction (both types are necessary)Differentiation of role; use od different paths

Model with Evolution :Each unit Phenotype :: Variable X = ( X 1 , X 2 ,.., X k )Gene :: Parameter in the modele.g., reaction rate

( g1 , g 2 ,..., g k )Parameter

Variable (dynamical systems)
X(t=0)ÆX(t)Reproduction when maturity threshold condition(given by X) is satisfied
Mutation ---- small change in parameter in reproduction
Competition for survival:( remove some units (either randomly or under some condition))

Characteristics of the Symbiotic Sympatric Speciation*Valid (possible) in the presence of strong interaction*Robust speciation; two groups coevolve; works undersexual and asexual cases as well(indeed, hybrid sterility is resulted)*Genetic separation always follows if there appears
interaction-induced phenotypic differentiation*Relevance of the phenotypic differentiation,rather than genetic change, to genetic diversification(Baldwin effect or genetic assimilationÆ speciation)

Plasticity in phenotype from loose dynamics Æ interaction-induced
phenotypic differentiation
Consolidated to Genes Æ Mating Æ Allele-correlation, Space..
Prove the above scenario?? From observation-- often remains a guess…
Real experiment wanted:
E Coli ; interaction-induced phenotypic differentiation observed
Evolution (Yomo’s group)
genetic fixation ---not yet; but

coexistence of diverse types by ‘crowded’ condition is confirmed

Spontaneous Adaptation• For all possible changes in environment,
signal transduction network is alreadyprovided?
• Or, is there any general (primitive)
mechanism to make spontaneous
adaptation?
• Æ Constructive Experiment with artificial
Gene and theory assuming only growth
condition and stochsticity

Questions(1) All chemicals have such large fluctuations?
Important ones are protected??
Origin of heredity (genetic information)
Minority control mechanism(KK,Yomo JtheorBiol.2002)(2)Large phenotypic fluctuation Æ
relevance to biology ?
ans. evolution (Sato et al., PNAS, 2003)
adaptation,differentiation….

(ex) Adaptive response without signal transduction
Unexpected； beyond designed
Embedded gene network
Selection of preferable state
Phenomenological theory of attractor selection
rfp

lacI

tetR

gfp

folA

glnA

Ptet

Env. Without glutamine

Mutual inhibition

Gultamine synthetase
Ptrc

Ptrc
rfp

tetR

folA

lacI

gfp

glnA

Ptrc
rfp

tetR

folA

lacI

gfp

glnA

Ptet
Ptet

Rich environment

Enzyme for Tet

Env. Without Tetrahydro..

fluctuation
Metabolic activity
Kashiwagi,Yomo

Theory of attractor selection by
activity and noise• Embedded network: each of the two can be selected
equally. However, ‘good’ attractor in eachenvironment is selected. Why?
• Due to hidden signal network?
NO!: verified by exchanging the promoter• After each state is attracted with 50%,
cells in a ‘bad’ attractor cannot grow,cells in a good attractor can grow, so that
good attractors are selected?
NO!; the process occurs without (or before) the cell
division process
Novel Mechanism of Spontaneous Adaptation (without
the use of signal transduction) should exist!

• Growth-Induced-Attractor-Selection (Furusawa kk)• Basic Logic
dx_i/dt=f(x_i)-S({x_j})x_i+η(t)fÆ Synthesis SÆ dilution due to cell growthη Æ noise
Active state ： both f and S are large
deterministic part >> noise
Poor state ： both f and S are small
deterministic part ~ noise
Switch from Poor state to Active state by noise
Selection before reproduction
General logic in a system with growth and fluctuation

The mechanism for adaptive response by attractor selectiondsyn(act )− deg(act ) × m1 + η1
m1 =2
1 + m2dtdsyn(act )− deg(act ) × m2 + η 2
m2 =2
1 + m1dt

6act
syn(act ) =;deg(act ) = act ;2 + act

d
pro
act =
− cons × act
NutthreadNutthread
_
_
dt
1 n1
2
((
) + 1) × (() n2 + 1)
m1 + Nutrient1
m2 + Nutrient 2

m1

m2

Adaptive Response of thegenetic network to aenvironmental changeact

No Nutrient1

No Nutrient
Nutrient2
No depletion

No depletiondsyn(act )m1 =− deg(act ) × m1 + η1
2
dt
1 + m2dsyn(act )m2 =− deg(act ) × m2 + η2
2
dt
1 + m16act
syn(act ) =;deg(act ) = act ;2 + act

1.2

AttractorW

1

act

0.8

0.6

Attractor1

0.4

d
pro
act =
−cons×act
NutthreadNutthread
_
_
dt
1 n1
2 n2
((
) +1)×(() +1)
m1+Nutrient1
m2+Nutrient2

0.2

0
0

0.5

1

1.5

2

2.5

m1

Fraction that adaptive attractor is selected3dm1 = 0dt
2.5

Nutrient1 = 0
Nutrient 2 = 10

m2

2

1.5

separatrix

1dm2 = 0dt

Noise strength
0.5

Adaptive Attractor
0.5

1

1.5

m1

2

2.5

3

3

Gene network -> a huge number of attractors coexist with different
growth speeds

Spontaneous selection of optimal growth states
General in a system with noise and growthEcosystem
Phenotypic Plasticity vs Symbiosis
Or Ecological diversification

Multicelluarity
Consistency between
Multicelluar development
and cell repdorcutio

Cell
Adaptation asa result of consistency
between cell growth andgene expression dynamics

Molecule

Gene regulatio
network

Evolutionary relationship on
Robustness and Fluctuation
Genotype

Phenotype

Consisteny between Cell reproduction
and molecule replication

Catalytic reaction network

Summary
Consistency Principle for Biology-- replication of molecules and cells :Universal Laws(-- replication of cells and cell ensembles)--- adaptation of internal cellular state and growth--- genetic and phenotypic changes(+speciation)
・Biological relevance of phenotype fluctuations?
ÆPhenotypic Fluctuation ∝ Evolution Speed
Æ Relation between(isogenic)phenotype fluctuationｖｓ
phenotype variation by mutation• Robustness to mutation and to developmental noise
are linked• Growth system Æ general adaptation by noise• consequence of steady growth system

Collaborators
Chikara Furusawa
Katsuhiko Satoexperiment
Tetsuya Yomo
Yochiro Ito
Akiko Kashiwagi
Most papers (biology,
Dynamical systems)
Available at
http://chaos.c.u-tokyo.ac.jp
ERATO Complex Systems Biology Project(2006,August)Evolution of gene regulation network for more
complex function:
Choice of complex dynamical systems to give gene
expression pattern for segmentation
Found Two basic strategies to generate stripesÆ use of generic dynamics such as oscillation
Æ genetic control by logical (on/off) operations(pioneered ; Salzar-Ciudad, Newman, Sole, EvoDev2001)
Network evolution of body plans
Fujimoto,Ishihara,KK ( PLoS One 2008)
Also talk tomorrow by Fujimoto(>>4.4C1)

Method: Calculating development• Take Gene regulation networks withactivation and repression• These genes are located spatially andchemicals diffuse (reaction+diffusion)

Becoid,Drosophila•Development under external environment
as input (spatial gradientent imposed)
Red: activation
Blue: repression∂Y∂Y= −Y + fY ( X , K xy ) + Dy 2∂t∂l2

- Gene #0 is distributed with spatial gradient.
- Reaction-diffusion equation for each gene
expression.

Strategy: Numerical evolution of gene
regulatory networks to form stripe pattern.

Method: Numerical evolution

Cf. Salzar-Ciudad, Newman, Sole EvoDevo 2001

Development dynamics over >1000 evolved
networks are classified just into 3 modes
Long germ mode:
simultaneousIntermediate germmode: combinatorial

Short germ mode:sequential
3*Simultaneous generation

Combination of on/off regulations
by fixed expression dynamics

Sequential Generation
Use of oscillatory
gene expressionDifference in (core) network structureLong-germ uses feed forward loop (FFL) dominantly

Short-germ uses
mainly feed-backloop (FBL)Short-germ mode has higher robustness to mutation
to network, as the number of involved genes is fewer
Ratio of Long to ShortDistribution of thenumber of required
genes

Mutation rate
Number of required genes

Remarkably, however, Long Germ Mode development
has high robustness against changes in the parametersin the gene expression dynamics

Summary
1. We classified networks according to sequential or simultaneous
stripe formation.
2. They are characterized by network modules, FBL and FFL.
3. Compared them with observed short and long germ segmentationin arthropod.
4. Correspondences between numerical and real evolution suggestthat the diverse segmentation is an inevitable property of evolving
networks.
Segmentation
mode

Patternformation

Network
moduleSpatialHierarchy

Knockout
response

Develo Mutation
rate
pment

Short

sequential

FBL

No needsimpleSlowerHigherIntermediate

combinatorial

FBL +FFL?

varietyLong

simultaneous

FFLs

necessaryvariety

FasterLower