genes under weaker stabilizing selection increase network...

Genes under weaker stabilizing selection increase networkevolvability and rapid regulatory adaptation to an environmentalshift

T. LAARITS* , P. BORDALO† & B. LEMOS‡*Harvard College, Cambridge, MA, USA

†Department of Systems Biology, Harvard Medical School, Boston, MA, USA

‡Program in Molecular and Integrative Physiological Sciences, Department of Environmental Health, Harvard T. H. Chan School of Public Health, Boston, MA, USA

Keywords:

adaptation;

directional selection modularity;

environmental change;

gene expression;

regulatory network.

Abstract

Regulatory networks play a central role in the modulation of gene expres-

sion, the control of cellular differentiation, and the emergence of complex

phenotypes. Regulatory networks could constrain or facilitate evolutionary

adaptation in gene expression levels. Here, we model the adaptation of reg-

ulatory networks and gene expression levels to a shift in the environment

that alters the optimal expression level of a single gene. Our analyses show

signatures of natural selection on regulatory networks that both constrain

and facilitate rapid evolution of gene expression level towards new optima.

The analyses are interpreted from the standpoint of neutral expectations

and illustrate the challenge to making inferences about network adaptation.

Furthermore, we examine the consequence of variable stabilizing selection

across genes on the strength and direction of interactions in regulatory net-

works and in their subsequent adaptation. We observe that directional selec-

tion on a highly constrained gene previously under strong stabilizing

selection was more efficient when the gene was embedded within a net-

work of partners under relaxed stabilizing selection pressure. The observa-

tion leads to the expectation that evolutionarily resilient regulatory

networks will contain optimal ratios of genes whose expression is under

weak and strong stabilizing selection. Altogether, our results suggest that

the variable strengths of stabilizing selection across genes within regulatory

networks might itself contribute to the long-term adaptation of complex

phenotypes.

Introduction

Networks of regulatory interactions modulate the

expression of genomes to give rise to an astounding

diversity of cellular metabolism, function and shape

that is evident even between cell types within a single

organism (Raff, 1996). Moreover, gene expression vari-

ation is abundant and well documented across individ-

uals, populations and species (Jin et al., 2001; Ranz

et al., 2003; Townsend et al., 2003; Gibson et al., 2004;

Zhang et al., 2007). Hence, a consensus has emerged

regarding the prominent role of regulatory variation in

the specification of phenotypes and in evolutionary

adaptation. Nevertheless, adapted genomes have to

equate constant perturbation from new, recurrent and

abundant mutations exerting regulatory consequences

with the selective requirement to stably maintain

expression levels near an optimal state. Consequently,

both mutation rates and long-term stabilizing selection

are expected to be important determinants of the archi-

tecture of gene expression variation in natural popula-

tions (Hodgins-Davis et al., 2015). Their interaction is

expected to shape the underlying structure of regula-

tory networks and ultimately determine the expression

level and noise of a focal gene. Empirically, the drive to

ascertain regulatory network structure has translated

Correspondence: Bernardo Lemos, Program in Molecular and Integrative

Physiological Sciences, Department of Environmental Health, Harvard

T. H. Chan School of Public Health, Bldg 2, Rm 219, Boston, MA, USA.

Tel.: +1 617 432 2047; e-mail: [email protected]

ª 2016 EUROPEAN SOC I E TY FOR EVOLUT IONARY B IOLOGY . J . E VOL . B I O L .

1JOURNAL OF EVOLUT IONARY B IO LOGY ª 20 1 6 EUROPEAN SOC I E TY FOR EVOLUT IONARY B IO LOGY

doi: 10.1111/jeb.12897

into large-scale efforts to map the genetic determinants

of gene expression variation (Gibson & Weir, 2005;

Gaffney et al., 2012), with numerous studies in model

organisms and humans successfully documenting quan-

titative links between nucleotide variation and the

expression of a focal gene (expression quantitative trait

loci, or eQTL). One important consensus emerging from

these studies is that eQTL for transregulatory effects are

not limited to transcription factor or DNA-binding pro-

teins. For instance, metabolic enzymes have also been

found to harbour variable loci with dramatic regulatory

effects (Yvert et al., 2003). Indeed, even repetitive DNA

arrays have been shown to harbour transacting regula-

tory variation in natural populations (Lemos et al.,

2008; Paredes & Maggert, 2009; Paredes et al., 2011;

Gibbons et al., 2014).

The pervasive origin of regulatory variation emerges

in part from cascading effects in gene regulatory net-

works (GRNs). However, understanding how the regula-

tory effects of new mutations spread through the

regulatory network has remained a challenge. Whereas

the empirical task of uncovering the regulatory conse-

quences of variable loci has greatly benefited from

advances in genotyping and phenotyping, the concep-

tual challenge has remained. The challenge includes the

understanding of the coordinated functioning of regula-

tory networks, the cascading of effects from variable

genetic loci and the consequential modulation of the

expression of a focal gene. Similarly, the wiring and

rewiring of regulatory networks evolving under long-

term stabilizing selection, adapting to a novel environ-

ment under directional selection, or experiencing shift-

ing selective pressures remains mostly unaddressed (Fay

& Wittkopp, 2007; Wittkopp, 2007). Modelling of stereo-

typical networks and analyses of variation in known net-

works have yielded promising insights (Fowlkes et al.,

2011; Wunderlich & DePace, 2011). These studies help

understand the origins and spreading of variation within

regulatory networks and the role of natural selection

(Fay & Wittkopp, 2007; Wittkopp, 2007; Macneil & Wal-

hout, 2011; Rhon�e et al., 2011; Garfield et al., 2013;

Shaw et al., 2014). The variation includes intra-indivi-

dual diversity that emerges even within a cell type

within an organism (Shalek et al., 2014).

Here, we investigate the responses of regulatory net-

works to positive and stabilizing selection on gene

expression levels. Regulatory networks are modelled as

a matrix of gene–gene interactions, whereas a vector

represents steady-state gene expression levels. The

developmental process is modelled through sequential

matrix-by-vector multiplication until a stable vector

state is reached. We modelled gene expression as a

quantitative trait with continuous values ranging from

an off state (0) to a maximal expression state (1). Using

this framework, we investigated the consequences of

stabilizing and directional selection on regulatory net-

works, which we interpreted from the standpoint of

neutral evolution in the absence of natural selection.

Our observations highlight the challenge of making

inferences about adaptation from rates of evolution,

and reveal a rich dynamics of gene–gene interactions

when phenotypes are under stabilizing and directional

selection. Finally, our simulations suggest that the pres-

ence of genes under relaxed stabilizing selection in a

regulatory network allows for faster adaptive responses

to new optima in a focal gene that originally was nearly

invariant due to a recent history of strong stabilizing

selection. The data indicate that adaptation in the focal

gene is facilitated by the presence of a greater number

of genes under relaxed stabilizing selection within the

network.

Materials and methods

Model

Here, we build on a widely used framework for the

analysis of regulatory networks (e.g. Wagner, 1996; Sie-

gal & Bergman 2002; Huerta-Sanchez & Durrett, 2007;

Carneiro et al., 2011). The model describes a network

of N regulatory genes by linking the matrix of interac-

tions between the genes (the genotype) to the genes’

expression levels v = (v1, v2, . . ., vN) (the phenotype)

(Fig. 1). Genes’ influences on each other’s expression

are described by a genotype matrix w = (wij). The ele-

ments wij of this matrix capture the impact of gene j on

gene i (Fig. 1). If wij > 0, gene j activates (or boosts

transcription) of gene i, whereas if wij < 0, gene j

represses gene i. The elements wij can also be zero, in

which case gene i has no direct effect on the expression

of gene j. We call the share c of nonzero elements wij

the connectivity of the matrix. The element wij of a regu-

latory network is a measure of directional regulatory

strength (RS) from gene j into gene i (RSij) (Fig. 1).

A given genotype w gives rise to a stable phenotype v

(w) if the expression levels of the genes reach a unique

steady state, which is computed as follows. At the first

time step, the phenotype v(0) is set to be a random vec-

tor. At any following time step t + 1, the phenotype is

given by vi t þ 1ð Þ ¼ qPN

j¼1 wijvj tð Þ� �

. The termPNj¼1 wijvj tð ÞÞ captures updating of the expression level

of gene i according to the matrix W of interactions

between the genes. The function q is an ‘update rule’

that constrains expression levels to lie between 0 and 1.

This is a convenient normalization, which does not

constrain or bias regulatory interactions. As in previous

implementations, we set q(x) = 1/(1 + e�ax); thus, if a

gene is highly repressed (when x is large and negative),

its expression level goes to zero, whereas if it is highly

activated (when x is large and positive), its expression

level goes to 1. A steady-state phenotype – or simply a

phenotype – is a vector of gene expression levels v(t)

that is approximately constant after a sufficient number

of time steps t. Formally, define the difference between

ª 2016 EUROPEAN SOC I E TY FOR EVOLUT IONARY B IO LOGY . J . E VOL . B I OL . do i : 1 0 . 1 11 1 / j e b . 1 2 89 7

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2 T. LAARITS ET AL.

phenotypes v1 and v2 as the Hamming distance between

the two vectors D v1; v2ð Þ ¼ PNi¼1

jv1i � v2i j=N. A stable

phenotype v(t) satisfies:

U v tð Þð Þ ¼ 1

�

Xt

h¼t��DðvðhÞ; vðtÞÞ\e;

where s defines the range of phenotypes to be com-

pared and epsilon is a small error term. If a phenotype

does not satisfy the condition in t = 100 steps, it is con-

sidered not viable. A selection environment S = {VS, r}is described by the target phenotype VS as well as by

the selection pressure sigma that arises directly from

environmental pressures on each gene. We can thus

define the fitness of a phenotype v as its distance from

the target VS, weighted by selection strength encoded

in the vector r:

F vð Þ ¼ e�PN

i¼1

jVSi�vi jNri

small values of r to imply strong selection against devi-

ations from target value.

The evolutionary process is defined as follows. We

first generated a population of M identical random

matrices and their associated fixed points. Variation in

the genotype is produced in two ways: via point

mutations to the nonzero entries in the matrices and

(d)

(a) (b) (c)

Fig. 1 Modelling gene regulatory network (GRN) activity and evolution. (a) The regulatory network (genotype) is represented as an

N 9 N matrix of gene–gene interactions, whereas gene expression levels (phenotype) is represented as a vector of n = 19 genes. RS

denotes regulatory strength. (b) Regulatory strengths (RS) are drawn from a standard normal distribution. (c) The strength of stabilizing

selection originating from the environment and acting on gene expression levels is represented by a vector r. Black entries denote genes

under strong stabilizing selection. Grey entries denote genes under weak stabilizing selection. Weak stabilizing selection is modelled as 1/

1000 or 1/10 the strength of strong selection. (d) Matrix visualization to display the architecture of the regulatory network. It shows

sectors that correspond to regulatory interactions between genes experiencing weak or strong stabilizing selection pressure from the

environment (vector r).

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Regulatory network adaptation 3

via reproduction. At each generation, we select M/2

pairs for mating. The individual probability of being

selected for mating is proportional to the fitness of the

matrix, where fitness is defined as the Hamming dis-

tance from the target vector of optimal environmen-

tally selected expression values VS. One parent can be

selected into multiple mating pairs – that is, individu-

als are sampled with replacement. Each selected pair

W1 and W2 produces two offspring. Thus, after repro-

duction we again have a pool of size N. An offspring

matrix W0 of parents and W2 is created by picking

each row in the offspring matrix from the correspond-

ing parent rows with equal probability. In other

words, the offspring is sampled from the two parents

row by row. Allelic dominance is not modelled. The

pool of N offspring is then subjected to point muta-

tions. Point mutations replace a nonzero entry wij

with probability l/cN2, where c is the connectivity of

the matrix and N is the dimension of the phenotype.

This process results in an average of l mutations per

matrix per generation. Once we have evaluated the

fitness of the resulting phenotypes, we establish the

new generation of size N by drawing matrices with

probability proportional to their fitness. Note that the

same matrix can be drawn multiple times into the

new population.

Model parameters

We now define the parameters in the model. The con-

nectivity of the matrix – share of nonzero entries in

each matrix – is c = 0.6. Mutations in nonzero matrix

entries wij are drawn from a normal distribution, N(0,

1), and change the regulatory strength of a gene–geneinteraction (Fig. 1b). The mutation rate parameter is

fixed at l = 0.1. Hence, in the expectation there are

l = 0.1 mutations per matrix per generation. The

parameter a in the update rule is fixed at 0.4. The

choice was based on the observation that this value

results in expression levels that are roughly uniformly

distributed in the [0, 1] interval, and has been imple-

mented (Carneiro et al., 2011). This parameter choice is

essential for our implementation and rests on the

observation that naturally occurring gene expression

variation in a focal gene varies continuously across

genotypes and displays the polygenic behaviour that is

expected for quantitative traits (Gibson & Weir, 2005).

The steady-state threshold epsilon is set at e = 10�3

while s = 10. This means that a phenotype is consid-

ered stable in case it is on average within e = 10�3 of

any fixed value during 10 consecutive iterations under

the update rule q. Genes whose expression is within

i = 0.01 from the target phenotype in the correspond-

ing entry are assigned a distance of 0 and do not con-

tribute to the distance vector D. This means that we

consider that genes have reached the optimum once

they are within i = 0.01 of the target.

Finally, recall that selection strength is encoded in

the vector r, which allows us to impose additional

structure on the selection vector of optimal phenotypes

(Fig. 1c). We classify the entries of the phenotype vec-

tor into two categories:

1 strongly selected genes (ri = 1, i 2 strongly selected

set S and

2 weakly selected genes (ri ¼ 1000; i 2 weakly

selected setW).

Consequently, each of the weakly selected genes has

a direct contribution to fitness that is 1000 times lesser

than that of a strongly selected gene. A direct contribu-

tion to fitness is due to selection exerted by the exter-

nal environment through the vector of optimal

expression levels. Our reference simulation considers a

population of M = 100 individuals and networks of

N = 19 genes. We also conducted simulations with

ri = 10, N = 15 and c = 0.4. In regard to the parameter

r, empirical estimates of stabilizing selection in gene

expression suggest that variation in the strength of sta-

bilizing selection among genes that is > 3 orders of

magnitude is typical (Rifkin et al., 2003, 2005; Denver

et al., 2005; Lemos et al., 2005). Note that in this model,

the fitness function is applied to the vector of expres-

sion levels and not the elements of the regulatory net-

work.

Here, we introduce four key innovations worth

explaining. First, the regulatory sensitivity parameter a

is small such that in the absence of the selection vector,

the genotype will generate expression levels between 0

and 1 with roughly equal probability. Our choice of

a = 0.4 ensures the update function q by itself does not

constrain the gene expression levels towards any speci-

fic value. As a consequence, we are able to examine a

larger phenotypic space of expression values. Second,

selection is gene-specific: some genes might have their

expression under strong selection pressure, whereas

others might have a smaller direct consequence to fit-

ness. Selection strength is encoded in the vector r;genes under weak stabilizing selection experience an

environmental optimum that is selected at 1/1000 or 1/

10 the strength of selection on the strongly selected

genes. Third, we specify a lower bound on the distance

used for calculating fitness. This ensures the popula-

tions can undergo bona fide stabilizing selection. With-

out an arbitrary lower bound on the precision, a

residue of directional selection remains in the stabiliz-

ing selection plateau, with networks asymptotically

reaching the optimum phenotypes. Fourth, the selec-

tion profile through time is designed to investigate the

effects of directional selection in a single gene within a

network (Fig. 2a). Importantly, the strength of stabiliz-

ing selection that acts on the expression of genes pro-

duces four distinct sectors in the network of gene–geneinteractions (Fig. 1d): the regulatory effects of each

class of genes either on itself (strongly selected into

strongly selected or weakly selected into weakly



4 T. LAARITS ET AL.

selected) or on the alternative class (strongly selected

into weakly selected or weakly selected into strongly

selected). Each of these four modifications is necessary

for the analyses presented here.

Simulations

For most of our simulations, we consider a network size

of 19 genes and let the expression of 13 genes to be

under strong stabilizing selection, whereas the expres-

sion of the remaining six genes is under weak stabiliz-

ing selection. The reference network size of 19 genes is

arbitrary, and was chosen such that ~1/3 of the genes

were weakly selected and ~2/3 of the genes were

strongly selected, while also allowing for subsequent

simulations in which the number of genes under weak

stabilizing selection progressively decreases. Formally,

this is described by the target phenotype (VS) of the

type VS ¼ ½S 1 : 6ð ÞGOI 7ð ÞW 8 : 13ð ÞSð14 : 19Þ�, where S

and W are set of genes under strong and weak stabiliz-

ing selection, and GOI is the gene of interest. The loca-

tion of the GOI, strongly selected and weakly selected

genes in the vector does not modify the outcome of the

model. For the main simulations, the strongly selected

genes have a target value of 0.2. Weakly selected genes

were set to have a target value of 0.2 or 0.5. The con-

figuration was chosen for simplicity and is informed by

empirical observations. First, the vast majority of genes

are expressed at low levels (Kuznetsov et al., 2002;

Furusawa & Kaneko, 2003; Ghaemmaghami et al.,

2003). Second, genes that physically interact with each

other show more similar expression values than genes

whose protein products do not interact (Fraser et al.,

2004; Lemos et al., 2004). One strongly selected

(a)

(b)

(c)

Fig. 2 Average fitness and gene

expression dynamics through time. (a)

Cartoon displays the two evolutionary

scenarios contrasted here: the set of

populations under stabilizing selection

(PSS) and the set of populations after

recent directional selection (PDC). PSS

models evolution under continued

stabilizing selection across the entire

network between generation 6000 and

8000. PDC models evolution after

recent directional selection in a single

gene (the gene of interest – GOI). We

focus most analyses on the transition

interval that starts with the onset of

directional selection at T = 6000 and

the recovery of fitness and re-

establishment of stabilizing selection in

the GOI at ~T = 8000. (b) Average

fitness profile of populations that

experience directional selection on a

single gene (PDC set) due to a shift in

the optimum value of GOI from 0.8 to

0.2 at generation T = 6000. (c) Average

expression profile of the gene of

interest (GOI) in the PDC set. The

mean (blue line) and two standard

errors around the mean (red lines) are

calculated over 20 independent

experiments (populations) and 100

individuals per population. Figure S2

shows the converse experiment.




gene – the gene of interest (GOI) – has a target value of

either 0.2 or 0.8 and experiences the selection for the

alternative state.

The evolutionary profile of our simulations has a few

important elements that are worth highlighting

(Fig. 2a). First, the population of matrices evolve from

a randomly generated set at T = 0 to adapted networks

experiencing stabilizing selection by T = 2000. We con-

sider the initial phase of ~2000 generations to be a

burning period that is required to our subsequent anal-

yses. The second phase describes the population evolv-

ing under stabilizing selection: fitness is in the plateau

and the selective regimen has shifted from that in the

burning period to stabilizing selection maintaining

expression levels at the optimum for at least 4000 gen-

erations (i.e. from generation T = 2000 to T = 6000).

Stabilizing selection maintains stable phenotypes in

spite of continued variability introduced through muta-

tion and mating. For each run of our simulations, we

generate three alternative populations at T = 6000. One

population remains evolving under stabilizing selection.

This is referred to as the set of Populations under Stabiliz-

ing Selection (PSS) (Fig. 2a). Another duplicate popula-

tion experiences a shift in the environment that

modifies the optimal expression of a single strongly

selected gene. This is referred to as the set of Populations

after Directional Selection (PDC) (Fig. 2a). Our goal is to

contrast patterns of evolution between the populations

under continued stabilizing selection (PSS set) and the

populations experiencing directional selection in a sin-

gle gene (PDC set). We let both populations evolve

until time T = 12 000. A third population is allowed to

evolve without a target phenotype, with the only

requirement that networks be viable (i.e. reach a steady

state). This serves to measure expected substitution

rates in the absence of natural selection.

Results

Regulatory activity and evolution

Our analyses with the parameter a = 0.4 in the update

rule allow genotypes to generate all expression levels

with roughly equal probability. In the absence of selec-

tion, all values in the interval between zero (no expres-

sion) and 1 (maximum expression) would be equally

likely. That is, we do not allow the update function qto bias the gene expression levels towards any specific

values. Regulatory activity occurs when gene products

(i.e. the vector of expression levels) influence each

other through mutual interactions that are mediated by

the regulatory network. Regulatory activity proceeds

until the vector of expression levels (the phenotype)

converges on a stable steady state of expression. A

stable expression vector is one in which further regula-

tory activity (continued multiplication of vector by

matrix under the update rule) produces no further

change in the expression levels of individual genes. This

is analogous to the unfolding of an expression program

until a steady-state gene expression is reached. Such

programs occur, for instance, during cellular differentia-

tion and stop when a stable cell type is reached. In our

simulations, more than 95% of all networks that con-

verged to a fixed point did so in fewer than six steps.

Networks that failed to produce a stable expression

state in < 100 steps were given a fitness value of zero

(i.e. considered not to be viable).

In our simulations, evolutionary variation is intro-

duced in two ways: (i) through random mutations that

modify the strength of regulatory interactions between

genes, and (ii) through a mating procedure that combi-

nes regulatory networks from parents. Selection of reg-

ulatory networks that are most fit occurs through a

fitness function that imposes differential viability and

differential reproductive rates to competing regulatory

networks based on their output of expression levels. As

outlined before, the evolutionary profile of the experi-

ment is divided into distinct phases (Fig. 2a). During an

initial burn-in phase, populations of 100 randomly gen-

erated genotypes (networks) evolve towards a target

phenotype (Fig. 2b, c). We observed that at T = 1000

(< 10% of the total evolutionary time in the simula-

tions) expression levels for all genes typically matched

the target levels with accuracy > 95%. Subsequent

1000 generations improved this match to 1% in all 19

genes. After this burn-in period, regulatory networks

evolve through stabilizing selection (from generation

~2000 to 6000). Our evolutionary analyses focus on the

interval between generation 6000 and 8000.

Network evolution under stabilizing selection

First, we addressed the evolution of network fitness as

well as strength and directionality of gene interactions

under continued stabilizing selection. In this section,

we focus on the populations that evolved under long-

term stabilizing selection maintaining the original target

phenotype for all genes (the PSS set). Specifically, we

studied stabilizing selection between T = 6000 and

T = 8000. Recall that our simulations incorporate

heterogeneity in the strength of stabilizing selection

across genes of the network (a set of six genes experi-

ences 1000 times weaker stabilizing selection than that

experienced by the core set of 13 genes under strong

stabilizing selection), which is predicted to influence

the phenotypic distribution of expression levels. As

expected for the PSS set, we observed that expression

levels remained unchanged between T = 6000 and

T = 8000. Strong stabilizing selection caused regulatory

networks segregating in the population to faithfully

output the most fit expression value for the strongly

selected genes and led to a narrow distribution of

expression values in the population (Fig. 2c). On the

other hand, naturally occurring segregating variation is



6 T. LAARITS ET AL.

expected to be higher in genes under weaker selection,

as we observed (variance in gene expression levels

r2 = 0.126 in genes under weak stabilizing selection

versus r2 = 0.017 in genes under strong stabilizing

selection).

Next, we investigated variation in the rates of evolu-

tion of regulatory strengths across sectors of the

networks. To address the issue we contrasted ancestor–descendant networks evolving under stabilizing selec-

tion in the 2000 generation interval between T = 6000

and T = 8000 (Fig. 3). Fast turnover and stabilizing

selection on binding sites has been suggested even

when network output and fitness remain stable (Lud-

wig et al., 2000; Bradley et al., 2010; He et al., 2011). In

agreement with this expectation, we observed a

dynamic network with substantial changes in regula-

tory interactions in spite of stable expression levels

under stabilizing selection (the average divergence

between T = 6000 and T = 8000 across all elements of

the matrix = 0.25). Interestingly, however, the model

shows substantial stratification in the rates of evolution

of regulatory strength through time, with each GRN

sector exhibiting unique behaviours in the continued

stabilizing selection regime. For instance, the modula-

tion of strongly selected genes by weakly selected genes

was most constrained (Fig. 3a) with an average diver-

gence of 0.07 (SD = 0.01). On the other hand, the

modulation of weakly selected genes by strongly

selected genes is the least constrained with an average

divergence of 0.34 (SD = 0.02) (Fig. 3a).

Neutral rates of evolution provide the baseline todetect selection on regulatory strength

Patterns presumably arising due to directional or stabi-

lizing selection should be evaluated relative to neutral

models that predict rates of evolutionary change arising

in the absence of selection (Lande, 1976, 1977; Turelli

et al., 1988). Such rates of neutral evolution provide a

null model that serves as a benchmark against which

observed rates that might be modulated by natural

selection can be interpreted (Lande, 1976, 1977; Turelli

et al., 1988). Rates that are higher than the neutral

expectation indicate the action of directional selection.

Rates slower than the neutral expectation point to the

action of stabilizing selection. Hence, we developed

expectations for neutral divergence in our model as the

appropriate baseline to evaluate regulatory evolution in

the absence of directional and stabilizing selection. Note

that the rate of mutations, l = 0.1, is an assumption of

the model; it refers to the probability of changing a

nonzero entry in the network of gene–gene interac-

tions. New mutations are sampled from an N(0, 1) dis-

tribution. We are interested, however, in the realized

(a)

(b)

Fig. 3 Change in the regulatory strength of genes in networks subject to stabilizing and directional selection. Shown are average

divergences in regulatory strength (RS) per regulatory connection under stabilizing selection (a) or directional selection (b). In each case

we calculate the average difference in regulatory strength of each interaction pair between T = 6000 and T = 8000. The ancestral

regulatory networks at T = 6000 are identical in both panels. Derived regulatory networks at T = 8000 experienced continued stabilizing

selection across all genes [panel a; populations under stabilizing selection (PSS) set] or directional selection in a single gene (panel b;

populations after directional selection (PDC) set). The right panel of each figure shows average divergence and standard deviations (in

parentheses) for regulatory interactions in each sector of the network. Average divergence and standard deviations were calculated for each

ancestral-derived pair and averaged over 100 matrices in a population and 20 replicated populations. For comparison, the average

divergence over the 2000 generation interval in the absence of selection (neutral divergence) is ~0.44 (Figure S1).




rate of divergence in regulatory strengths in the

absence of selection. To that end, we measured the

realized rate of evolution as the distance in genotype

space between two populations, divided by the number

of evolutionary steps separating the two populations.

We calculated two estimates of the neutral rate using

measurements of divergence in a 2000-generation

interval. In the two cases, we allow regulatory net-

works to accumulate mutations for 2000 generations in

the absence of selection (i.e. turn off the fitness func-

tion by letting the elements in vector r approach infin-

ity). In the first case, we duplicate the matrix

population at T = 6000 and use that set of matrices as

the starting point in the calculation of neutral diver-

gence. In the second case, we used the original popula-

tions of matrices generated at T = 0 and used them as

the starting point in the calculation of neutral diver-

gence. The population size (M = 100) and mutation rate

(l = 0.1) are identical to those used in the original

experiments with selection. The population at T = 6000

had already experienced the burning period of 2000

generations and some 4000 generations of stabilizing

selection, whereas the second case uses random matri-

ces. The observed rates of neutral evolution estimated

using the two methods were similar and resulted in

similar divergence in the interval of 2000 generations

(Average divergence = 0.44 and 0.42; P > 0.05, Stu-

dent’s t-test; Figure S1). These estimates are significantly

larger than estimates obtained in any of the network

sectors (P < 0.0001) and underscore the prevalence of

stabilizing selection in all sectors of the regulatory net-

work. We conclude that whereas regulatory interac-

tions evolving under stabilizing selection might

accumulate substantial changes (especially in edges

connecting strongly selected genes to weakly selected

genes), they do so at a substantially slower rate than

that expected in the absence of selection.

Network signature of rapid gene expressionadaptation to an environmental shift

Here, we investigate whether the regulatory inputs into

a gene experiencing a shift in expression optimum

might be rapidly and specifically modified through

directional natural selection. To address the issue we

modelled an environmental shift that changes the opti-

mum expression value of a single gene of the network.

At time T = 6000, we shift the target value for one

strongly selected gene – the gene of interest (GOI) –

from 0.8 to 0.2 (or vice versa). The environmental shift

causes a sharp fitness drop followed by a rapid adapta-

tion of the regulatory network towards the new opti-

mal phenotype by directional selection (Fig. 2b). In all

simulations, the expression level of the GOI successfully

evolved to within 5% of the new target in fewer than

3000 generations. Noteworthy, it took a relatively

longer time for adaptation to occur – about three times

longer than what was needed to evolve the whole set

of 19 genes from random networks into ones that pro-

duced the optimal phenotype. Our interpretation is that

the slower adaptation is due to intrinsic constraints in

the networks at T = 6000 relative to the random net-

works at time T = 0. These constraints might be both

structural and reflect the availability of new mutations

when the distribution of interaction strengths is shifted

away from the distribution of interaction strengths of

new mutations.

Rates of evolution in regulatory strength under direc-

tional selection should be interpreted from the stand-

point of the neutral estimates in the absence of

selection. Hence, we recorded each regulatory network

lineage in the population and compared the rate of

change per regulatory connection after the GOI expres-

sion level shifted from 0.8 to 0.2 expression units. This

was done by comparing ancestral networks exactly

before the environmental shift at T = 6000 to derived

networks right after the transition had been fully

accomplished at T = 8000. In agreement with our

expectations, we observed dramatically increased rates

of evolution in the incoming regulatory interactions

leading into the GOI (Fig. 3b). Accordingly, incoming

interactions rapidly changed from activation to repres-

sion (Figs 3 and 4), with a four-fold faster rate of regu-

latory evolution in the edges connecting with the GOI

compared with rates of change in other connections

(difference between regulatory strength before and after

the shift is 0.83 in the GOI vs 0.22 across the whole

network; Figs 3 and 4). Notably, connections between

weakly selected genes and the GOI evolved significantly

faster than those between strongly selected genes and

the GOI (divergence in regulatory strength in edges

from weakly selected genes to the GOI = 1.11 vs. diver-

gence in regulatory strength in edges from strongly

selected genes to the GOI = 0.70, P < 0.0001, Kruskal–Wallis test; Fig. 3). The rates of evolution in the edges

connecting with the GOI are significantly above the

neutral expectation (P < 0.001; Kruskal–Wallis). All

parameters in our simulations were kept constant, such

Fig. 4 Distribution of regulatory strength (RS) within sectors of the network. Panels show the distribution of RS within each network

sector in the populations under stabilizing selection (PSS) and populations after directional selection (PDC) populations. For clarity, data

from equivalent sectors in Fig. 3 were combined. Note that the distribution of regulatory effects of strongly and weakly selected genes on

both strongly and weakly selected genes remain mostly similar between the PSS and PDC sets. Note the shifts in the interactions with the

GOI (e.g. autoregulatory interactions in the GOI shift from activation to repression). The calculation averages over 100 matrices in a

population and over 20 independent experiments. Red bars represent the null (i.e. mutational) distribution of regulatory strength.



8 T. LAARITS ET AL.

(a)

(b)




that the faster rate of regulatory evolution is attributed

to directional selection on the GOI. Indeed, directional

selection caused the average value of the strength of

the regulatory connections to the GOI to change from

+0.39 to �0.40 (Fig. 4). Altogether, our analyses show

that regulatory strengths within our simulated net-

works are highly responsive to directional natural selec-

tion on gene expression levels.

Genes under weak stabilizing selection facilitaterapid regulatory network adaptation

Our observation regarding the disproportionally high

rate of evolution in the inputs from genes under weak

stabilizing selection into the gene undergoing direc-

tional selection was intriguing. We hypothesized that

genes under weak stabilizing selection might facilitate

rapid adaptation in highly constrained genes that were

previously maintained under strong stabilizing selection

pressure. To address the issue we simulated networks

with varying numbers of genes under weak stabilizing

selection. All other parameters remained unchanged. In

agreement with the hypothesis, we observed that the

number of weakly selected genes embedded in the net-

work with the GOI, was relevant in modulating the

speed of adaptation in the GOI (Fig. 5a). In the popula-

tion of matrices with six weakly selected genes, the

average value of GOI was within 5% of the target value

after 1000 generations. In contrast, populations with

four weakly selected genes took ~2000 generations, and

populations with two weakly selected genes took

> 4000 generations to be within 5% of the target value.

Interestingly, the results remain qualitatively

unchanged whether the strength of stabilizing selection

on the genes under weaker stabilizing selection is set at

1/1000 or 1/10 the strength selection in strongly

selected genes (Fig. 5a, b). Similarly, qualitatively iden-

tical patterns were observed when the GOI evolves in

networks with reduced connectivity (c = 0.4; Fig. 6a;

Figures S2–S5) and smaller size (Fig. 6b; Figures S2–S5)or from low to high expression (Fig. 7; Figures S2–S5).We conclude that the number of genes under relaxed

stabilizing selection in a network is a relevant determi-

nant of evolvability and rapid gene expression adapta-

tion to an environmental shift.

Discussion

Stabilizing selection is the most prevalent mode of

selection in natural populations (Gingerich, 1983, 2001;

Turelli et al., 1988; Kingsolver et al., 2001; Lemos et al.,

2001, 2005; Gilad et al., 2006; Estes & Arnold, 2007;

Kingsolver & Diamond, 2011), and it has been shown

to effectively operate to maintain stable gene expression

levels over long evolutionary timescales (Jordan et al.,

2005; Lemos et al., 2005; Rifkin et al., 2005). Here, we

contrasted populations that differed in a single feature:

a shift in the environment such that the optimum

(a) (b)

Fig. 5 Rate of adaptation increases with the number of genes under weak stabilizing selection within the network. Genes under weak

stabilizing selection contribute to faster optimization in the expression of GOI. Data are shown for regulatory networks with equal size

[gene regulatory networks (GRN) = 19 genes] and connectivity (c = 0.6). (a) r = 1000; genes under weak stabilizing selection experience

direct selection from the environment (vector r) at 1/1000 the strength of stabilizing selection in the strongly selected genes. (b) r = 10;

genes under weaker stabilizing selection experience direct selection from the environment (vector r) at 1/10 the strength of stabilizing

selection in the strongly selected genes. Shown are profiles of GOI adaptation in networks with 2, 4 and 6 genes under weak stabilizing

selection. The mean (blue line) and two standard errors around the mean (red lines) are calculated over 100 matrices in a population and

over 20 independent experiments.



10 T. LAARITS ET AL.

expression level of a single gene (the gene of interest,

or GOI) changed from high to low (or vice versa),

whereas the other genes remained under stabilizing

selection at a stable point. In Fisher’s geometric model

of adaptation (Orr, 2005), the number of phenotypes

under stabilizing selection is a measure of complexity.

A feature of the isotropic model is that all traits are

equivalent with respect to selection and complexity is

the dimensionality of the phenotypic space (roughly

equivalent to GRN size). One important result is that

(a) (b)

Fig. 6 The number of genes under weak stabilizing selection within the network is relevant for networks of sparser connectivity or smaller

size. Data are shown for regulatory networks with r = 1000. (a) Adaptation profiles for regulatory networks with sparser connectivity

(c = 0.4). (b) Adaptation profiles for regulatory networks with smaller size (GRN size = 15). Shown are profiles of GOI adaptation in

networks with 2, 4 and 6 genes under weak stabilizing selection. The mean (blue line) and two standard errors around the mean (red

lines) are calculated over 100 matrices in a population and over 20 independent experiments.

(a) (b)

Fig. 7 The number of genes under weak stabilizing selection within the network remains relevant when GOI evolves from smaller to

higher expression. (a) GOI evolves from 0.2 to 0.8. (b) GOI evolves from 0.8 to 0.2. Data are shown for regulatory networks with equal

size (GRN = 19 genes), connectivity (c = 0.6) and r = 1000. For both panels, simulations were performed with the optimum expression

level for all weakly and strongly selected genes set to 0.2 (except for GOI in panel b). Shown are profiles of GOI adaptation in networks

with 2, 4 and 6 genes under weak stabilizing selection. The mean (blue line) and two standard errors around the mean (red lines) are

calculated over 100 matrices in a population and over 20 independent experiments.




organismal complexity diminishes the rate of adaptation

to the environment (Orr, 2000). This cost emerges

because the model assumes universal pleiotropy and

therefore leads to the challenge of optimizing many

phenotypes simultaneously. The model studied here

differs in that only a single gene is under direct expo-

sure to selection at the onset of the environmental

shift. Nevertheless, we observed a slightly faster rate of

adaptation under directional selection in GRNs of 15

genes relative to GRNs with 19 genes (cf. Figs 5a and

6b). Finally, the model implemented here does not

assume universal pleiotropy and allow for the evolution

of a modular organization. In this regard, whereas con-

nectivity had a limited contribution to adaptation in

the GOI relative to the number of weakly selected

genes (cf. Figs 5a and 6a), future analyses that con-

strain specific structural features of the network or

examine the consequences of mutational effects could

be informative.

Here, we hypothesized that lower or higher strengths

of stabilizing selection on the expression of a focal gene

will have repercussions to the rates of evolution in the

incoming and outgoing connections of this gene. We

observed that the equilibrium distribution of regulatory

strengths of strongly selected genes on weakly selected

genes most closely approximated the expected muta-

tional distribution (Fig. 4). Note that panels displaying

regulatory strengths of strongly selected onto weakly

selected genes are nearly symmetrical around zero.

Conversely, panels displaying regulatory effects of

weakly selected onto strongly selected genes display the

slowest rate of evolution and show a significant shift

towards low negative values of regulatory strength

(P < 0.0001). This pattern on the outgoing effects of

weakly selected onto strongly selected genes appears to

have evolved from indirect selection originating from

strongly selected genes. Finally, regulatory inputs into

the GOI matched expectations: they are positive when

the GOI is under stabilizing selection at 0.8 (Fig. 4) but

negative when the GOI is under stabilizing selection at

0.2 (Fig. 4). Interestingly, the shifts away from the

mutational distribution are more pronounced in GOI

inputs that originate from weakly selected genes

(P < 0.05, Kolmogorov–Smirnov test). The variability in

the rates of evolution across nodes emerged as a by-

product of selection acting on gene expression levels

rather than selection on the regulatory network itself.

The data highlight the relevance of differential stabiliz-

ing selection pressure across genes for rates of regula-

tory network evolution.

Adaptive shifts in phenotypes under directional selec-

tion might also leave signatures on regulatory networks.

It has been suggested that regulatory interactions

between transcription factors and transcription factor

binding motifs might be rapidly strengthened or weak-

ened due to phenotypic changes driven by natural selec-

tion (Bradley et al., 2010; He et al., 2011; Ni et al., 2012).

Mechanistically, this can be achieved if directional selec-

tion towards higher or lower expression led to the fixa-

tion of DNA-binding proteins with increased or

decreased affinity to promoter motifs. Conversely, pro-

moter evolution might lead to increased binding. The

outcome of these processes is the modulation of regula-

tory strength between two genes. It is noteworthy that

whereas rates of evolution in the connection leading

into the GOI were unusually high and unequivocally

driven by directional selection on the GOI, there was

large heterogeneity in the rate of evolution of each

input. Altogether, the data revealed a rich landscape

with variable rates of evolution in the inputs of different

sections of the regulatory network. The observation,

moreover, suggests the relevance of genes under weak

stabilizing to the rapid transition of the GOI under direc-

tional selection, and led us to hypothesize that the influ-

ence of weakly selected genes on the GOI might

facilitate the rapid transition under directional selection.

Quantitative genetic models of phenotypic evolution

based on the neutral theory (Lande, 1976, 1977; Turelli

et al., 1988) predict much greater gene expression

diversity than is actually observed (Lemos et al., 2005).

These models describe the contributions of mutation

rate, time of divergence and population sizes to gene

expression divergence between species in the absence

of natural selection (Kimura, 1968). In particular,

empirically estimated mutation variance for a variety of

phenotypes is typically large and usually falling

between 10�4 and 10�2 (Lynch, 1988), and only

slightly higher for estimates of mutation variance in

gene expression traits (Denver et al., 2005; Rifkin et al.,

2005; Landry et al., 2007). Large estimates for the

mutational variance in gene expression predict that

genes might be able to shift between the minimum and

maximum possible expression in a few hundred genera-

tions (Lemos et al., 2005). On the other hand, variation

in gene expression is heavily constrained by stabilizing

natural selection, although the strength of stabilizing

selection is not homogeneous across all genes (Lemos

et al., 2005). Whereas some genes remain invariable

across species and over millions of generations, others

have severalfold differences in steady-state levels

between closely related populations. Accordingly,

> 10 000-fold variation in gene expression diversity can

be observed across genes, and some biological functions

harbour larger levels of segregating variation in gene

expression than others. For instance, metabolic

enzymes have larger extant gene expression diversity

than transcription factors (Lemos et al., 2005), and this

cannot be explained by variation in mutation rate

(Landry et al., 2007). The established interpretation is

that the expression of metabolic enzymes shows greater

variability because, on average, fluctuations in enzyme

dosage might have lowered consequences to gene

expression genomewide (Birchler et al., 2005; Birchler

& Veitia, 2012). Conversely, transcription factors show




reduced gene expression diversity presumably due to

their higher consequences towards destabilizing gene

expression genomewide and thus stronger stabilizing

selective pressure. Hence, the expression of metabolic

enzymes is considered to be under a more relaxed sta-

bilizing selection pressure than the expression of tran-

scription factors.

In summary, our simulations indicate that genes

under weak stabilizing selection facilitated rapid adap-

tive transitions in genes that were previously con-

strained due to strong stabilizing selection. The data

suggests that properties of the selective landscape might

be important to maintain cryptic regulatory variability in

highly constrained nodes. Such cryptic variability in net-

works might, in turn, be manifested as rapid adaptation

in phenotypes that are ordinarily maintained under

strong stabilizing selection (Gibson & Dworkin, 2004;

Milloz et al., 2008; Schlichting, 2008; Damkiaer et al.,

2013; Iwasaki et al., 2013). We expect that regulatory

networks that include genes under weaker stabilizing

selection might display higher evolvability. Our observa-

tions add to the list of evolutionary attributes that have

been implicated in determining the rate of adaptation

and the genetic architecture of complex phenotypes

and, together with previous findings, illustrate the utility

of modelling gene regulatory networks (Wagner, 1996;

Siegal & Bergman, 2002; Ciliberti et al., 2007; Fay & Wit-

tkopp, 2007; Huerta-Sanchez & Durrett, 2007; Siegal

et al., 2007; Wittkopp, 2007; Carneiro et al., 2011; Mac-

neil & Walhout, 2011; Rhon�e et al., 2011; Garfield et al.,

2013; Shaw et al., 2014; Watson & Walhout, 2014).

Attributes that modulate the rate of adaptation include,

for instance, the mutation rate (Sniegowski et al., 1997,

2000; Kopp & Hermisson, 2007), the strength of direc-

tional selection (Kingsolver et al., 2001; Kingsolver &

Diamond, 2011), the mode of selection (Hansen et al.,

2006), the mode of reproduction (sexual vs. asexual)

(Arjan et al., 1999; Azevedo et al., 2006), the rate of

recombination (Cooper, 2007; Schoustra et al., 2007;

Neher et al., 2010), the distance from the optimum (Bar-

ton & Partridge, 2000; Orr, 2002, 2005), modularity

(Wagner et al., 2007; Parter et al., 2008; Pavlicev et al.,

2011), connectivity (Frank, 1999; Milo et al., 2002; Babu

et al., 2004; Barabasi & Oltvai, 2004), patterns of positive

and negative epistasis (Hermisson et al., 2003; Carter

et al., 2005) and others. We suggest that variable

strengths of natural selection across elements of gene

regulatory networks might be a potent and underappre-

ciated component of GRN evolvability.

In conclusion, variable strengths of stabilizing selec-

tion across genes within regulatory networks might

itself contribute to long-term adaptation in complex

phenotypes through rapid remodelling of gene–geneinteractions. Specifically, genes under weaker stabilizing

selection could drive faster adaptation in highly con-

strained focal genes that lacked variation in gene

expression before an environmental shift. The data also

highlight signatures of stabilizing and directional selec-

tion on regulatory networks and underscore the chal-

lenge of rigorously ascertaining directional selection

with neutral benchmarks that are based on the speed

of adaptation. We expect that ascertaining directional

selection on empirical regulatory networks might

require not only refined estimates of regulatory net-

work interactions for several species but also biological

knowledge that allows stratification of regulatory inputs

from nodes under distinct strengths of selection.

Finally, our observations raise the expectation that evo-

lutionarily resilient regulatory networks will contain

optimal ratios of genes whose expression is under weak

and strong stabilizing selection.

References

Arjan, J.A., Visser, M., Zeyl, C.W., Gerrish, P.J., Blanchard,

J.L. & Lenski, R.E. 1999. Diminishing returns from mutation

supply rate in asexual populations. Science 283: 404–406.Azevedo, R.B., Lohaus, R., Srinivasan, S., Dang, K.K. & Burch,

C.L. 2006. Sexual reproduction selects for robustness and

negative epistasis in artificial gene networks. Nature 440:

87–90.Babu, M.M., Luscombe, N.M., Aravind, L., Gerstein, M. &

Teichmann, S.A. 2004. Structure and evolution of tran-

scriptional regulatory networks. Curr. Opin. Struct. Biol. 14:

283–291.Barabasi, A.L. & Oltvai, Z.N. 2004. Network biology: under-

standing the cell’s functional organization. Nat. Rev. Genet. 5:

101–113.Barton, N. & Partridge, L. 2000. Limits to natural selection.

BioEssays 22: 1075–1084.Birchler, J.A. & Veitia, R.A. 2012. Gene balance hypothesis:

connecting issues of dosage sensitivity across biological disci-

plines. Proc. Natl. Acad. Sci. USA 109: 14746–14753.Birchler, J.A., Riddle, N.C., Auger, D.L. & Veitia, R.A. 2005.

Dosage balance in gene regulation: biological implications.

Trends Genet. 21: 219–226.Bradley, R.K., Li, X.Y., Trapnell, C., Davidson, S., Pachter, L.,

Chu, H.C. et al. 2010. Binding site turnover produces perva-

sive quantitative changes in transcription factor binding

between closely related Drosophila species. PLoS Biol. 8:

e1000343.

Carneiro, M.O., Taubes, C.H. & Hartl, D.L. 2011. Model tran-

scriptional networks with continuously varying expression

levels. BMC Evol. Biol. 11: 363.

Carter, A.J., Hermisson, J. & Hansen, T.F. 2005. The role of

epistatic gene interactions in the response to selection and

the evolution of evolvability. Theor. Popul. Biol. 68: 179–196.Ciliberti, S., Martin, O.C. & Wagner, A. 2007. Innovation and

robustness in complex regulatory gene networks. Proc. Natl.

Acad. Sci. USA 104: 13591–13596.Cooper, T.F. 2007. Recombination speeds adaptation by reduc-

ing competition between beneficial mutations in populations

of Escherichia coli. PLoS Biol. 5: e225.

Damkiaer, S., Yang, L., Molin, S. & Jelsbak, L. 2013. Evolu-

tionary remodeling of global regulatory networks during

long-term bacterial adaptation to human hosts. Proc. Natl.

Acad. Sci. USA 110: 7766–7771.




Denver, D.R., Morris, K., Streelman, J.T., Kim, S.K., Lynch, M.

& Thomas, W.K. 2005. The transcriptional consequences of

mutation and natural selection in Caenorhabditis elegans. Nat.

Genet. 37: 544–548.Estes, S. & Arnold, S.J. 2007. Resolving the paradox of stasis:

models with stabilizing selection explain evolutionary diver-

gence on all timescales. Am. Nat. 169: 227–244.Fay, J.C. & Wittkopp, P.J. 2007. Evaluating the role of natural

selection in the evolution of gene regulation. Heredity 100:

1–9.Fowlkes, C.C., Eckenrode, K.B., Bragdon, M.D., Meyer, M.,

Wunderlich, Z. & Simirenko, L. et al. 2011. A conserved

developmental patterning network produces quantitatively

different output in multiple species of Drosophila. PLoS Genet.

7: e1002346.

Frank, S.A. 1999. Population and quantitative genetics of regu-

latory networks. J. Theor. Biol. 197: 281–294.Fraser, H.B., Hirsh, A.E., Wall, D.P. & Eisen, M.B. 2004.

Coevolution of gene expression among interacting proteins.

Proc. Natl. Acad. Sci. USA 101: 9033–9038.Furusawa, C. & Kaneko, K. 2003. Zipf’s law in gene expres-

sion. Phys. Rev. Lett. 90: 088102.

Gaffney, D.J., Veyrieras, J.B., Degner, J.F., Pique-Regi, R.,

Pai, A.A. & Crawford, G.E. et al. 2012. Dissecting the regu-

latory architecture of gene expression QTLs. Genome Biol.

13: R7.

Garfield, D.A., Runcie, D.E., Babbitt, C.C., Haygood, R., Niel-

sen, W.J. & Wray, G.A. 2013. The impact of gene expres-

sion variation on the robustness and evolvability of a

developmental gene regulatory network. PLoS Biol. 11:

e1001696.

Ghaemmaghami, S., Huh, W.K., Bower, K, Howson, R.W.,

Belle, A. & Dephoure, N. et al. 2003. Global analysis of pro-

tein expression in yeast. Nature 425: 737–741.Gibbons, J.G., Branco, A.T., Yu, S. & Lemos, B. 2014. Riboso-

mal DNA copy number is coupled with gene expression vari-

ation and mitochondrial abundance in humans. Nat.

Commun. 5: 4850.

Gibson, G. & Dworkin, I. 2004. Uncovering cryptic genetic

variation. Nat. Rev. Genet. 5: 681–690.Gibson, G. & Weir, B. 2005. The quantitative genetics of tran-

scription. Trends Genet. 21: 616–623.Gibson, G., Riley-Berger, R., Harshman, L., Kopp, A., Vacha,

S., Nuzhdin, S. et al. 2004. Extensive sex-specific nonadditiv-

ity of gene expression in Drosophila melanogaster. Genetics 167:

1791–1799.Gilad, Y., Oshlack, A. & Rifkin, S.A. 2006. Natural selection on

gene expression. Trends Genet. 22: 456–461.Gingerich, P.D. 1983. Rates of evolution: effects of time and

temporal scaling. Science 222: 159–161.Gingerich, P.D. 2001. Rates of evolution on the time scale of

the evolutionary process. Genetica 112–113: 127–144.Hansen, T.F., Alvarez-Castro, J.M., Carter, A.J., Hermisson, J.

& Wagner, G.P. 2006. Evolution of genetic architecture

under directional selection. Evolution 60: 1523–1536.He, B.Z., Holloway, A.K., Maerkl, S.J. & Kreitman, M. 2011.

Does positive selection drive transcription factor binding site

turnover? A test with Drosophila cis-regulatory modules.

PLoS Genet. 7: e1002053.

Hermisson, J., Hansen, T.F. & Wagner, G.P. 2003. Epistasis in

polygenic traits and the evolution of genetic architecture

under stabilizing selection. Am. Nat. 161: 708–734.

Hodgins-Davis, A. & Rice, D. P., Townsend, J. P. 2015. Gene

expression evolves under a house-of-cards model of stabiliz-

ing selection. Mol. Biol. Evol. 32: 2130–2140.Huerta-Sanchez, E. & Durrett, R. 2007. Wagner’s canalization

model. Theor. Popul. Biol. 71: 121–130.Iwasaki, W.M., Tsuda, M.E. & Kawata, M. 2013. Genetic and

environmental factors affecting cryptic variations in gene

regulatory networks. BMC Evol. Biol. 13: 91.

Jin, W., Riley, R.M., Wolfinger, R.D., White, K.P., Passador-

Gurgel, G. & Gibson, G. 2001. The contributions of sex,

genotype and age to transcriptional variance in Drosophila

melanogaster. Nat. Genet. 29: 389–395.Jordan, I.K., Marino-Ramirez, L. & Koonin, E.V. 2005. Evolu-

tionary significance of gene expression divergence. Gene 345:

119–126.Kimura, M. 1968. Evolutionary rate at the molecular level.

Nature 217: 624–626.Kingsolver, J.G. & Diamond, S.E. 2011. Phenotypic selection

in natural populations: what limits direction selection. Am.

Nat. 177: 346–357.Kingsolver, J.G., Hoekstra, H.E., Hoekstra, J.M., Berrigan, D.,

Vignieri, S.N. & Hill, C.E. et al. 2001. The strength of pheno-

typic selection in natural population. Am. Nat. 157: 245–261.Kopp, M. & Hermisson, J. 2007. Adaptation of a quantitative

trait to a moving optimum. Genetics 176: 715–719.Kuznetsov, V.A., Knott, G.D. & Bonner, R.F. 2002. General

statistics of stochastic process of gene expression in eukary-

otic cells. Genetics 161: 1321–1332.Lande, R. 1976. Natural selection and random genetic drift in

phenotypic evolution. Evolution 30: 314–334.Lande, R. 1977. Statistical tests for natural selection on quanti-

tative characters. Evolution 31: 442–444.Landry, C.R., Lemos, B., Rifkin, S.A., Dickinson, W.J. & Hartl,

D.L. 2007. Genetic properties influencing the evolvability of

gene expression. Science 317: 118–121.Lemos, B., Marroig, G. & Cerqueira, R. 2001. Evolutionary

rates and stabilizing selection in large-bodied opossum skulls

(Didelphimorphia: Didelphidae). J. Zool. 255: 181–189.Lemos, B., Meiklejohn, C.D. & Hartl, D.L. 2004. Regulatory

evolution across the protein interaction network. Nat. Genet.

36: 1059–1060.Lemos, B., Meiklejohn, C.D., Caceres, M. & Hartl, D.L. 2005.

Rates of divergence in gene expression profiles of primates,

mice, and flies: stabilizing selection and variability among

functional categories. Evolution 59: 126–137.Lemos, B., Araripe, L.O. & Hartl, D.L. 2008. Polymorphic Y

chromosomes harbor cryptic variation with manifold func-

tional consequences. Science 319: 91–93.Ludwig, M.Z., Bergman, C., Patel, N.H. & Kreitman, M. 2000.

Evidence for stabilizing selection in a eukaryotic enhancer

element. Nature 403: 564–567.Lynch, M. 1988. The rate of polygenic mutation. Genet. Res. 51:

137–148.Macneil, L.T. & Walhout, A.J. 2011. Gene regulatory networks

and the role of robustness and stochasticity in the control of

gene expression. Genome Res. 21: 645–657.Milloz, J., Duveau, F., Nuez, I. & Felix, M.A. 2008. Intraspecific

evolution of the intercellular signaling network underlying a

robust developmental system. Genes Dev. 22: 3064–3075.Milo, R., Shen-Orr, S., Itzkovitz, S., Kashtan, N., Chklovskii,

D. & Alon, U. 2002. Network motifs: simple building blocks

of complex networks. Science 298: 824–827.




Neher, R.A., Shraiman, B.I. & Fisher, D.S. 2010. Rate of

adaptation in large sexual populations. Genetics 184:

467–481.Ni, X., Zhang, Y.E., Negre, N., Chen, S., Long, M. & White,

K.P. 2012. Adaptive evolution and the birth of CTCF binding

sites in the Drosophila genome. PLoS Biol. 10: e1001420.

Orr, H.A. 2000. Adaptation and the cost of complexity.

Evolution 54: 13–20.Orr, H.A. 2002. The population genetics of adaptation: the

adaptation of DNA sequences. Evolution 56: 1317–1330.Orr, H.A. 2005. The genetic theory of adaptation: a brief his-

tory. Nat. Rev. Genet. 6: 119–127.Paredes, S. & Maggert, K.A. 2009. Ribosomal DNA contributes

to global chromatin regulation. Proc. Natl. Acad. Sci. USA 106:

17829–17834.Paredes, S., Branco, A.T., Hartl, D.L., Maggert, K.A. & Lemos,

B. 2011. Ribosomal DNA deletions modulate genome-wide

gene expression: rDNA-sensitive genes and natural variation.

PLoS Genet. 7: e1001376.

Parter, M., Kashtan, N. & Alon, U. 2008. Facilitated variation:

how evolution learns from past environments to generalize

to new environments. PLoS Comput. Biol. 4: e1000206.

Pavlicev, M., Cheverud, J.M. & Wagner, G.P. 2011. Evolution

of adaptive phenotypic variation patterns by direct selection

for evolvability. Proc. Biol. Sci. 278: 1903–1912.Raff, R.A. 1996. The Shape of Life: Genes, Development, and the

Evolution of Animal Form. The University of Chicago Press,

Chicago, IL.

Ranz, J.M., Castillo-Davis, C.I., Meiklejohn, C.D. & Hartl, D.L.

2003. Sex-dependent gene expression and evolution of the

Drosophila transcriptome. Science 300: 1742–1745.Rhon�e, B., Brandenburg, J.T. & Austerlitz, F. 2011. Impact of

selection on genes involved in regulatory network: a mod-

elling study. J. Evol. Biol. 24: 2087–2098.Rifkin, S.A., Kim, J. & White, K.P. 2003. Evolution of gene

expression in the Drosophila melanogaster subgroup. Nat.

Genet. 33: 138–144.Rifkin, S.A., Houle, D., Kim, J. & White, K.P. 2005. A muta-

tion accumulation assay reveals a broad capacity for rapid

evolution of gene expression. Nature 438: 220–223.Schlichting, C.D. 2008. Hidden reaction norms, cryptic genetic

variation, and evolvability. Ann. N. Y. Acad. Sci. 1133: 187–203.Schoustra, S.E., Debets, A.J., Slakhorst, M. & Hoekstra, R.F.

2007. Mitotic recombination accelerates adaptation in the

fungus Aspergillus nidulans. PLoS Genet. 3: e68.

Shalek, A.K., Satija, R., Shuga, J., Trombetta, J.J., Gennert, D.

& Lu, D. et al. 2014. Single-cell RNA-seq reveals dynamic

paracrine control of cellular variation. Nature 510: 363–369.Shaw, J.R., Hampton, T.H., King, B.L., Whitehead, A., Galvez,

F. & Gross, R.H. et al. 2014. Natural selection canalizes

expression variation of environmentally induced plasticity-

enabling genes. Mol. Biol. Evol. 31: 3002–3015.Siegal, M.L. & Bergman, A. 2002. Waddington’s canalization

revisited: developmental stability and evolution. Proc. Natl.

Acad. Sci. USA 99: 10528–10532.Siegal, M.L., Promislow, D.E. & Bergman, A. 2007. Functional

and evolutionary inference in gene networks: does topology

matter? Genetica 129(1): 83–103.

Sniegowski, P.D., Gerrish, P.J. & Lenski, R.E. 1997. Evolution

of high mutation rates in experimental populations of

E. coli. Nature 387: 703–705.Sniegowski, P.D., Gerrish, P.J., Johnson, T. & Shaver, A. 2000.

The evolution of mutation rates: separating causes from con-

sequences. BioEssays 22: 1057–1066.Townsend, J.P., Cavalieri, D. & Hartl, D.L. 2003. Population

genetic variation in genome-wide gene expression. Mol. Biol.

Evol. 20: 955–963.Turelli, M., Gillespie, J.H. & Lande, R. 1988. Rate tests for

selection on quantitative characters during macroevolution

and microevolution. Evolution 42: 1085–1089.Wagner, A. 1996. Does evolutionary plasticity evolve? Evolu-

tion 50: 1008–1023.Wagner, G.P., Pavlicev, M. & Cheverud, J.M. 2007. The road

to modularity. Nat. Rev. Genet. 8: 921–931.Watson, E. & Walhout, A.J. 2014. Caenorhabditis elegans

metabolic gene regulatory networks govern the cellular

economy. Trends Endocrinol. Metab. 25: 502–508.Wittkopp, P.J. 2007. Variable gene expression in eukaryotes: a

network perspective. J. Exp. Biol. 210: 1567–1575.Wunderlich, Z. & DePace, A.H. 2011. Modeling transcriptional

networks in Drosophila development at multiple scales. Curr.

Opin. Genet. Dev. 21: 711–718.Yvert, G., Brem, R.B., Whittle, J., Akey, J.M., Foss, E. &

Smith, E.N. et al. 2003. Trans-acting regulatory variation in

Saccharomyces cerevisiae and the role of transcription factors.

Nat. Genet. 35: 57–64.Zhang, Y., Sturgill, D., Parisi, M., Kumar, S. & Oliver, B. 2007.

Constraint and turnover in sex-biased gene expression in

the genus Drosophila. Nature 450: 233–237.

Supporting information

Additional Supporting Information may be found

online in the supporting information tab for this article:

Figure S1. Neutral rates of regulatory network evolution.

Figure S2. Average fitness and gene expression when

GOI evolves from 0.2 to 0.8.

Figure S3. Variable rates of evolution among sectors of

the regulatory network when GOI evolves from 0.2 to

0.8.

Figure S4. Rate of adaptation to a new target when

GOI evolves from 0.2 to 0.8.

Figure S5. Modes of selection and variable rates of

evolution among sectors of the regulatory network

(network size = 15 genes).

Data deposited at Dryad: doi: 10.5061/dryad.h8017

Received 22 January 2016; revised 3 May 2016; accepted 13 May

2016




genes under weaker stabilizing selection increase network...

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