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
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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
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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.
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Regulatory network adaptation 5
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
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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).
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Regulatory network adaptation 7
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.
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8 T. LAARITS ET AL.
(a)
(b)
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Regulatory network adaptation 9
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.
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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.
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Regulatory network adaptation 11
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
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12 T. LAARITS ET AL.
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.
ª 2016 EUROPEAN SOC I E TY FOR EVOLUT IONARY B IOLOGY . J . E VOL . B I O L . do i : 1 0 . 1 1 11 / j e b . 1 2 89 7
JOURNAL OF EVOLUT IONARY B IO LOGY ª 20 1 6 EUROPEAN SOC I E TY FOR EVOLUT IONARY B IO LOGY
Regulatory network adaptation 13
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.
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
JOURNAL OF EVOLUT IONARY B IOLOGY ª 2016 EUROPEAN SOC I E TY FOR EVOLUT IONARY B IO LOGY
14 T. LAARITS ET AL.
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
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