Developmental nonlinearity drives phenotypic robustness

Abstract

Robustness to perturbation is a fundamental feature of complex organisms. Mutations are the raw material for evolution, yet robustness to their effects is required for species survival. The mechanisms that produce robustness are poorly understood. Nonlinearities are a ubiquitous feature of development that may link variation in development to phenotypic robustness. Here, we manipulate the gene dosage of a signaling molecule, Fgf8, a critical regulator of vertebrate development. We demonstrate that variation in Fgf8 expression has a nonlinear relationship to phenotypic variation, predicting levels of robustness among genotypes. Differences in robustness are not due to gene expression variance or dysregulation, but emerge from the nonlinearity of the genotype–phenotype curve. In this instance, embedded features of development explain robustness differences. How such features vary in natural populations and relate to genetic variation are key questions for unraveling the origin and evolvability of this feature of organismal development.

Full text

ARTICLE
Developmental nonlinearity drives phenotypic
robustness
Rebecca M. Green 1, Jennifer L. Fish 2, Nathan M. Young 3, Francis J. Smith4, Benjamin Roberts 2,
Katie Dolan2, Irene Choi4, Courtney L. Leach1, Paul Gordon5, James M. Cheverud6, Charles C. Roseman7,
Trevor J. Williams4, Ralph S. Marcucio 3& Benedikt Hallgrímsson 1
Robustness to perturbation is a fundamental feature of complex organisms. Mutations are the
raw material for evolution, yet robustness to their effects is required for species survival. The
mechanisms that produce robustness are poorly understood. Nonlinearities are a ubiquitous
feature of development that may link variation in development to phenotypic robustness.
Here, we manipulate the gene dosage of a signaling molecule, Fgf8, a critical regulator of
vertebrate development. We demonstrate that variation in Fgf8 expression has a nonlinear
relationship to phenotypic variation, predicting levels of robustness among genotypes.
Differences in robustness are not due to gene expression variance or dysregulation, but
emerge from the nonlinearity of the genotype–phenotype curve. In this instance, embedded
features of development explain robustness differences. How such features vary in natural
populations and relate to genetic variation are key questions for unraveling the origin and
evolvability of this feature of organismal development.
DOI: 10.1038/s41467-017-02037-7 OPEN
1Department of Cell Biology & Anatomy, Alberta Children’s Hospital Research Institute and McCaig Bone and Joint Institute, Cumming School of Medicine,
University of Calgary, Calgary, AB T2N 4N1, Canada. 2Department of Biological Sciences, University of Massachusetts Lowell, Lowell, MA 01854, USA.
3Department of Orthopaedic Surgery, School of Medicine, University of California San Francisco, San Francisco, CA 94110, USA. 4Department of Craniofacial
Biology, School of Dental Medicine, University of Colorado Anschutz Medical Campus, Aurora, CO 80045, USA. 5Alberta Children’s Hospital Research
Institute, Cumming School of Medicine, University of Calgary, Calgary, AB T2N 4N1, Canada. 6Department of Biology, Loyola University Chicago, Chicago, IL
60660, USA. 7Department of Animal Biology, University of Illinois Urbana Champaign, Urbana, IL 61801, USA. Rebecca M. Green and Jennifer L. Fish
contributed equally to this work. Ralph S. Marcucio and Benedikt Hallgrimsson jointly supervised this work. Correspondence and requests for materials should
be addressed to R.S.M. (email: Ralph.Marcucio@UCSF.edu) or to B.H. (email: bhallgri@ucalgary.ca)
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Waddington proposed that selection tends to stabilize
development along particular paths, a phenomenon he
called “canalization”1. He tested this idea by selecting
for an induced trait in the presence of a teratogen (e.g., ether and
the bithorax phenotype) and obtained individuals in which the
trait appeared without the teratogen2. He hypothesized that
selection had stabilized development around the induced
trait such that it no longer needed the environmental stimulus.
Concurrent work by Waddington and others showed that
mutations with major effects tended to be more variable than the
wild type3–6. This observation was also explained by invoking
canalization. Mutations were hypothesized to increase variance by
disrupting evolved mechanisms that buffered variation around a
phenotypic mean7. This tendency for resistance to perturbation in
development, or robustness, is widely thought to be a funda-
mental property of complex life8. Yet, the mechanisms respon-
sible for promoting and modulating robustness remain largely
unknown9.
Wagner et al.10 defined canalization as suppression of pheno-
typic variation among individuals due to insensitivity to either
genetic or environmental effects. This definition hinges on a
distinction between the frequency distribution of the genetic or
environmental factors that cause variation and the magnitudes of
phenotypic effect associated with those factors. A mutation or
environmental effect disrupts or decreases canalization when
phenotypic variance is increased, while all other genetic or
environmental effects are unchanged.
Two kinds of mechanisms have been proposed to explain
canalization. In one, specific molecular mechanisms such as
heat shock and other chaperone proteins11–14 or microRNAs15
buffer against perturbations and suppress the expression of
variation. In the other, canalization emerges from redundancies,
feedback loops, and other features of developmental
systems9,16–20. These explanations are not mutually exclusive,
and multiple mechanisms may act simultaneously at different
levels of development9. However, they differ in that one posits the
existence of organism-wide buffering processes that reduce var-
iation, while the other holds that robustness emerges from the
same mechanisms that generate variation in specific traits. A
common feature of developmental systems explanations for
robustness is the importance of nonlinearity21–24.
Ligand–receptor binding, often described with a Hill function, is
commonly nonlinear25. The same is true for transcriptional
regulation26. Within tissues, processes such as the diffusion of a
morphogen are nonlinear in ways that depend on anatomical
context27. Genetic variation influences the phenotype via devel-
opmental processes that act at different scales, times, and loca-
tions within the organism, complicating the relationship between
genotype and phenotype17,28. Therefore, it is not clear how
nonlinearities in specific mechanisms translate to quantitative
relationships between genetic and phenotypic variation.
Lewontin introduced the genotype–phenotype (G–P) map to
conceptualize relationships between genetic and phenotypic var-
iation29.G–P maps are often nonlinear, as evident in dominance
and epistasis30,31. While much has been learned about the
developmental mechanisms that construct vertebrate morphol-
ogy, much less is known about the relationship between devel-
opmental and quantitative phenotypic variation. Alberch32
suggested a framework for incorporating development into G–P
maps, and Rice33 developed quantitative genetic theory to for-
mally relate variation in development to phenotypic variation.
Curvatures in the developmental landscape indicate nonlinear
relationships between developmental processes and phenotypic
variation. More recently, Morrissey34 provided a theoretical fra-
mework to quantitatively relate developmental and phenotypic
variation for such nonlinearities. A consequence of such non-
linear G–P relations is modulation of the amount of phenotypic
Genotype
Means
Mean Fgf8 level
Variances
Variance in Fgf8 level
Genotype
Gene expression Changes in
downstream GRN
Fgf8 level
Magnitude of
downstream changes
Fgf8 level
Variance in expression of
downstream genes
Morphology
Fgf8 level
Rate of midfacial cell
proliferation
Fgf8 level
Variance of
morphology
Compensatory
changes
Downstream
changes
bFGF pathway and canalization
aGeneral model
Same magnitude
of variation in mechanism
Mechanism (gene expression)
Phenotype
Altered
phenotypic
variance
Fig. 1 Nonlinearities at multiple levels across development modulate variance. aGeneral model of a nonlinear genotype–phenotype map where the amount
of a particular developmental process (e.g., cell survival, proliferation, and Fgf signaling) determines mean phenotype. Note that the same amount of
variation in the mechanism (“wild-type”gene expression—blue vertical bar, “mutant”gene expression—red vertical bar) can generate vastly different
amounts of phenotypic variation. This model yields a canalized region where variance is buffered (“wild-type”shape variation, blue horizontal bar) and an
area where canalization is lost (“mutant”shape variation, red horizontal bar). bHypothetical model of how nonlinear genotype–phenotype relationships are
generated at multiple biological levels. The top left panel shows that gene expression will relate linearly to cranial phenotype. The top mid panel shows that
changes in the gene regulatory network (GRN) downstream to Fgf8 respond either nonlinearly, driving change in the phenotypic mean (red line), or act in a
compensatory manner, buffering the effect of variation in Fgf8 (green line). The top right panel shows that morphology will relate nonlinearly to Fgf8 level,
potentially due to nonlinear changes in the underlying cell biological processes. Variances are influenced at the level at which the nonlinearity arises
(lower panels)
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variance for a given amount of variation in some developmental
factor (Fig. 1a)16–18,35.
We previously demonstrated significant nonlinearity in the
relationship between sonic hedgehog signaling and embryonic
facial shape36. Variation in the three-dimensional morphology of
the face is far removed from nonlinear molecular processes or
the theoretical dynamics of gene regulatory networks. For this
reason, it is not at all clear that the theoretical predictions
that link nonlinearity to phenotypic variance should hold across
the vast complexity of the G–P map. To test the hypothesis that
a nonlinear G–P relationship predicts variation in robustness,
we examine how variation in Fgf8 expression affects the mean
and phenotypic variance for craniofacial shape.
Fgf8 is appropriate for this study as it drives a central pathway
in craniofacial development37–39.Fgf8 is a signaling factor that is
expressed in the facial and oral ectoderm, where it directs
craniofacial pattern and polarity40,41.Fgf8 is absolutely required
for proper development of facial structures42,43.Fgf8-expressing
cells form a boundary with Shh-expressing cells to form the
frontonasal ectodermal zone, which directs the outgrowth of the
facial prominences and has also been implicated in their
evolution44,45.
We predict that Fgf8 expression relates nonlinearly to cranio-
facial phenotype. Further, we predict that the shape of the
curve relating mean phenotype to Fgf8 level will dictate the
phenotypic variance within and between genotypes. Genotypes
falling on the steeper portions of the curve will have higher
variances (differences among individuals within genotype) than
the genotypes falling on flatter portions. Likewise, different
genotypes that fall along the steeper portions of the curve will
have higher genetic variances, while those along the flatter
portion of the curve will show little phenotypic variation (Fig. 1a).
At the transcriptome level, we further predict that there will be
both compensatory and downstream gene expression changes
(Fig. 1b). We show that once Fgf8 falls below a threshold level,
there is both a change in the mean cranial shape and an increase
in the variance of that shape. We further show that changes in
phenotypic variance do not relate to increases in gene expression
variance and that there are both nonlinear and linear downstream
gene expression changes.
Results
Allelic series generation. To modulate Fgf8 expression during
facial morphogenesis, we used two allelic series of mice varying in
Fgf8 dosage. The first, Fgf8neo, was generated from the Fgf8
neomycin cassette insertion series46. This series includes a full
null allele, as well as a hypomorphic allele due to the retention of
the neomycin insertion. The second series, Fgf8;Crect uses the
floxed allele that was generated after the removal of the neomycin
cassette to delete Fgf8 specifically in the ectoderm using the
ectodermal cre, Crect47 (Fig. 2a). In the Fgf8neo series, Fgf8 levels
are affected globally from fertilization46.Fgf8;Crect embryos show
loss of Fgf8 in the ectoderm and decreased Fgf8 in the forebrain
beginning by E10.0 (Fig. 2b). We chose these two series because
their combination results in nine alleles of Fgf8 generating a series
E9.5 E10.5
Rosa26-LacZ;CRECT Fgf8flox/wt Fgf8flox/wt;CRECT
b
0.0
0.5
1.0
1.5
+/+ (WT)
Flox/+ (WT)
Neo/+
Flox/–
+/– (het)
Flox/+; CRECT
Flox/–; CRECT
Neo/Neo
Neo/–
Relative Fgf8 expression
Genotype
+/+ (WT)
Flox/+ (WT)
Neo/+
Flox/–
+/– (Het)
Flox/+;CRECT
Flox/–;CRECT
Neo/Neo
Neo/–
c
a
WT mean
Fig. 2 Generation of the allelic series. aE9.5 and E10.5 expression of CRECT as detected by crossing CRECT males with B6;129S4-Gt(ROSA)26Sortm1Sor/J
(R26R) females and staining the embryos for beta-galactosidase expression. Note the thin layer of blue present over the entire embryo showing the
ectodermal CRE expression. bIn situ hybridization showing regions of decreased Fgf8 in the E10.0 Fgf8flox/flox;Crect embryos. cqRT-PCR of cranial tissue
showing Fgf8 levels by genotype; sample size is between 2 and 22 samples per group. The box represents 1.5× the interquartile range of the data. Allelic
series for Fgf8 generates gradual loss of Fgf8 mRNA. Data shown is the delta–delta-CT value, where data were normalized against the mean delta-CT for
the WT group. The homozygous null is not included as it is lethal
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of gradations in Fgf8 dosage (Fig. 2c, Supplementary Table 1).
Mean Fgf8 levels in the head for the nine genotypes relative to the
wild-type embryos from the Fgf8neo series vary significantly
(ANOVA, df =69, 8, P<1*10–7), ranging from 0.14 to 1.1
(Fig. 2c), yet we detect no difference in the variance of gene
expression across the genotypes (Levene’s test, df =69, 8,
P=0.2043). Further, by deleting Fgf8 in two different ways, we are
able to show consistency between different mechanisms of Fgf8
loss. Facial phenotype is assessed by geometric morphometric
analysis48,49 at embryonic day 10.5 (E10.5) and immediately after
birth, postnatal day 0 (P0). These time points capture early face
formation and late fetal skull formation.
Generation of a genotype–phenotype map. To determine the
shape of the G–P map for Fgf8 expression, we determined Fgf8
expression by quantitative real-time PCR (qRT-PCR) of the head
and craniofacial shape via three-dimensional landmark-based
geometric morphometrics48,50. Here, the perturbation is the
modification of Fgf8 level across genotypes, while the phenotype
is a multivariate measure of facial shape as determined from
three-dimensional landmark data. The nine genotypes also vary
significantly in facial shape at both E10.5 and P0, as determined
by ANOVA (P<0.01). Using principal component analysis
(PCA), we determined that the allelic series ordinates along the
first principal component (PC) of craniofacial shape (Fig. 3). At
both developmental stages, Fgf8 expression accounts for a
significant proportion of shape variation (7.1% of shape variation
at E10.5 and 16.4% at P0), as determined by multivariate
regression after standardizing for embryo age (E10.5) or size
(P0)51. At E10.5, the genotypes vary along PC1 by Fgf8 level
(Fig. 3a, b). A similar pattern is seen at P0, showing that the
correlation is preserved throughout embryogenesis (Fig. 3c, d).
To model the relationship between Fgf8 expression and
phenotypic variation, we used Morissey’s34 quantitative model
for nonlinear G–P maps. This model produces a prediction of the
amount of variance that should be observed given a nonlinear
G–P map. To generate the curve used to test Morrissey’s model,
we fit the Fgf8 gene expression data, and the phenotypic data
(3D landmark data) to a von Bertalanffy curve using least-squares
regression. The phenotype data used was the regression score
from a multivariate regression of our normalized Procrustes
coordinates on Fgf8 level—which generates single variable shape
score48. These curves are shown in Fig. 4a, b.
Loss of Fgf8 affects phenotypic variance. The Morrissey model,
based on the mean and standard deviation of our Fgf8 gene
expression data, predicts that variation in Fgf8 expression has
little effect on shape metrics (phenotypic value or regression
score) when Fgf8 expression is >40% of the wild-type level,
while below this point, variation in Fgf8 expression produces
increasingly large effects on the mean phenotype. Figure 4c, d
shows the predicted relationship between the variance of Fgf8
a
b
PC1
E10.5
Low
Low Low
High
High High
High
PC1
P0
PC2
E10.5
Mean shape
PC2
P0
Mean shape
PC2 – 21% of variance
c
PC1 – 28% of variance
d
0.25
0.50
0.75
1.00
Fgf8 level
PC2 – 11% of variance
0.25
0.50
0.75
1.00
PC1 – 20% of variance
PC2 – 11% of variance
Series
Neo
Crect
Fgf8 level
PC2 21% of variance
Genotype
–/– (WT)
Flox/– (WT)
Neo/–
+/– (Het)
Flox/–
Flox/+;CRECT
Flox/–;CRECT
Neo/Neo
Neo/–
–0.1
0.0
-0.1 0.0 0.1
–0.2
–0.1
0.0
0.1
0.0 0.1 0.2
–0.2
–0.1
0.0
0.1
0.0 0.1 0.2
–0.1
0.0
–0.1 0.0 0.1
PC1 – 28% of variance
Low
PC1 – 20% of variance
Fig. 3 Shape changes in response to decreased Fgf8 gene dosage. Principal component analysis (PCA) of shape at E10.5 (a,b) and P0 (c,d). Gray embryos
(E10.5) show shape change trajectories for PC1 (horizontal) and PC2 (vertical), and the middle vertical image represents the mean shape for each time
point. Gold skulls show the same shape change trajectories for the P0 data. a,cPC plots colored by Fgf8 level with warm colors representing wild-type
embryos and cool colors and purples showing around 20% Fgf8 mRNA expression (mean per group by qRT-PCR). bColoration by genotypic series,
genotypes separate by allelic series, but the differences between low PC1 and low PC2 are small. The mean shape of individual genotypes is already
significantly different (Procrustes permutation test, P<0.001) by E10.5. dColoration by genotype as used in the rest of the paper. A total of 187 neonates
were analyzed and divided between groups as follows: WT (+/+) =22, Flox/+ =29, Neo/+ =41, Flox/−=10, ±=25, Flox/+;Crect =21, Flox/−;Crect =19,
Neo/Neo =17, and Neo/−=3 (w/all landmarks present). A total of 156 embryos were analyzed and divided between groups as follows: WT (+/+) =27,
Flox/+ =15, Neo/+ =30, Flox/−=13, ±=16, Flox/+;Crect =16, Flox/−;Crect =19, Neo/Neo =12, and Neo/−=8
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expression and phenotypic variance at four mean expression
levels for the E10.5 and P0 samples. These results show that the
variance of Fgf8 expression will have little effect on phenotypic
variance when Fgf8 level is >50% of the wild-type level, while the
phenotypic variance becomes increasingly sensitive to gene
expression variance below this point.
Figure 5a, b shows the individual-level data for the regression
of shape against mean Fgf8 level. The von Bertalanfy curve
explains 54% of the phenotypic variance at E10.5 and 84% at P0.
Fgf8 expression measured by RT-PCR in the head relates
nonlinearly to craniofacial morphology. Following the prediction
of the Morrissey model, when Fgf8 levels are above 40% of wild-
type levels, the effect on mean shape is minimal. Below this point,
however, the phenotype deviates sharply. When Fgf8 expression
levels are reduced below 40% of wild-type levels, small differences
in Fgf8 expression have large phenotypic effects.
To determine whether nonlinearity predicts robustness, we
plotted variance in face shape against Fgf8 expression across
genotypes. No change in shape variance, measured as the
Procrustes variance or morphological disparity48,49, is seen until
Fgf8 expression drops below 40% of wild-type levels (Fig. 5c). As
predicted, shape variance dramatically increases below 40%
expression in both the E10.5 and P0 samples, corresponding to
the point at which the phenotype becomes sensitive to Fgf8 levels
(Pvalues between groups—Supplementary Table 2). The only
exception is for E10.5 Fgf8;Crect embryos, likely due to the fact
that Crect does not activate until E9.5. By P0, this group has
significantly increased phenotypic variance (Supplementary
Table 2). At P0, the Fgf8neo/−embryos are so highly dysmorphic
that most of them could not be landmarked and so were not
included in the variance analysis (Supplementary Fig. 1).
Effects on gene expression. To eliminate the possibility that
differences in genetic variance across the allelic series account for
the differences in phenotypic variance, we quantified genetic
variance from high-resolution SNP data. These results show no
relationship between genetic variance and phenotypic variance
across the allelic series (Supplementary Fig. 2).
We determined the genome-wide changes in expression across
the allelic series at E10.5 using RNAseq. We reduced the
transcriptome data using PCA. The pattern of gene expression
within genotypes varies across the allelic series. PC1 of the
transcriptome accounts for 44% of variation in gene expression.
We interpret this PC to reflect the coordinated genome-wide
changes in gene expression across the allelic series. This PC1
ordinates the allelic series (Fig. 6a). Mean Fgf8 expression level by
genotype accounts for 30% of the variation in PC1 of the
transcriptome (Fig. 6b). For further analysis, the data were
separated into three groups: all genes, the MapK Kegg pathway,
and a hand-curated list of 15 known, direct Fgf target genes
(Supplementary Table 3). The MapK Kegg pathway was selected
as Fgf signaling falls within the MapK signaling cascade. In all the
genes and in the MapK pathway, there appears to be a curve in
the data; however, each group is statistically different from its
neighbor (Fig. 6c, d). This nonlinearity becomes more pro-
nounced for the Fgf downstream targets. For these genes,
expression level does not differ significantly among the hetero-
zygote genotypes (Ttest, P=0.96; Fig. 6e). The lack of change
between these groups generates a flat region in the curve with an
inflection point at 40–50% of the wild-type Fgf8 level,
demonstrating nonlinearity.
To test the hypothesis that the low Fgf8 expression genotypes
have increased phenotypic variation because of less coordinated
Phenotypic value
Variance in phenotype
0.04
E10.5
ab
cd
P0
P0
0.02
–0.02
–0.04
–0.06
–0.08
–0.10
–0.12
–0.14
0.30
0.25
0.20
0.15
0.10
0.05
0.00
0.2
0.4
0.6
1.0
0.0 0.5 1.0 0.0 0.2 0.4 0.6 0.8 1.0
Fgf8 expression level
Variance in phenotype
E10.5
0.0040
0.0035
0.0030
0.0025
0.0020
0.0015
0.0005
0.0000
0.00 0.05 0.10 0.15
0.2
0.4
0.6
1.0
0.0010
Variance in Fgf8 expression
0.00 0.05 0.10 0.15
Variance in Fgf8 expression
Fgf8 expression level
0.00
Phenotypic value
0.05
–0.05
–0.10
–0.15
–0.20
–0.25
–0.30
0.00
Fig. 4 Mathematical modeling of phenotypic variance. a,bFitting the shape data (regression residuals) to a nonlinear, von Bertalanffy growth curve.
Colored dots highlight the location on curves of four gene expression values that are modeled in b,c. Least-squares regression models the curve as
z=0.01765−(0.01765–(−0.12787))e(−5.3003*x)at E10.5 (A) and z=0.0288–(0.0288–(−1.333))e(−13.049*x)at P0. c,dPredicted relationship between the
variance of Fgf8 expression and phenotypic variance at four different levels of Fgf8 expression. Expression levels were not extrapolated below zero. This led
to the use of truncated normal distributions for expression variance and is responsible for the nonlinearities in c,d
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or dysregulated gene expression, we obtained the complete set of
pairwise correlations between gene expression levels across
individuals within genotypes. If phenotypic variances are low
within a genotype, one might expect the genomes of individuals
to be expressed in similar ways, while high phenotypic variance
might be associated with large differences in gene expression
among individuals. High correlations indicate a high degree of
consistency among individuals within genotypes. We performed
this analysis for both genome-wide and for each of the two groups
of genes known to be downstream of Fgf8. This analysis revealed
no evidence of dysregulation of gene expression across the allelic
series. The pairwise correlations genome wide or within likely
downstream targets show no detectable pattern across genotypes
(Fig. 6f–h).
To determine whether the transcriptomic data show evidence
of compensatory changes that could explain the lack of
phenotypic response above 40% of the wild-type Fgf8 expression
level, we searched for significant correlations between groups of
genes and Fgf8 level across individuals and genotypes. Resam-
pling revealed elevated (P<0.05) correlations for the reactome
Fgf downstream-signaling pathway, but not for Wnt, apoptosis,
MapK Kegg, and hedgehog pathways. Eight individual genes fell
outside of the 95% confidence interval based on genome-wide
resampling of a similar number of genes. This list includes Fgf4
and Trib3 that are negatively correlated with Fgf8, and Fgf17,
Etv4,Prkcg,Spry1,Spry4, and Rictor that correlate positively. The
two Sprouty (Spry) genes and Etv4 are known to be downstream
of Fgf8, suggesting that Fgf8 signaling modulates downstream
genes across the entire range of expression. A MANOVA
shows that the genotypes vary significantly in the expression of
these downstream genes (Pillai’s trace =2.1, P<1*10–5). As a
confirmation, we performed RT-PCR analysis on these eight
genes and compared them against the Fgf8 levels for each sample
(Fig. 7). While Fgf4 failed to reach statistical significance, Trib3
does appear to be weakly, but significantly negatively correlated
with Fgf8 level. All other genes were positively and significantly
correlated with Fgf8 level. Fgf17, for example, trends toward mild
upregulation in the Neo/+ group (1.27 ±0.16 vs. 1.06 ±0.32,
Student’sttest, P=0.15). Mean levels by genotype and standard
deviations have been listed in Supplementary Table 4. These
results suggest that there may be genes that change in expression
to compensate for loss of Fgf8, though this requires further
investigation.
Discussion
We show that nonlinearity in the G–P relationship for Fgf8
expression predicts phenotypic robustness. Progressive reduction
in Fgf8 yields a nonlinear relationship to phenotype, affecting
both mean facial shape and the magnitude of phenotypic
variance. Development tolerates a large amount of change in Fgf8
expression around wild type, but only to a point, after which
small changes in Fgf8 lead to large changes in phenotype, thus
permitting more morphological variance to be generated in a
population for a given amount of variation in Fgf8. These findings
show that nonlinearity in a single pathway can propagate across
the many levels of organization (molecular, cellular, tissue, etc.)
that channel information from genotype to phenotype, providing
a viable mechanistic explanation for canalization (Fig. 1).
Our results are consistent with the hypothesis that the non-
linear G–P map for Fgf8 explains the differences in phenotypic
variance across the Fgf8 allelic series. There are minor differences
among individuals in Fgf8 expression within each genotype for
the allelic series. Our model predicts that these minor differences
will translate to different magnitudes of phenotypic variance
along the curve that describes the relationship between Fgf8
expression and the mean cranial phenotype at each point along
the curve. This result implies that robustness can emerge in
developmental context as a consequence of nonlinearities in
development. This contrasts with explanations for canalization
that involve dedicated mechanisms such as heat shock proteins
that regulate variability organism wide. Our results do not
Genotypes
+/+ (WT)
Flox/+ (WT)
Neo/+
+/– (Het)
Flox/–
Flox/+;CRECT
Neo/Neo
Flox/–;CRECT
Neo/–
Genotypes
+/+ (WT)
Flox/+ (WT)
Neo/+
+/– (Het)
Flox/–
Flox/+;CRECT
Flox/–;CRECT
Neo/Neo
Neo/–
a
Age
P0
E10.5
c
E10.5 phenotypic effect
P0 phenotypic effect
Genotypes
+/+ (WT)
Flox/+ (WT)
Neo/+
+/– (Het)
Flox/–
Flox/+;CRECT
Flox/–;CRECT
Neo/Neo
Neo/–
Robustness
b
0.00
0.01
0.02
0.03
0.04
0.3 0.6 0.9
Fgf8 expression level
Morphological disparity
–0.2
–0.1
0.0
0.3 0.6 0.9
Fgf8 expression level
Regression residual
–0.1
0.0
0.3 0.6 0.9
Fgf8 expression level
Regression residual
Fig. 5 Shape and shape variance relate nonlinearly to Fgf8 mRNA
expression. Shape is defined using the common allometric component of
shape (CAC). a,bMultivariate regression of shape on Fgf8 level at aE10.5
and bP0. The black line shows the von Bertalanffy curve modeled in Fig. 4.
cVariance as calculated by the Procrustes variance or morphological
disparity49,80. The white vertical line shows an apparent threshold near
40% of wild-type Fgf8 level. Pvalues between groups are shown in
Supplementary Table 2
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preclude the existence of such mechanisms, but they provide an
additional and, perhaps, more general explanation for genetic and
environmental influences on phenotypic robustness.
An alternative explanation to the changes in variance along the
range of Fgf8 expression is that disruptions to Fgf8 expression
dysregulate downstream gene regulatory networks, producing
increased variance in gene expression that translates to increased
phenotypic variance. Such disruptions might be specificto
downstream targets of Fgf8 or be more widespread. By this
explanation, differences among individuals are greater at the
lower range of Fgf8 expression because these individuals also
vary in expression of downstream genes. It predicts that as Fgf8
dosage falls below the threshold, the variance of downstream gene
expression increases. This explanation relies on the idea that
extreme changes in gene expression may have systemic destabi-
lizing effects on development. This is implicit in the Hsp9012
explanation for the source of robustness, as well as in several
older explanations for canalization such as Lerner’s genetic
homeostasis model52. However, we found no evidence of
increased variance of gene expression, suggesting that the
increased phenotypic variance in genotypes producing low levels
of Fgf8 is not attributable to greater instability of the downstream
gene regulatory network.
–5
0
5
–10 0 10
PC1: 44% variance
PC2: 16% variance
Genotype
+/+ (WT)
Neo/+
+/– (Het)
Neo/Neo
Neo/–
a
PCA for gene expression
–10
0
10
0.0 0.25 0.50 0.75 1.0 1.25
Fgf8 level by RT-PCR
PC1 (44% variance)
Adj R
2
= 0.30684
b
PC1 regressed on Fgf8 expression
cde
fgh
0.0
0.2
0.4
Average fold change difference
Genotype
Neo/+
+/– (Het)
Neo/Neo
Neo/–
0.0
0.2
0.4
0.25 0.50 0.75 1.00
Fgf8 level
0.25 0.50 0.75 1.00
Fgf8 level
0.25 0.50 0.75 1.00
Fgf8 level
0.25 0.50 0.75 1.00
Fgf8 level
0.25 0.50 0.75 1.00
Fgf8 level
0.25 0.50 0.75 1.00
Fgf8 level
Average fold change difference
0.0
0.2
0.4
Average fold change difference
0.6 0.6
0.6
*
*
*
*
*
*
**
2.0
2.5
3.0
3.5
Z transformed -correlation
All genes
All genes
3.5
4.0
4.5
Z transformed -correlation
MapK Kegg pathway
MapK Kegg pathway
2.0
2.5
3.0
3.5
4.0
Z transformed -correlation
Genotype
+/+ (WT)
Neo/+
+/– (Het)
Neo/Neo
Neo/–
Fgf8 downstream targets
Fgf8 downstream targets
**
*
*
*
P = 0.010019
Fig. 6 Gene expression changes across the Fgf8 allelic series. aPC 1 and 2 plot of RNAseq data (18 samples). No differences in dispersion are observed
between groups. bRelationship between PC1 of the RNAseq data and Fgf8 level for each sample as quantified by RT-PCR. The blue line shows the line of
best fit, gray shows the 20% error around the line. c–eAverage absolute value fold change (dot) and average absolute value standard error of the fold
change (error bar) between each mutant genotype and wild type, call measured genes, dMapK Kegg gene list (174 genes), and eFgf8 downstream targets
(15 genes). The asterisk represents P<0.05 (bootstrap resampling) between nearest-neighbor groups (shown between the groups). The white vertical line
shows an Fgf8 level of ∼40%. f–hZ-transformed covariance between each embryo within a genotype on fall genes, gMapK Kegg gene list (174 genes),
and h15 known Fgf8 downstream targets (Supplementary Table 3). The asterisk represents P<0.05 (bootstrap resampling) between group and wild type
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We did find, however, that genes downstream of Fgf8 respond
nonlinearly to Fgf8 expression. In other words, the increased
phenotypic effects at low Fgf8 levels are mirrored by increased
changes in gene expression, particularly in genes known to be
downstream of Fgf8. This suggests that the nonlinear G–P map is
a feature of a larger gene regulatory pathway, and that the phe-
notypic effects at low Fgf8 levels are occurring because many
genes are more responsive to Fgf8 levels within that range than at
levels closer to the wild type.
Interestingly, the phenotypic effects of the loss of Fgf8 become
more marked between E10.5 and P0. At P0, the genotypes
separate more clearly and the increase in phenotypic variance at
the steep part of the curve becomes more marked. Fgf8 is
expressed throughout facial prominence outgrowth and face
formation53. Our results suggest that the effects of perturbing
Fgf8 expression below the threshold of 40% are exacerbated
during late embryonic and fetal development.
0.6
0.9
1.2
Spry4 level
0.5
1.0
1.5
Prkcg level
0.5
1.0
1.5
Rictor level
0
2
4
Trib3 level
0.0
0.5
1.0
1.5
Fgf17 level
0
1
2
3
4
5
Fgf4 level
0.5
1.0
1.5
Etv4 level
0.50
0.75
1.00
1.25
0.5 1.0 1.5
Fgf8 level
0.5 1.0 1.5
Fgf8 level
0.5 1.0 1.5
Fgf8 level
0.5 1.0 1.5
Fgf8 level
0.5 1.0 1.5
Fgf8 level
0.5 1.0 1.5
Fgf8 level
0.5 1.0 1.5
Fgf8 level
0.5 1.0 1.5
Fgf8 level
Spry1 level
Genotypes
+/+ (WT)
Neo/+
+/– (Het)
Neo/Neo
Neo/–
P < 0.022
R2 = 0.23
R2 = 0.12
P < 0.0016
R2 = 0.24
P < 0.0000
R2 = 0.59
P < 0.0015
R2 = 0.24
P < 0.14
R2 = 0.37
P < 0.018
R2 = 0.1352
P < 0.087
R2 = 0.059
P < 0.0018
Fig. 7 RT-PCR validation of correlation eight genes with Fgf8 level. Thirty-seven samples from across the genotypes were analyzed for each of the eight
genes plus Fgf8 and modeled for a linear relationship. The linear relationship is shown in red (line±SE shaded). R2values and the adjusted Pvalues from the
linear model are shown
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Here, we build on earlier work in which we show a nonlinear
G–P map for Shh expression and facial shape in chicks36. This
study did not determine how phenotypic variance is modulated
along the expression curve, however. Further, that study
manipulated Shh expression directly rather than via a genetic
model as we have done here. The advantage of the genetic
approach is that we can eliminate experimental error as a source
of among-individual variance within groups.
Our findings have important implications for the evolvability
of morphology. Applying Morrisey’s model34 shows that even
with strong selection on midfacial shape and substantial expres-
sion variation in Fgf8 levels, there would be little to no response to
selection on facial morphology through alterations of Fgf8
expression levels. The correlated response of Fgf8 expression
would be very low. On the other hand, at lower mean Fgf8
expression levels, response to selection on midfacial shape would
be achieved, at least in part, by changes in Fgf8 expression. There
would be a substantial correlated response in Fgf8 levels. These
contrasting results flow directly from the nonlinear relationship
between Fgf8 levels and midfacial morphology and suggest that
while Fgf8 clearly plays a pivotal role in craniofacial development,
it is unlikely to contribute directly to microevolutionary changes
in craniofacial form under a wide range of expression levels, from
40% of wild-type expression to full wild-type expression.
Similarly, the nonlinear G–P map for Fgf8 expression and
craniofacial shape helps us understand a puzzling and emerging
trend in the genetics of complex traits. Why is it that the genes
known from developmental biology to play major roles in the
construction of morphology so often appear to play minimal roles
in determining the variation of that morphology? Studies of
craniofacial shape variation in mice and humans reveal a growing
list of causal variants54–56. While some have known roles in facial
development, many of the major players such as Shh or Fgf8 are
conspicuously absent from these lists. Nonlinear G–P maps for
such central genes would explain this result.
But how do nonlinear G–P maps for key developmental factors
such as Fgf8 arise in the first place? The developmental origins of
nonlinearities can be at various levels of organization from receptor
ligand relationships to spatiotemporal tissue interactions. Simula-
tions of developmental mechanisms such as Zhang et al.’s57 mul-
tiscale model of limb development, often generate nonlinear effects
simply as a consequence of spatiotemporal dynamics of cellular and
tissue-level processes. Even so, nonlinear effects in development are
presumably evolvable. For instance, the relationship between Fgf8
expression and its various downstream effects is likely heritable.
Such nonlinearities might evolve through stabilizing selection acting
on epistatic variance, although this has not been demonstrated in
nature8,58. If this is true, then, genes deeply embedded within
developmental systems, such as Fgf8 should relate more nonlinearly
to phenotypic variation than genes with more peripheral roles. This
might occur for key signaling factors like Fgf8 because insufficiency
produces highly deleterious effects, while overexpression may have
less deleterious consequences. Excess production of important
proteins has been suggested as an explanation for canalization59
andisalsothebasisforSewallWright’s hypothesis for the devel-
opmental basis of dominance60.
Canalization influences long-term evolvability because of an
accumulation of cryptic variation that can be uncovered by
changes in the genome or the environment25. Positing the exis-
tence of canalizing mechanisms that are specifically adapted to
harbor reservoirs of variation requires an implausible group
selection explanation. Our finding that nonlinearity in Fgf8 sig-
naling modulates phenotypic robustness suggests instead that
cryptic variation can emerge as a side effect of nonlinearities in
developmental processes. Any genetic or environmental influence
that affects a developmental factor that relates nonlinearly to a
phenotype has the potential to affect the phenotypic variance61.
Importantly, such genetic influences can just as plausibly be
changes in allele frequencies as novel mutations.
A key challenge in evolutionary developmental biology is to
relate the quantitative genetic theory that underpins evolutionary
biology to developmental mechanisms. This is important because
the evolvability of phenotypes is determined in large part by how
development structures phenotypic variation62–64. Our study
contributes to this goal by connecting the concept of canalization
to developmental mechanisms. In quantitative genetics, gene
interactions generate epistasis65, and canalization can evolve by
selection on epistatic variance66. However, once a nonlinearity
occurs in development, it will generate gene interactions if the
differential variation along the curve is heritable. Seen in this
light, developmental nonlinearities are a cause rather than a
consequence of epistasis. Epistasis is widely thought to contribute
to missing heritability for complex traits because it can cause
similarity among relatives not accounted for in QTL or GWAS
studies67. For these reasons, the developmental basis for canali-
zation is central to both the evolvability and the genetics of
complex traits.
Methods
Mouse breeding and embryo generation. The Fgf8neo series is a five-member
series generated from a combination of the neomycin insertion into the intron
between exons 2 and 3 of the Fgf8 locus and a null allele generated from loss of
exon 2. The Fgf8;Crect series contains combinations of a floxed allele for Fgf8,a
null allele for Fgf8, and then Fgf8 is deleted from the ectoderm around E9.5 using
an ectodermal Cre (CRECT) (Fig. 2). The two series of mice were generated
independently by different labs (Crect, T. Williams) (Neo, R. Marcucio/J. Fish).
Both series of Fgf8 mice were generated from the Fgf8 flp/floxed allele originally
developed by Meyers et al.46. The neo cassette was maintained in the Fgf8Neo mice.
To generate the floxed allele for the CRECT studies, the neomycin resistance
cassette was removed by crossing these mice to β-actin-flp(B6.CgTg (ACTFLPe)
9205Dym/J), generating the floxed allele. Deletion constructs were developed by
crossing with β-actin Cre (FVB/N-Tg(ACTB-cre)2Mrt/J), to delete exons 2 and 3
from all cells.
To generate the Fgf8neo series, crosses were performed between mice that were
heterozygous for the Neo (flp) allele or heterozygous for the Neo (flp) allele and the
null allele. The Neo allele was genotyped with the following primers (5′–3′): F: CTG
CAG AAC GCC AAG TA G; R: AGC TCC CGC TGG ATT CCT C. The null allele
(UCSF/UMass) was genotyped with the following primers (5′–3′): F: GCC GTC
TGA ATT TGA CCT GAG CGC; R: GAA ACC GAC ATC GCA GGC TTC TGC.
The null and Neo alleles can be genotyped simultaneously at an annealing
temperature of 58 °C. The floxed allele was genotyped using the following primers:
(5′–3′) EM 99: CTT AGG GCT ATC CAA CCC ATC and EM32: GGT CTC CAC
AAT GAG CTT C. The null allele (UCDenver) was genotyped using EM41: AGC
TCC CGC TGG ATT CCT C and EM99. These three can also be genotyped
simultaneously at 58 °C. The Crect deletion series was generated by crossing the
Crect, early ectodermal Cre (Fig. 2)47, with the null allele, and then males from this
cross were crossed to Fgf8 flox/flox females on an FVB background. Genotyping for
this allele was performed using general Cre primers68 (5′–3′): Cre1: GCT GGT
TAG CAC CGC AGG TGT AGA G; Cre3: CGC CAT CTT CCA GCA GGC GCA
CC with a 67 °C annealing temperature.
For embryos, pregnant dams were sacrificed at embryonic day (E) 10.5 based on
visualization of a postcoital plug at E0.5. Embryos were dissected on ice and fixed
in 4% paraformaldehyde and 5% glutaraldehyde prior to μCT scanning. Neonates
were killed in CO
2
on ice and then fixed in 4% paraformaldehyde and 5%
glutaraldehyde prior to μCT scanning.
Mouse experiments were approved by the UC Denver Institutional Animal Care
and Use Committee (Crect series mice) and by the UCSF and University of
Massachusetts Lowell Institutional Animal Care and Use Committee (Neo series
mice).
The strains in the allelic series are highly inbred but not completely isogenic.
We estimated genetic variation in each strain to verify that differences in
phenotypic variance among genotypes are not explained by genomic variation
(Supplementary Fig. 2).
SNP analysis to estimate genetic variance. Following genotyping, five DNA
samples per each wild-type (WT), Neo/+, WT/−, Neo/Neo, and Neo/−groups were
sent to GeneSeek Inc. (a NeoGene company, Lincoln, Nebraska USA). DNA
samples were run on the GigaMuga mouse genotyping chips (Illumina), for a total
of 143,000 SNPs. After quality control and removal of the X and Y chromosomes,
we performed analyses using 133,559 SNPs on each of 17 samples, 4–5 per group.
QC and SNP calls were done using the GenomeStudio Package (Illumina) by
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GeneSeek. Further analysis was performed using the SNPRelate Package in R to
calculate the SNP frequencies and the relative inbreeding69. The SNP frequencies
were used to calculate the additive genetic variance70.
Scanning and landmarking. All samples were μCT scanned on a μCT35 scanner
to visualize facial shape. Prior to scanning, embryos were submersed in CystoCon
Ray II (iothalamate meglumine) contrast agent for 1 h, and then scanned at 7.5-μm
resolution. Neonates were scanned at 19-μm resolution without contrast agent to
allow resolution of the bone. Scans were then reconstructed and landmarked using
Meshlab (Version 1.3.2, Visual Computing Lab, meshlab.sourceforge.net)
(embryos) or Amira (Version 5.2, FEI) (neonates). Landmarks for embryos were as
developed by Percival et al.50. Neonate landmarks for the cranium are from
Gonzalez et al.71, with the addition of the landmarks on the mandible. Landmarks
for each age group were placed by a single observer who was blinded to a genotype.
A total 38 landmarks were placed on the embryos and 76 were placed on the
neonates. Samples with shrinkage artifacts, or missing landmarks were removed
from analysis.
Geometric morphometrics. Landmark data were imported into R, and Procrustes
superimposition was performed to remove scaling and orientation differences
between samples using the Geomorph package72,73 in R74. Embryo data were
regressed against tail somite number to remove ontogenetic effects before further
analysis. Neonate data were regressed against centroid size only. Background effects
due to lab of origin were mitigated by removing the difference between the wild-
type groups from all specimens. A total of 187 neonates were analyzed and divided
between groups as follows: WT (+/+) =22, Flox/+ =29, Neo/+ =41, Flox/−=10, ±
=25, Flox/+;Crect =21, Flox/−;Crect =19, Neo/Neo =17, and Neo/−=3 (w/all
landmarks present). A total of 156 embryos were analyzed and divided between
groups as follows: WT (+/+) =27, Flox/+ =15, Neo/+ =30, Flox/−=13, ±=16,
Flox/+;Crect =16, Flox/−;Crect =19, Neo/Neo =12, and Neo/−=8. Sample sizes
were based on previous work36,75,76. Our power analysis shows that 10 embryos are
needed to detect a 15–30% increase in variance and five embryos are needed to
detect a 20–30% increase in variance with a power of 0.8. Due to the large number
of genotypes, we focus on trends across the data set rather than between-group
differences. The size- and lab-normalized shapes (Procrustes coordinates) were
then regressed against Fgf8 level in Figs. 4and 5. Residuals from both the age
regression and the Fgf8 regression were obtained using a linear model, as implanted
by the procD.Allometry function in geomorph. To represent these regressions as a
single variable, we used the common allometric coefficient (CAC). When calculated
from a pooled analysis with multiple groups, this is mathematically identical to a
regression score72 and plots these values as the dependent variables against the
independent variables (Fgf8 level and tail somite stage).
Modeling of phenotypic variance. To model the relationship between Fgf8
expression and the phenotypic mean and within-genotype variance, we used
Morrissey’s model for the quantitative genetics of nonlinear G–P maps34. This
model shows how the phenotypic mean is determined by the functional relation-
ship between developmental processes (ϵ) and the phenotype (z):
z¼ZfðϵÞNϵ;ϵ;σ2
ϵ

dϵ;ð1Þ
where f(ϵ) is the functional relationship between the developmental process and the
phenotype and N(ϵ;ϵ;σ2
ϵ) is the normal distribution of developmental values (Fgf8
expression) with the specified mean and variance. The relationship between
developmental and phenotypic variance is given by
σ2
z¼Φ2σ2
ϵ;ð2Þ
where
Φ¼Zf′ðϵÞpðϵÞdϵ;ð3Þ
f′ϵ
ðÞ
is the first derivative of function f(ϵ) and p(ϵ) is the frequency of specific
developmental values.
Modeling of the G–P curve.Wefit the phenotype to Fgf8 expression at E10.5 and
at P0 using a nonlinear least-squares regression to a von Bertalanffy curve of the
formula:
z¼LmLmL0
ðÞekϵ
;ð4Þ
where L
m
is the maximum phenotype, L
0
is the mean phenotype at zero expression
(y-intercept), and kis a rate constant describing the decrease in slope per unit of ε.
In this curve, the initial rate of change of a phenotype given εdecreases at a rate
proportional to kuntil it reaches an asymptote (L
m
).
RNA collection for gene expression analyses. E10.5 embryos were dissected into
PBS on ice and snap frozen at −80 °C. Heads were dissected from between the
mandibular arch and the hyoid arch. All RNA work was performed on the RNA
extracted from the head. RNA was extracted in batch preps using Trizol. cDNA
was made from 500 ng of RNA in a 20-µl reaction mix using an iScript cDNA
synthesis kit (Bio-Rad).
qPCR. Reverse transcription quantitative real-time PCR (RT-qPCR) was performed
as previously described77. Briefly, we use a C1000 Thermal Cycler with a CFX96
Real-Time System (Bio-Rad). Forward and reverse primers, 2 µl of cDNA, RNase-
free dH
2
O, and SYBR-Select Master Mix (Thermo-Fisher), containing dNTPs, iTaq
DNA polymerase, MgCl
2
, SYBR Green I, enhancers, stabilizers, and fluorescein,
were manually mixed in a 20-µl reaction to amplify each cDNA of interest. Primer
sequences were GAPDH (F: 5′-AGGTCGGTGTGAACGGATTTG-3′;R:5′-
GGGGTCGTTGATGGCAACA-3′) and FGF8 (F: 5′-GTAGTTGTTCTCCAG-
CACGAT-3′;R:5′-GACAGGTCTCTACATCTGCAT-3′). Each sample was run in
triplicate, all results were normalized to the expression of GAPDH, and fold
changes were calculated using the delta–delta C(t) method78. Primers for qRT-PCR
were selected for optimal G/C concentrations and tested for ideal melt curves and
optimized for amplification efficiency: GAPDH, 92% at 61.5 °C and FGF8, 102% at
61.6 °C79. Primers for Fgf8 were located in the 3′end of the transcript to prevent
detection of nonfunctional transcript generated from the Neo or LacZ insertions.
Real-time PCR quantification of the RNAseq data was performed as follows. cDNA
was generated using the Maxima First Strand Kit (Thermo-Fisher) and amplified
using the IDT mastermix and IDT PrimeTime probes and primers (Mm.
PT.58.10694850, Mm.PT.58.7996582, Mm.PT.58.45983184, Mm.PT.58.29112396,
Mm.PT.58.33292921, Mm.PT.58.43880967, Mm.PT.58.42634782.g, Mm.
PT.58.33469229, and Mm.PT.58.41340681.gs). Samples were run on an Applied
BioSystems QunatiStudio 6. Data were normalized by averaging Gapdh and β-actin
expression levels. ddCT values were used in all downstream analysis. Correlation
analysis was performed in R. The mean deltaCT for the controls was calculated
before the log transformation for each sample, resulting in a slight alteration of the
wild-type mean from 1.
RNAseq. RNA quality was assessed using an Agilent TapeStation and RIN scores
of 9–10 were obtained. Stranded mRNA libraries for sequencing were prepared
from ~1 µg of total RNA using the TruSeq Stranded mRNA library prep kit and
Illumina protocol. The indexed libraries were quantitated for pooling by qPCR
using a Kapa Library Quantification Kit and the pooled libraries were sequenced on
two successive 75-bp high-output sequencing runs on an Illumina NextSeq
500 sequencer. An average of 46 million reads per sample was obtained. Reads were
mapped using HT-Seq count, and then data were analyzed using DESeq2. Cor-
relation analysis was run on the normalized counts, and other analyses were
performed using the fold-change data. The gene lists used in the analysis are
presented in Supplementary Table 3.
Statistical note. All Pvalues are based on two-tailed tests unless otherwise noted.
Code availability. A code for all analysis as well as associated landmark data files
can be found at http://www.ucalgary.ca/morpho/code-and-raw-data.
Data availability. RNAseq data have been uploaded to GEO with accession
number GSE87366 and are available at https://www.ncbi.nlm.nih.gov/geo/query/
acc.cgi?token=mtiveeyipxmhvkr&acc=GSE87366.
Morphometric data are available with the analysis code at http://www.ucalgary.
ca/morpho/code-and-raw-data. All raw data are available at the FaceBase Hub:
(www.facebase.org) with accession number FB00000927: https://www.facebase.org/
data/recordset/#1/isa:dataset./*::facets::N4IghgdgJiBcDaoDOB7ArgJwMYFM4gCo
QAaEJHMbACznhADEAhABldYE4AmAdhAF0AvoKA@sort(release_date::desc::,
id).
Received: 30 October 2016 Accepted: 2 November 2017
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Acknowledgements
This work was supported by grants NIH R01 2R01DE019638 to R.S.M. and B.H., NSERC
238992-17 to B.H. and C.C.R., and NIDCR R01 DE019843 to T.J.W. We thank Richard
Hawkes for his valuable comments on the manuscript.
Author contributions
R.M.G., J.L.F., B.H., R.S.M. and T.J.W. designed the experiments. R.M.G., J.L.F., I.C. and
K.D. generated the embryos for analysis. R.M.G. and F.J.S. did the microCT scanning and
landmarked the embryos. R.M.G. and B.H. analyzed the morphometric data. B.R. and
K.D. generated the RNA, DNA, and ran the qPCR along with C.L.L., J.L.F. and R.M.G.
analyzed the qPCR data. R.M.G., C.C.R. and P.G. analyzed the RNAseq data. C.C.R.
analyzed the S.N.P. data. N.M.Y., J.M.C., C.C.R., R.S.M., B.H., J.L.F. and R.M.G. helped
interpret the data and develop the initial model. J.M.C. generated the mathematical
modeling. R.M.G., J.L.F. and B.H. wrote the paper. All authors revised and approved the
final manuscript.
Additional information
Supplementary Information accompanies this paper at https://doi.org/10.1038/s41467-
017-02037-7.
Competing interests: The authors declare no competing financial interests.
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