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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.
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Developmental nonlinearity drives phenotypic
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 genotypephenotype 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 Childrens 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 Childrens 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: or to B.H. (email:
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Waddington proposed that selection tends to stabilize
development along particular paths, a phenomenon he
called canalization1. 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 type36. 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
Wagner et al.10 dened canalization as suppression of pheno-
typic variation among individuals due to insensitivity to either
genetic or environmental effects. This denition 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, specic molecular mechanisms such as
heat shock and other chaperone proteins1114 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
systems9,1620. 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 specic traits. A
common feature of developmental systems explanations for
robustness is the importance of nonlinearity2124.
Ligandreceptor 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 inuences 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 specic mechanisms translate to quantitative
relationships between genetic and phenotypic variation.
Lewontin introduced the genotypephenotype (GP) map to
conceptualize relationships between genetic and phenotypic var-
iation29.GP 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 GP
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 GP relations is modulation of the amount of phenotypic
Mean Fgf8 level
Variance in Fgf8 level
Gene expression Changes in
downstream GRN
Fgf8 level
Magnitude of
downstream changes
Fgf8 level
Variance in expression of
downstream genes
Fgf8 level
Rate of midfacial cell
Fgf8 level
Variance of
bFGF pathway and canalization
aGeneral model
Same magnitude
of variation in mechanism
Mechanism (gene expression)
Fig. 1 Nonlinearities at multiple levels across development modulate variance. aGeneral model of a nonlinear genotypephenotype 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-typegene expressionblue vertical bar, mutantgene expressionred vertical bar) can generate vastly different
amounts of phenotypic variation. This model yields a canalized region where variance is buffered (wild-typeshape variation, blue horizontal bar) and an
area where canalization is lost (mutantshape variation, red horizontal bar). bHypothetical model of how nonlinear genotypephenotype 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 inuenced 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)1618,35.
We previously demonstrated signicant 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 GP map. To test the hypothesis that
a nonlinear GP 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 development3739.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
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 atter portions. Likewise, different
genotypes that fall along the steeper portions of the curve will
have higher genetic variances, while those along the atter
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.
Allelic series generation. To modulate Fgf8 expression during
facial morphogenesis, we used two allelic series of mice varying in
Fgf8 dosage. The rst, 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
oxed allele that was generated after the removal of the neomycin
cassette to delete Fgf8 specically 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
+/+ (WT)
Flox/+ (WT)
+/– (het)
Flox/+; CRECT
Flox/–; CRECT
Relative Fgf8 expression
+/+ (WT)
Flox/+ (WT)
+/– (Het)
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 Fgf8ox/ox;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 deltadelta-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 signicantly
(ANOVA, df =69, 8, P<1*107), ranging from 0.14 to 1.1
(Fig. 2c), yet we detect no difference in the variance of gene
expression across the genotypes (Levenes 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 genotypephenotype map. To determine the
shape of the GP 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
modication 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
signicantly 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
rst principal component (PC) of craniofacial shape (Fig. 3). At
both developmental stages, Fgf8 expression accounts for a
signicant 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 Morisseys34 quantitative model
for nonlinear GP maps. This model produces a prediction of the
amount of variance that should be observed given a nonlinear
GP map. To generate the curve used to test Morrisseys model,
we t 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 levelwhich 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
Low Low
High High
Mean shape
Mean shape
PC2 – 21% of variance
PC1 – 28% of variance
Fgf8 level
PC2 – 11% of variance
PC1 – 20% of variance
PC2 – 11% of variance
Fgf8 level
PC2 21% of variance
–/– (WT)
Flox/– (WT)
+/– (Het)
-0.1 0.0 0.1
0.0 0.1 0.2
0.0 0.1 0.2
–0.1 0.0 0.1
PC1 – 28% of variance
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
signicantly 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 groupsSupplementary 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
signicantly 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 quantied 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 reect 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 signicantly among the hetero-
zygote genotypes (Ttest, P=0.96; Fig. 6e). The lack of change
between these groups generates a at region in the curve with an
inection point at 4050% 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
0.0 0.5 1.0 0.0 0.2 0.4 0.6 0.8 1.0
Fgf8 expression level
Variance in phenotype
0.00 0.05 0.10 0.15
Variance in Fgf8 expression
0.00 0.05 0.10 0.15
Variance in Fgf8 expression
Fgf8 expression level
Phenotypic value
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. 6fh).
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 signicant 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% condence 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 signicantly in the expression of
these downstream genes (Pillais trace =2.1, P<1*105). As a
conrmation, 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 signicance, Trib3
does appear to be weakly, but signicantly negatively correlated
with Fgf8 level. All other genes were positively and signicantly
correlated with Fgf8 level. Fgf17, for example, trends toward mild
upregulation in the Neo/+ group (1.27 ±0.16 vs. 1.06 ±0.32,
Studentsttest, 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
We show that nonlinearity in the GP 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 ndings
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 GP 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
+/+ (WT)
Flox/+ (WT)
+/– (Het)
+/+ (WT)
Flox/+ (WT)
+/– (Het)
E10.5 phenotypic effect
P0 phenotypic effect
+/+ (WT)
Flox/+ (WT)
+/– (Het)
0.3 0.6 0.9
Fgf8 expression level
Morphological disparity
0.3 0.6 0.9
Fgf8 expression level
Regression residual
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 dened 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 inuences 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 specicto
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 Lerners 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.
–10 0 10
PC1: 44% variance
PC2: 16% variance
+/+ (WT)
+/– (Het)
PCA for gene expression
0.0 0.25 0.50 0.75 1.0 1.25
Fgf8 level by RT-PCR
PC1 (44% variance)
Adj R
= 0.30684
PC1 regressed on Fgf8 expression
Average fold change difference
+/– (Het)
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
Average fold change difference
0.6 0.6
Z transformed -correlation
All genes
All genes
Z transformed -correlation
MapK Kegg pathway
MapK Kegg pathway
Z transformed -correlation
+/+ (WT)
+/– (Het)
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 quantied by RT-PCR. The blue line shows the line of
best t, gray shows the 20% error around the line. ceAverage 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%. fhZ-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 nd, 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 GP 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.
Spry4 level
Prkcg level
Rictor level
Trib3 level
Fgf17 level
Fgf4 level
Etv4 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
0.5 1.0 1.5
Fgf8 level
Spry1 level
+/+ (WT)
+/– (Het)
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
GP 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 ndings have important implications for the evolvability
of morphology. Applying Morriseys 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 ow 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 GP 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 variants5456. 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 GP maps for
such central genes would explain this result.
But how do nonlinear GP maps for key developmental factors
such as Fgf8 arise in the rst 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 insufciency
produces highly deleterious effects, while overexpression may have
less deleterious consequences. Excess production of important
proteins has been suggested as an explanation for canalization59
andisalsothebasisforSewallWrights hypothesis for the devel-
opmental basis of dominance60.
Canalization inuences 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 specically adapted to
harbor reservoirs of variation requires an implausible group
selection explanation. Our nding 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 inuence
that affects a developmental factor that relates nonlinearly to a
phenotype has the potential to affect the phenotypic variance61.
Importantly, such genetic inuences 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 variation6264. 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.
Mouse breeding and embryo generation. The Fgf8neo series is a ve-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 oxed 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 p/oxed allele originally
developed by Meyers et al.46. The neo cassette was maintained in the Fgf8Neo mice.
To generate the oxed allele for the CRECT studies, the neomycin resistance
cassette was removed by crossing these mice to β-actin-p(B6.CgTg (ACTFLPe)
9205Dym/J), generating the oxed 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 (p) allele or heterozygous for the Neo (p) allele and the
null allele. The Neo allele was genotyped with the following primers (5′–3): F: CTG
(UCSF/UMass) was genotyped with the following primers (5′–3): F: GCC GTC
The null and Neo alleles can be genotyped simultaneously at an annealing
temperature of 58 °C. The oxed allele was genotyped using the following primers:
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 ox/ox females on an FVB background. Genotyping for
this allele was performed using general Cre primers68 (5′–3): Cre1: GCT GGT
CC with a 67 °C annealing temperature.
For embryos, pregnant dams were sacriced at embryonic day (E) 10.5 based on
visualization of a postcoital plug at E0.5. Embryos were dissected on ice and xed
in 4% paraformaldehyde and 5% glutaraldehyde prior to μCT scanning. Neonates
were killed in CO
on ice and then xed 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
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, ve 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, 45 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,
(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 1530% increase in variance and ve embryos are needed to
detect a 2030% 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 coefcient (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
Morrisseys model for the quantitative genetics of nonlinear GP maps34. This
model shows how the phenotypic mean is determined by the functional relation-
ship between developmental processes (ϵ) and the phenotype (z):
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 specied mean and variance. The relationship between
developmental and phenotypic variance is given by
is the rst derivative of function f(ϵ) and p(ϵ) is the frequency of specic
developmental values.
Modeling of the GP curve.Wet the phenotype to Fgf8 expression at E10.5 and
at P0 using a nonlinear least-squares regression to a von Bertalanffy curve of the
where L
is the maximum phenotype, L
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
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. Briey, 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
O, and SYBR-Select Master Mix (Thermo-Fisher), containing dNTPs, iTaq
DNA polymerase, MgCl
, SYBR Green I, enhancers, stabilizers, and uorescein,
were manually mixed in a 20-µl reaction to amplify each cDNA of interest. Primer
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 deltadelta C(t) method78. Primers for qRT-PCR
were selected for optimal G/C concentrations and tested for ideal melt curves and
optimized for amplication efciency: GAPDH, 92% at 61.5 °C and FGF8, 102% at
61.6 °C79. Primers for Fgf8 were located in the 3end of the transcript to prevent
detection of nonfunctional transcript generated from the Neo or LacZ insertions.
Real-time PCR quantication of the RNAseq data was performed as follows. cDNA
was generated using the Maxima First Strand Kit (Thermo-Fisher) and amplied
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 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 910 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 Quantication 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 les
can be found at
Data availability. RNAseq data have been uploaded to GEO with accession
number GSE87366 and are available at
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:
( with accession number FB00000927:
Received: 30 October 2016 Accepted: 2 November 2017
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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
nal manuscript.
Additional information
Supplementary Information accompanies this paper at
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... As demonstrated in Fig. 1, the effects of genotypes on phenotypes can be mediated by multiple layers of omics features through mechanisms such as regulatory cascades from epigenome, to transcriptome, and to proteome (Ritchie et al. 2015;Sun and Hu 2016;Wu et al. 2018). This multilayer regulation works as a unified system to connect genome variations to the trait, and the relationships between different layers can be complex with interactions and nonlinear relationships (Kitano 2002;Devijver et al. 2017;Green et al. 2017Green et al. , 2019. For example, Green et al. (2017) observed that the relationship between gene expression level and phenotype was nonlinear, which was approximated by a generalized logistic function. ...
... This multilayer regulation works as a unified system to connect genome variations to the trait, and the relationships between different layers can be complex with interactions and nonlinear relationships (Kitano 2002;Devijver et al. 2017;Green et al. 2017Green et al. , 2019. For example, Green et al. (2017) observed that the relationship between gene expression level and phenotype was nonlinear, which was approximated by a generalized logistic function. ...
... In our simulation analysis, when the underlying relationship between intermediate omics features and phenotypes was nonlinear, using the nonlinear activation function in NN-MM had significantly better performance than using the linear activation function. Given the observations that the relationships between intermediate omics features and the phenotypes might be nonlinear (Kitano 2002;Devijver et al. 2017;Green et al. 2017Green et al. , 2019, NN-MM may be a more biological realistic approach than the approach with the system of two linear models. ...
Full-text available
With the growing amount and diversity of intermediate omics data complementary to genomics (e.g., DNA methylation, gene expression, and protein abundance), there is a need to develop methods to incorporate intermediate omics data into conventional genomic evaluation. The omics data helps decode the multiple layers of regulation from genotypes to phenotypes, thus forms a connected multi-layer network naturally. We developed a new method named NN-LMM to model the multiple layers of regulation from genotypes to intermediate omics features, then to phenotypes, by extending conventional linear mixed models (“LMM”) to multi-layer artificial neural networks (“NN”). NN-LMM incorporates intermediate omics features by adding middle layers between genotypes and phenotypes. Linear mixed models (e.g., pedigree-based BLUP, GBLUP, Bayesian Alphabet, single-step GBLUP, or single-step Bayesian Alphabet) can be used to sample marker effects or genetic values on intermediate omics features, and activation functions in neural networks are used to capture the nonlinear relationships between intermediate omics features and phenotypes. NN-LMM had significantly better prediction performance than the recently proposed single-step approach for genomic prediction with intermediate omics data. Compared to the single-step approach, NN-LMM can handle various patterns of missing omics measures, and allows nonlinear relationships between intermediate omics features and phenotypes. NN-LMM has been implemented in an open-source package called “JWAS”.
... Several exciting recent studies have demonstrated how embedded properties of development, (processes inherent to trait development rather than mechanisms specific for canalization), can modulate phenotypic variation. [5][6][7] Together, these studies indicate that nonlinearity in the genotype-phenotype map may provide a general developmental mechanism for canalization. For example, Green et al. demonstrated a nonlinear relationship between Fgf8 expression and craniofacial development in mice, wherein mouse facial development was robust to a 60% reduction in Fgf8 levels, whereas beyond this threshold, small changes in gene expression resulted in large phenotypic effects. ...
... For example, Green et al. demonstrated a nonlinear relationship between Fgf8 expression and craniofacial development in mice, wherein mouse facial development was robust to a 60% reduction in Fgf8 levels, whereas beyond this threshold, small changes in gene expression resulted in large phenotypic effects. 6 Through this nonlinear relationship, a large amount of genetic variation can be tolerated without phenotypic consequence. While there is compelling evidence that the effects of genetic and environmental insults can be buffered by specific, dedicated developmental mechanisms such as the action of heat shock proteins, [8][9][10] microRNAs, 11 and methylation, 12,13 for complex traits such as skull shape, phenotypic robustness may arise more commonly through general developmental mechanisms such as nonlinearities. ...
... Because the different mutant mice are on separate genetic backgrounds, 36,42 superimposed landmark data were centered for each genotype on the grand mean to remove the effects of mouse strain and allow comparison between mutant mice. 6 2.1 | At age 3 months, mutant skulls are smaller than wildtype with greatest size reduction observed in the G60S/+ strain To determine the effects of reduced Cx43 function on skull size, centroid size was calculated from landmark data and scaled for body mass. To enable measurement and comparison of localized effects associated with each mutation, we created subsets of landmarks based on tissue origin (neural crest-derived and mesoderm-derived) and mode of ossification (intramembranous and endochondral; Figure 1A). ...
Background: We compared skull shape and variation among genetically modified mice that exhibit different levels of connexin43 (Cx43) channel function, to determine whether Cx43 contributes to craniofacial phenotypic robustness. Specifically, we used two heterozygous mutant mouse models (G60S/+ and I130T/+) that, when compared to their wildtype counterparts, have an ~80% and ~50% reduction in Cx43 function, respectively. Results: Both mutant strains showed significant differences in skull shape compared to wildtype littermates and while these differences were more severe in the G60S/+ mouse, shape differences were localized to similar regions of the skull in both mutants. However, increased skull shape variation was observed in G60S/+ mutants only. Additionally, covariation of skull structures was disrupted in the G60S/+ mutants only, indicating that while a 50% reduction in Cx43 function is sufficient to cause a shift in mean skull shape, the threshold for Cx43 function for disrupting craniofacial phenotypic robustness is lower. Conclusions: Collectively, our results indicate Cx43 can contribute to phenotypic robustness of the skull through a nonlinear relationship between Cx43 gap junctional function and phenotypic outcomes. This article is protected by copyright. All rights reserved.
... There are some biological factors that might suggest that such an approach to validation may be unsuccessful. Given common dominance patterns, and the likely non-linear genotypephenotype relationships of most genetic effects, small to moderate changes in gene function may result in modest phenotypic effects (Green et al., 2017;Melo et al., 2019;Wright, 1934). ...
Full-text available
Identifying the genetic architecture of complex traits is of interest to many geneticists, including those interested in human disease, plant and animal breeding and evolutionary genetics. Despite advances in sequencing technologies and GWAS statistical methods improving our ability to identify variants with smaller effect sizes, many of these identified polymorphisms fail to be replicated in subsequent studies. In addition to sampling variation, this reflects the complexities introduced by factors including environmental variation, genetic background and differences in allele frequencies among populations. Using Drosophila melanogaster wing shape, we ask if we can replicate allelic effects of polymorphisms first identified in a GWAS (Pitchers et al. 2019) in three genes: dachsous (ds), extra-macrochaete (emc) and neuralized (neur) , using artificial selection in the lab and bulk segregant mapping in natural populations. We demonstrate that shape changes associated with these genes is aligned with major axes of phenotypic and genetic variation in natural populations. Following 7 generations of artificial selection along ds and emc shape change vectors, we observe genetic differentiation of variants in ds and in genomic regions with other genes in the hippo signaling pathway, indicating available genetic diversity of a population summarized in G influences alleles captured by selection. Despite the success with artificial selection, bulk segregant analysis using natural populations did not detect these same variants, likely due to the contribution of environmental variation, low minor allele frequencies coupled with small effect sizes of the contributing variants.
... The observed differences in magnitude between suborders could be related to such factor. As developmental trajectories are strongly nonlinear (Green et al., 2017), variation in the onset of postnatal growth will affect the linear approximation of the postnatal trajectory leading to variation in angles in relation to differential duration of the gestation. Again, variation between suborders seems to be related to such an effect. ...
In mammals, significant changes take place during postnatal growth, linked to changes in diet (from sucking to gnawing). During this period, mandible development is highly interconnected with muscle growth and the epigenetic interactions between muscle and bone control the spatialization of bone formation and remodeling in response to biomechanical strain. This mechanism contributes to postnatal developmental plasticity, and may have influenced the course of evolutionary divergences between species and clades. We sought to model postnatal changes at a macroevolutionary scale by analyzing ontogenetic trajectories of mandible shape across 16 species belonging mainly to two suborders of Rodents, Myomorpha and Hystricomorpha, which differ in muscle attachments, tooth growth, and life-history traits. Myomorpha species present a much stronger magnitude of changes over a shorter growth period. Among Hystricomorpha, part of the observed adult shape is set up prenatally, and most postnatal trajectories are genus-specific, which agrees with non-linear developmental trajectories over longer gestational periods. Beside divergence at large scale, we find some collinearities between evolutionary and developmental trajectories. A common developmental trend was also observed, leading to enlargement of the masseter fossa during postnatal growth. The tooth growth, especially hypselodonty, seems to be a major driver of divergences of postnatal trajectories. These muscle- and tooth-related effects on postnatal trajectories suggest opportunities for developmental plasticity in the evolution of the mandible shape, opportunities that may have differed across Rodent clades.
... In this sense, the nonlinearity of developmental interactions has been claimed to be responsible for the emergence of robustness at different levels of organization (e.g. Green et al. 2017). The modularity of traits may be an intrinsic property of G-P maps as well, as illustrates the modular structure of simple molecules such as RNA. ...
Ribosomal RNA (rRNA) transcription and ribosome biogenesis are global processes required for growth and proliferation of all cells, yet perturbation of these processes in vertebrates leads to tissue-specific defects termed ribosomopathies. Mutations in rRNA transcription and processing proteins often lead to craniofacial anomalies; however, the cellular and molecular reasons for these defects are poorly understood. Therefore, we examined the function of the most abundant nucleolar phosphoprotein, Nucleolin (Ncl), in vertebrate development. ncl mutant (ncl−/−) zebrafish present with craniofacial anomalies such as mandibulofacial hypoplasia. We observed that ncl−/− mutants exhibited decreased rRNA synthesis and p53-dependent apoptosis, consistent with a role in ribosome biogenesis. However, we found that Nucleolin also performs functions not associated with ribosome biogenesis. We discovered that the half-life of fgf8a mRNA was reduced in ncl−/− mutants, which perturbed Fgf signaling, resulting in misregulated Sox9a-mediated chondrogenesis and Runx2-mediated osteogenesis. Consistent with this model, exogenous FGF8 treatment significantly rescued the cranioskeletal phenotype in ncl−/− zebrafish, suggesting that Nucleolin regulates osteochondroprogenitor differentiation. Our work has therefore uncovered tissue-specific functions for Nucleolin in rRNA transcription and post-transcriptional regulation of growth factor signaling during embryonic craniofacial development.
Background: Asymmetries in craniofacial anomalies are commonly observed. In the facial skeleton, the left side is more commonly and/or severely affected than the right. Such asymmetries complicate treatment options. Mechanisms underlying variation in disease severity between individuals as well as within individuals (asymmetries) are still relatively unknown. Results: Developmental reductions in Fibroblast growth factor 8 (Fgf8) have a dosage dependent effect on jaw size, shape, and symmetry. Further, Fgf8 mutants have directionally asymmetric jaws with the left side being more affected than the right. Defects in lower jaw development begin with disruption to Meckel's cartilage, which is discontinuous. All skeletal elements associated with the proximal condensation are dysmorphic, exemplified by a malformed and mis-oriented malleus. At later stages, Fgf8 mutants exhibit syngnathia, which falls into 2 broad categories: bony fusion of the maxillary and mandibular alveolar ridges and zygomatico-mandibular fusion. All of these morphological defects exhibit both inter- and intra-specimen variation. Conclusions: We hypothesize that these asymmetries are linked to heart development resulting in higher levels of Fgf8 on the right side of the face, which may buffer the right side to developmental perturbations. This mouse model may facilitate future investigations of mechanisms underlying human syngnathia and facial asymmetry. This article is protected by copyright. All rights reserved.
Full-text available
Complex morphological traits are the product of many genes with transient or lasting developmental effects that interact in anatomical context. Mouse models are a key resource for disentangling such effects, because they offer myriad tools for manipulating the genome in a controlled environment. Unfortunately, phenotypic data are often obtained using laboratory-specific protocols, resulting in self-contained datasets that are difficult to relate to one another for larger scale analyses. To enable meta-analyses of morphological variation, particularly in the craniofacial complex and brain, we created MusMorph, a database of standardized mouse morphology data spanning numerous genotypes and developmental stages, including E10.5, E11.5, E14.5, E15.5, E18.5, and adulthood. To standardize data collection, we implemented an atlas-based phenotyping pipeline that combines techniques from image registration, deep learning, and morphometrics. Alongside stage-specific atlases, we provide aligned micro-computed tomography images, dense anatomical landmarks, and segmentations (if available) for each specimen ( N = 10,056). Our workflow is open-source to encourage transparency and reproducible data collection. The MusMorph data and scripts are available on FaceBase ( , 10.25550/3-HXMC ) and GitHub ( ).
Full-text available
Realistic mappings of genes to morphology are inherently multivariate on both sides of the equation. The importance of coordinated gene effects on morphological phenotypes is clear from the intertwining of gene actions in signaling pathways, gene regulatory networks, and developmental processes underlying the development of shape and size. Yet, current approaches tend to focus on identifying and localizing the effects of individual genes and rarely leverage the information content of high dimensional phenotypes. Here, we explicitly model the joint effects of biologically coherent collections of genes on a multivariate trait-craniofacial shape - in a sample of n = 1,145 mice from the Diversity Outbred (DO) experimental line. We use biological process gene ontology (GO) annotations to select skeletal and facial development gene sets and solve for the axis of shape variation that maximally covaries with gene set marker variation. We use our process-centered, multivariate genotype-phenotype (process MGP) approach to determine the overall contributions to craniofacial variation of genes involved in relevant processes and how variation in different processes corresponds to multivariate axes of shape variation. Further, we compare the directions of effect in phenotype space of mutations to the primary axis of shape variation associated with broader pathways within which they are thought to function. Finally, we leverage the relationship between mutational and pathway-level effects to predict phenotypic effects beyond craniofacial shape in specific mutants. We also introduce an online application which provides users the means to customize their own process-centered craniofacial shape analyses in the DO. The process-centered approach is generally applicable to any continuously varying phenotype and thus has wide-reaching implications for complex-trait genetics.
Full-text available
rRNA transcription and ribosome biogenesis are global processes required for growth and proliferation of all cells, yet perturbation of these processes in vertebrates leads to tissue-specific defects termed ribosomopathies. Mutations in rRNA transcription and processing proteins often lead to craniofacial anomalies, however the cellular and molecular reasons for this are poorly understood. Therefore, we examined the function of the most abundant nucleolar phosphoprotein, Nucleolin (Ncl), in vertebrate development. We discovered that Nucleolin is dynamically expressed during embryonic development with high enrichment in the craniofacial tissues. Consistent with this pattern of expression, ncl homozygous mutant (ncl-/-) zebrafish present with craniofacial anomalies such as mandibulofacial hypoplasia. We observe that ncl-/- mutants exhibit decreased rRNA synthesis and p53-dependent neuroepithelial cell death. In addition, the half-life of fgf8a mRNA is reduced in ncl-/- mutants, which perturbs Fgf signaling, resulting in misregulation of Sox9a mediated chondrogenesis and Runx2 mediated osteogenesis. Exogenous addition of human recombinant FGF8 to the mutant zebrafish significantly rescues the cranioskeletal phenotype, suggesting that Nucleolin regulates osteochondroprogenitor differentiation during craniofacial development by post-transcriptionally regulating Fgf signaling. Our work has therefore uncovered a novel tissue-specific function for Nucleolin in rRNA transcription and growth factor signaling during embryonic craniofacial development.
Full-text available
Many enzymes in intermediary metabolism manifest saturation kinetics in which flux is a concave function of enzyme activity and often of the Michaelis-Menten form. The result is that, when natural selection favors increased enzyme activity so as to maximize flux, a point of diminishing returns will be attained in which any increase in flux results in a disproportionately small increase in fitness. Enzyme activity ultimately will reach a level at which the favorable effect of an increase in activity is of the order 1/(4Ne) or smaller, where Ne is the effective population number. At this point, many mutations that result in small changes in activity will result in negligible changes in fitness and will be selectively nearly neutral. We propose that this process is a mechanism whereby conditions for the occurrence of nearly neutral mutations and gene substitutions can be brought about by the long-continued action of natural selection. Evidence for the hypothesis derives from metabolic theory, direct studies of flux, studies of null and other types of alleles in Drosophila melanogaster and chemostat studies in Escherichia coli. Limitations and complications of the theory include changes in environment or genetic background, enzymes with sharply defined optima of activity, overdominance, pleiotropy, multifunctional enzymes and branched metabolic pathways. We conclude that the theory is a useful synthesis that unites many seemingly unrelated observations. The principal theoretical conclusion is that the conditions for the occurrence of neutral evolution can be brought about as an indirect result of the action of natural selection.
Full-text available
High-order epistasis has been observed in many genotype-phenotype maps. These multi-way interactions between mutations may be useful for dissecting complex traits and could have profound implications for evolution. Alternatively, they could be a statistical artifact. High-order epistasis models assume the effects of mutations should add, when they could in fact multiply or combine in some other nonlinear way. A mismatch in the "scale" of the epistasis model and the scale of the underlying map would lead to spurious epistasis. In this paper, we develop an approach to estimate the nonlinear scales of arbitrary genotype-phenotype maps. We can then linearize these maps and extract high-order epistasis. We investigated seven experimental genotype-phenotype maps for which high-order epistasis had been reported previously. We find that five of the seven maps exhibited nonlinear scales. Interestingly, even after accounting for nonlinearity, we found statistically significant high-order epistasis in all seven maps. The contributions of high-order epistasis to the total variation ranged from 2.2% to 31.0%, with an average across maps of 12.7%. Our results provide strong evidence for extensive high-order epistasis, even after nonlinear scale is taken into account. Further, we describe a simple method to estimate and account for nonlinearity in genotype-phenotype maps.
Full-text available
The human face is a complex assemblage of highly variable yet clearly heritable anatomic structures that together make each of us unique, distinguishable, and recognizable. Relatively little is known about the genetic underpinnings of normal human facial variation. To address this, we carried out a large genomewide association study and two independent replication studies of Bantu African children and adolescents from Mwanza, Tanzania, a region that is both genetically and environmentally relatively homogeneous. We tested for genetic association of facial shape and size phenotypes derived from 3D imaging and automated landmarking of standard facial morphometric points. SNPs within genes SCHIP1 and PDE8A were associated with measures of facial size in both the GWAS and replication cohorts and passed a stringent genomewide significance threshold adjusted for multiple testing of 34 correlated traits. For both SCHIP1 and PDE8A, we demonstrated clear expression in the developing mouse face by both whole-mount in situ hybridization and RNA-seq, supporting their involvement in facial morphogenesis. Ten additional loci demonstrated suggestive association with various measures of facial shape. Our findings, which differ from those in previous studies of European-derived whites, augment understanding of the genetic basis of normal facial development, and provide insights relevant to both human disease and forensics.
Full-text available
Numerous lines of evidence point to a genetic basis for facial morphology in humans, yet little is known about how specific genetic variants relate to the phenotypic expression of many common facial features. We conducted genome-wide association meta-analyses of 20 quantitative facial measurements derived from the 3D surface images of 3118 healthy individuals of European ancestry belonging to two US cohorts. Analyses were performed on just under one million genotyped SNPs (Illumina OmniExpress+Exome v1.2 array) imputed to the 1000 Genomes reference panel (Phase 3). We observed genome-wide significant associations (p < 5 x 10⁻⁸) for cranial base width at 14q21.1 and 20q12, intercanthal width at 1p13.3 and Xq13.2, nasal width at 20p11.22, nasal ala length at 14q11.2, and upper facial depth at 11q22.1. Several genes in the associated regions are known to play roles in craniofacial development or in syndromes affecting the face: MAFB, PAX9, MIPOL1, ALX3, HDAC8, and PAX1. We also tested genotype-phenotype associations reported in two previous genome-wide studies and found evidence of replication for nasal ala length and SNPs in CACNA2D3 and PRDM16. These results provide further evidence that common variants in regions harboring genes of known craniofacial function contribute to normal variation in human facial features. Improved understanding of the genes associated with facial morphology in healthy individuals can provide insights into the pathways and mechanisms controlling normal and abnormal facial morphogenesis.
Although numerous studies have found that fluctuating asymmetry (FA) can have a heritable component, the genetic and developmental basis of FA is poorly understood. We used a developmental model of a trait, according to a diffusion-threshold process, whose parameters are under genetic control. We added a small amount of random variation to the parameter values of this model to simulate developmental noise. As a result of the nonlinearity of the model, different genotypes differed in their sensitivity to developmental noise, even though the noise is completely random and independent of the genotype. The heritable component of FA can thus be understood as genetically modulated expression of variation that is itself entirely nongenetic. The loci responsible for this genetic variation of FA are the same that affect the left/right mean of the trait, showing that genetic variation for FA does not require genes that specifically control FA. Furthermore, the model offers alternative explanations for phenomena widely discussed in the literature on FA, for instance, the correlations between FA and heterozygosity and between FA and trait size. The model underscores the importance of dominance and epistasis, and therefore unites the study of FA with the classical theory of quantitative genetics.
Evolution can change the developmental processes underlying a character without changing the average expression of the character itself. This sort of change must occur in both the evolution of canalization, in which a character becomes increasingly buffered against genetic or developmental variation, and in the phenomenon of closely related species that show similar adult phenotypes but different underlying developmental patterns. To study such phenomena, I develop a model that follows evolution on a surface representing adult phenotype as a function of underlying developmental characters. A contour on such a "phenotype landscape" is a set of states of developmental characters that produce the same adult phenotype. Epistasis induces curvature of this surface, and degree of canalization is represented by the slope along a contour. I first discuss the geometric properties of phenotype landscapes, relating epistasis to canalization. I then impose a fitness function on the phenotype and model evolution of developmental characters as a function of the fitness function and the local geometry of the surface. This model shows how canalization evolves as a population approaches an optimum phenotype. It further shows that under some circumstances, "decanalization" can occur, in which the expression of adult phenotype becomes increasingly sensitive to developmental variation. This process can cause very similar populations to diverge from one another developmentally even when their adult phenotypes experience identical selection regimes.