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Shared rules of development predict patterns of evolution in vertebrate segmentation

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Phenotypic diversity is not uniformly distributed, but how biased patterns of evolutionary variation are generated and whether common developmental mechanisms are responsible remains debatable. High-level ‘rules’ of self-organization and assembly are increasingly used to model organismal development, even when the underlying cellular or molecular players are unknown. One such rule, the inhibitory cascade, predicts that proportions of segmental series derive from the relative strengths of activating and inhibitory interactions acting on both local and global scales. Here we show that this developmental design rule explains population-level variation in segment proportions, their response to artificial selection and experimental blockade of putative signals and macroevolutionary diversity in limbs, digits and somites. Together with evidence from teeth, these results indicate that segmentation across independent developmental modules shares a common regulatory ‘logic’, which has a predictable impact on both their short and long-term evolvability.
Normal population-level and induced variation is consistent with predictions of an inhibitory cascade. (a) Proximal-distal tradeoffs in experimental groups are statistically indistinguishable from wildtype/controls (likelihood ratio=3.391, df=2, P=0.184), and together they are consistent with IC model predictions (yellow line: sn+2=−0.97 × sn+0.69, r2=0.813, P=0.000; r=−0.063, df=199, P=0.375). (b) An impermeable barrier between developing the s0–sn joint leads to a significant increase in proximal phalangeal proportions (sn) and decrease in distal segment (sn+2) proportions, while middle segment (sn+1) proportions remain unchanged (ANCOVA, P<0.001). (c) The rock dove (Columba livia) and domesticated/feral pigeons follow the same proximal-distal tradeoff (yellow), paralleling the predicted IC model trajectory (red dashed) (r=0.060, df=34, P=0.729). (d) The ‘Racing Homer’ domesticated pigeon breed has significantly shifted proximal-distal (s1–s3) wing element proportions, but no difference was found in zeugopod (s2) proportion (ANCOVA, P<0.001, N=54). Note that digits were not included in this analysis, thus s2 proportions are inflated, but otherwise does not impact the s1–s3 tradeoff prediction. (e,f) When decomposed into local three-segment series, somites and their skeletal derivatives (principally vertebral centra) exhibit a PD trajectory consistent with the IC model predictions (sn+1=0.331±0.001; sn+2=−1.01 × s1+0.67, r2=0.83, P<0.001; [sn+/2]/[sn] = 2.02 × [s2/s1]−1.01, r2=0.74, P<0.001).
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ARTICLE
Received 21 Jul 2014 |Accepted 19 Feb 2015 |Published 1 Apr 2015
Shared rules of development predict patterns
of evolution in vertebrate segmentation
Nathan M. Young1,*, Benjamin Winslow2, Sowmya Takkellapati2& Kathryn Kavanagh2,*
Phenotypic diversity is not uniformly distributed, but how biased patterns of evolutionary
variation are generated and whether common developmental mechanisms are responsible
remains debatable. High-level ‘rules’ of self-organization and assembly are increasingly used
to model organismal development, even when the underlying cellular or molecular players are
unknown. One such rule, the inhibitory cascade, predicts that proportions of segmental series
derive from the relative strengths of activating and inhibitory interactions acting on both local
and global scales. Here we show that this developmental design rule explains population-level
variation in segment proportions, their response to artificial selection and experimental
blockade of putative signals and macroevolutionary diversity in limbs, digits and somites.
Together with evidence from teeth, these results indicate that segmentation across inde-
pendent developmental modules shares a common regulatory ‘logic’, which has a predictable
impact on both their short and long-term evolvability.
DOI: 10.1038/ncomms7690
1Department of Orthopaedic Surgery, University of California, San Francisco, California 94110, USA. 2Department of Biology, University of Massachusetts,
285 Old Westport Road, Dartmouth, Massachusetts 02747, USA. * These authors contributed equally to this work. Correspondence and requests for
materials should be addressed to N.M.Y. (email: nathan.m.young@gmail.com) or to K.K. (email: kkavanagh@umassd.edu).
NATURE COMMUNICATIONS | 6:6690 | DOI: 10.1038/ncomms7690 | www.nature.com/naturecommunications 1
&2015 Macmillan Publishers Limited. All rights reserved.
Amajor goal of evolutionary developmental biology is to
identify whether there are rules governing the generation
of phenotypic variation and how these might
impact evolvability1. Some of the most recognizable evolved
differences among taxa are variations in the number and/or size
of iterative segments such as teeth2, limbs3, phalanges4and
somites5. Despite apparent diversity, evidence suggests that
developmental interactions create predictable, non-random
patterns of variation (for example, in digits4and limbs6). While
morphogenesis of each of these organ systems utilizes similar
developmental processes of ‘outgrowth and segmentation’7–9,a
lack of genetic and structural homology among them has led to
the presumption that different developmental principles must
apply to each system.
Commonalities in regulatory ‘logic’ may predict similar
underlying ‘rules’ of variation even when the underlying identity
of cellular or molecular players differs10–13. One such model,
the inhibitory cascade (IC)14, is particularly promising for
understanding iterative segmentation in a range of disparate
organ systems. Originally described in teeth, the IC can be
generalized to any sequentially forming structure that develops at
the balance between auto-regulatory ‘activator’ and ‘inhibitor’
signals. In, limbs15 and somites16, such signals are analogous to
internal ‘clock’-like mechanisms posited to control timing of
condensation formation and molecular gradients or ‘wavefronts’
that inhibit them. In contrast to previous models, the IC makes
explicit quantitative predictions of how proportional variation is
apportioned among segments, thus both comparative and
experimental data from segmented structures can be used as
direct tests.
Specifically, the IC can be modelled by equation (1):
sn
½¼1þðaiÞ
i
hi
ðn1Þ
Where sis a segment, nis the segment position expressed as an
integer, ais the activator strength and iis the inhibitor strength15.
Assuming a linear effect of activator to inhibitor, solving
equation (1) for a three-segment system yields sizes of: [s
1
]¼1,
s2
½¼a
i
 and s3
½¼2a
i1

. Expressed as proportions,
equation (1) further predicts that for a three-segment system
the middle segment is one-third the total size (that is, s1
½¼ i
3a

,
s2
½¼1
3
, and s3
½¼2ai
3a

(see Methods)), the proximal and
distal segment proportions function as a tradeoff that accounts
for the remainder (that is, s
nþ2
¼1s
n
þ2/3) and the ratio of
the size of the first two segments predicts the ratio of the first and
third (that is, [s
nþ2
/s
n
]¼2[s
nþ1
/s
n
]1).
The IC model can be further extended to predict sizes and
proportions for any total number of segments (see Supplementary
Table 1). Importantly, equation (1) can be generalized such that
any three adjacent segments or blocks of segments (the ‘local’
effect) within a series are predicted to exhibit the same behaviour
regardless of the total segment number (see Methods). Because
the overall pattern (the ‘global effect) results from the sum of local
effects from all adjacencies, the partitioning of total variance is
reflected in a parabolic relationship with total segment number,
with the middle segment(s) at the vertex or minima and
equivalent to either 1/n(when odd numbered) or 2/n(when
even numbered). As with the three-segment solution, the
proximal-most and distal-most segments or blocks receive the
most variance, and proportions act as a ‘tradeoff’, which is further
reflected in diagnostic covariation among individual segment
proportions.
If the IC is a generalizable developmental rule, then it should
be able to predict how size proportion variation is both structured
within populations and responds to selection or experimental
perturbations in a range of segmented structures. Furthermore,
because biases in the generation of variation impact evolvability17,
the signal of this mechanism would be evident in the patterning
of macroevolutionary diversity among species (Fig. 1). As
alternative ‘rules’ for generating proportions, we modelled
segment variation in which the strength of size covariation
ranged from 0 (that is, completely random) to 1 in which segment
sizes had a constant directionality (that is, they did not alternate),
but the amount is random between segments. These alternatives
predicted outcomes distinct from the IC, such as: (1) all types of
segment proportions occur with equal frequency, (2) normalized
variances are non-parabolic and (3) relationships between
adjacent segments are weaker and more distributed. In this
context, the IC model represents a specific subset of these
alternatives, in which activator–inhibitor interactions are
constant among segments.
Here we test the quantitative predictions of the IC model in
developmental experiments, species under artificial selection, and
microevolutionary and macroevolutionary data sets of segmented
structures including limbs, phalanges, somites and vertebrae. We
find that all these systems follow the expectations of the model,
including predictable variation of size proportions, a proximo-
distal trade-off in size and variance apportioned parabolically.
Rakali
Field mouse
Wooly rat
Ostrich
Whale
Kingfisher
Owl
Whale
Chicken
Lizard
Human
Pigeon
Horse
Whale
Bat
Limbs Vertebrae/
somites
Phalanges Molars
Elephant
Middle
(sn+1)Proximal
(sn)
Distal
(sn+2)
Figure 1 | Iteratively segmented structures exhibit similar variational features predicted by the inhibitory cascade model. The middle segment averages
one-third of total size and exhibits reduced variance, while proximal and distal segment proportions function as a tradeoff for any series of three adjacent
individual segments or blocks of segments. From left to right, example specimens include: a bat wing (Carollia perspicillata), dolphin flipper (Tursiops
truncatus), horse forelimb (Equus ferus caballus ), pigeon wing (Columbia livia), human arm (Homo sapiens), elephant hindlimb (Loxodonta africana), lizard
vertebrae (Varanus indicus), chick somites (Gallus gallus), humpback whale tail vertebrae (Megaptera novaeangliae), Saw whet owl foot digit III phalanges
(Aegolius acadicus), Kingfisher foot digit III phalanges (Alcedo atthis), Whale forelimb phalanges (Megaptera novaeangliae), ostrich foot digit III phalanges
(Struthio camelus) Woolly rat molars (Mallomys rothschildi), field mouse molars (Apodomus agrarius) and Rakali rodent molars (Hydromys chrysogaster).
ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms7690
2NATURE COMMUNICATIONS | 6:6690 | DOI: 10.1038/ncomms7690 | www.nature.com/naturecommunications
&2015 Macmillan Publishers Limited. All rights reserved.
These widely shared segmentation rules raise questions about the
extent of developmental bias in the structural design of animal
bodies.
Results
The IC model predicts experimental outcomes in phalanges.
We first tested model predictions in digits by quantifying pha-
langeal proportions in normal chicken (Gallus gallus) embryos
immediately post-patterning (Supplementary Data 1). We found
they followed the expectations of the IC model, with a proximo-
distal tradeoff (s
nþ2
¼1.00 s
n
þ0.70, r2¼0.790, Po0.001),
significantly lower variation in the middle segment (Levene’s test,
Po0.001) and a mean just under B1/3 of proportions (s
nþ1
¼0.297±0.023) (Fig. 2a). Next, we tested the IC model predic-
tion that altering the relative balance of the strength of activation
to inhibition would affect segmental outcomes and proportions.
We reasoned that, even without a priori knowledge of the exact
signals involved, if segments were generated via an activator–
inhibitor dynamic interaction, an impermeable barrier would
alter their balance and phenotypic outcomes. Specifically, we
hypothesized that if s
1
plays an inhibitory role on subsequent s
2
,
then by disrupting the signal between them we would see a shift
in proximo-distal proportions of the downstream s
2
s
3
s
4
series.
Consistent with these predictions, we observed that even when
controlled for reductions in total size (sum of all phalanges within
a digit), the barrier significantly increased proximal s
2
propor-
tions relative to controls (from 0.422±0.024 to 0.448±0.048,
analysis of covariance (ANCOVA), Po0.001) and decreased
distal s
4
proportions (from 0.286±0.025 to 0.250±0.024,
ANCOVA, Po0.001), but in all cases left the middle segment [s
3
]
statistically unchanged (0.292±0.013 to 0.300±0.016,
ANCOVA, P¼0.433; Fig. 2b). Moreover, experimental, control
and wild-type segment proportions share a common proximo-
distal trajectory (likelihood ratio ¼3.391, df ¼2, P¼0.184)
that is statistically indistinguishable from model prediction
(s
nþ2
¼0.97 s
n
þ0.69, r2¼0.813, Po0.001; r¼0.063,
df ¼199, P¼0.375).
The IC model predicts microevolution of limb segment size
proportions. We next analysed intraspecific variation in the
forelimbs (wings) of the adult rock dove (Columba livia).
Consistent with the IC model predictions, we found that rock
dove proximal-distal wing proportions (s
3
¼1.06 s
1
þ0.61,
r2¼0.184, P¼0.009) are not significantly different from the
predicted tradeoff slope (r¼0.060, df ¼34, P¼0.729) or inter-
cept (t¼1.026, df ¼34, P¼0.312; Fig. 2c). We next compared
these results to domesticated pigeon breeds and related ferals
(C. livia domestica; Supplementary Data 2). Pigeons have
been domesticated for at least 10,000 years, with breeders
targeting a range of phenotypic traits, including overall body
size and limb length, while ferals are domesticated pigeons that
have escaped into the wild and populated novel ecological
niches18 and maintain significant gene flow introgression19.
We reasoned that the effect of selection and population
expansion would be to increase variation in these groups,
but along a trajectory consistent with rock doves and the IC
model. Indeed, when compared with rock doves, in both
domesticated (s
3
¼1.24 s
1
þ0.67, r2¼0.45) and feral
groups (s
3
¼1.06 s
1
þ0.61, r2¼0.38) there was no
significant difference in slope (likelihood ratio ¼1.679, df ¼2,
Carpometacarpus (%)
0.23
0.25
0.28
Humerus (%)
0.32 0.34 0.37
Homer
Domesticated
Rock dove
Feral
sn+2 (%)
0.10
0.19
0.28
0.36
0.45
sn (%)
0.25 0.37 0.48 0.60
Barrier
Control
Wildtype
WT/control/barrier:
sn+2=–0.97×sn+0.69
r2=0.813, P<0.001
Segment proportion (%)
0.20
0.27
0.34
0.41
0.48
0.55
snsn+1 sn+2
WT/control
Barrier
P=0.000
P=0.143
P=0.009
Segment proportion (%)
0.20
0.32
0.43
0.55
s1s2s3
Rock dove
Racing homer
P=0.230
P<0.001
P<0.001
Phalanges Limbs Somites/vertebrae
sn+2 (%)
0.00
0.33
0.66
sn (%)
0.00 0.33 0.66
Somites
Vertebrae
sn+2/sn
0.00
3.50
7.00
sn+1/sn
0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50
Somites
Vertebrae
All pigeons:
s3=–1.09×s1+0.62
r2=0.43, P=0.000
Somites/vertebrae:
sn+2=–1.01×s1+0.67
r2=0.83, P<0.001
Somites/Vertebrae:
[sn+/2]/[sn]=2.02×[s2/s1]– 1.01
r2=0.74, P<0.001
Figure 2 | Normal population-level and induced variation is consistent with predictions of an inhibitory cascade. (a) Proximal-distal tradeoffs in
experimental groups are statistically indistinguishable from wildtype/controls (likelihood ratio ¼3.391, df ¼2, P¼0.184), and together they are consistent
with IC model predictions (yellow line: s
nþ2
¼0.97 s
n
þ0.69, r2¼0.813, P¼0.000; r¼0.063, df ¼199, P¼0.375). (b) An impermeable barrier
between developing the s
0
s
n
joint leads to a significant increase in proximal phalangeal proportions (s
n
) and decrease in distal segment (s
nþ2
) proportions,
while middle segment (s
nþ1
) proportions remain unchanged (ANCOVA, Po0.001). (c) The rock dove (Columba livia) and domesticated/feral pigeons
follow the same proximal-distal tradeoff (yellow), paralleling the predicted IC model trajectory (red dashed) (r¼0.060, df ¼34, P¼0.729). (d) The
‘Racing Homer’ domesticated pigeon breed has significantly shifted proximal-distal (s
1
s
3
) wing element proportions, but no difference was found in
zeugopod (s
2
) proportion (ANCOVA, Po0.001, N¼54). Note that digits were not included in this analysis, thus s
2
proportions are inflated, but otherwise
does not impact the s
1
s
3
tradeoff prediction. (e,f) When decomposed into local three-segment series, somites and their skeletal derivatives (principally
vertebral centra) exhibit a PD trajectory consistent with the IC model predictions (s
nþ1
¼0.331±0.001; s
nþ2
¼1.01 s
1
þ0.67, r2¼0.83, Po0.001;
[s
nþ/2
]/[s
n
]¼2.02 [s
2
/s
1
]1.01, r2¼0.74, Po0.001).
NATURE COMMUNICATIONS | DOI: 10.1038/ncomms7690 ARTICLE
NATURE COMMUNICATIONS | 6:6690 | DOI: 10.1038/ncomms7690 | www.nature.com/naturecommunications 3
&2015 Macmillan Publishers Limited. All rights reserved.
P¼0.432) or elevation (Wald Statistic ¼1.304, df ¼2, P¼0.520)
although both groups were significantly shifted along this
common axis (Wald Statistic ¼85.53, df ¼2, P¼0.000).
Relevant to this final observation, one breed in particular,
the ‘Racing Homer’, has been selectively bred in the last 100
years for speed, and relative to the rock dove, is significantly
shifted in proximal-distal proportions (humerus: 0.343±0.002
versus 0.337±0.002, ANCOVA, Po0.001; carpo-metacarpus:
0.254±0.002 versus 248±0.002, ANCOVA, Po0.001, N¼54),
yet the zeugopod is not significantly different in proportions, even
when controlled for differences in wing length (P¼0.232)
(Fig. 2d). These results indicate that selection on size alone
cannot explain the observed changes in homer wing proportions;
rather selective breeding has evolved proportions along a line of
developmental ‘least resistance’ present within ancestral rock
doves and predicted by the IC model.
The IC model predicts variation of somites and their derivatives.
We next asked whether variation in somites is also consistent
with quantitative predictions of the IC model using available data.
Previous reports suggest somites form as an antero-posterior
gradient in which sizes do not alternate (for example, increasing
size in mice20, decreasing size in amphibians21 or equal size in
avians22). Analysis of the somite data matches those of the
IC predictions (s
nþ1
¼0.325±0.001; s
nþ2
¼1.00s
n
þ0.67,
r2¼0.935, Po0.001; [s
nþ2
]/[s
n
]¼2.10[s
nþ1
]/[s
n
]1.03, r2¼
0.932, Po0.001) (Supplementary Data 3; Fig. 2e). As a further
test, we analysed vertebral column proportions in primates,
rodents, carnivores and amphibians. Although individual
vertebrae are derived from adjacent somites, we reasoned that if
each vertebra forms from one half of two adjacent somites and if
growth of adjacent vertebrae were similar, then the local pattern
(that is, among any three adjacent segments or blocks) should
follow the IC model. Indeed, we found that when decomposed
into local adjacencies or blocks, combined data from the
vertebral columns were consistent with the IC model trade-
off (s
nþ1
¼0.332±0.001; s
nþ2
¼1.01s
n
þ0.67, r2¼0.810,
Po0.001; [s
nþ2
]/[s
n
]¼1.98[s
nþ1
]/[s
n
]0.97, r2¼0.651, Po0.001)
Supplementary Data 3; Fig. 2f).
The IC model predicts macroevolutionary diversity.AnIC
mechanism should also impact evolvability, which on a macro-
evolutionary scale would be reflected in biased distributions of
species-level segment proportions along a common ‘line of least
resistance’, in this case the proximal-distal tradeoff14,23. Limbs,
phalanges and somites exhibit a range of proximo-distally
arranged total segments, from 3 (for example, in limbs and
most mammalian digits) to as many as 28 (for example, in the
digits of ichthyosaurs or in vertebral columns) (Supplementary
Data 4–11). We first compared limb data, which have three
defined segments, to digital rays that numbered three total
phalangeal segments. We found that these data sets had similar
properties to those predicted by the IC model, including a middle
segment proportion centre of B1/3 (digit: s
2
¼0.334±0.037,
limb: s
2
¼0.356±0.014) with significantly reduced variance
relative to proximal and distal segments (Levene’s test,
Po0.001) (Supplementary Tables 2a–c). Furthermore, proximal
and distal segment proportions operated as a tradeoff (limb:
s
3
¼1.05s
1
þ0.67, r2¼0.793, P¼0.000; digit: s
3
¼0.93s
1
þ0.65, r2¼0.671, P¼0.000) (Supplementary Fig. 4a–d), with
elevations statistically indistinguishable from the IC model (limb:
t¼0.035, df ¼826, P¼0.972; digit: t¼1.189, df ¼226,
P¼0.236) and slopes at (digit: r¼0.041, df ¼226, P¼0.541) or
near the prediction (limb 95% confidence interval ¼1.08 to
1.02) (Fig. 3a–e).
To facilitate comparison among segmental types of varying
lengths (for example, long digit and somite series), we next
broke global series for the comparative data sets into all adjacent
s3/s1
0.00
8.00
16.00
s2/s1
0.00 5.00 10.00
s3
0.0
0.2
0.4
0.6
0.8
s1
0.0 0.2 0.4 0.6 0.8 s3
0.00 0.33 0.67 1.00
s1s2s3
IC
Null/RR
s1
s2
IC
N/RR # Segments
123456789
Normalized variance
Null
Data
IC model
[s3/s1]= 1.82×[s2/s1]– 0.91
r2=0.88
s3=–0.96×s1+0.64
r2=0.89
Data-IC
rv=0.999
P=0.000
Figure 3 | Three-segment phalangeal and limb proportions exhibit patterning consistent with the IC model. (a) Proportional data distributions sorted in
ascending order for the first segment (s
1
). Linear estimates (yellow line) for the PD tradeoff (b) and ratio prediction (c) compared with
model (red) and null (AD, blue) predictions. (d) Ternary diagrams with estimated PC1 (IC ¼inhibitory cascade, red; N/RR ¼null/random relay, blue).
Each point represents a single limb or phalangeal segment series or block. (e) Normalized variance profiles for segments from three to nine segments
in null, observed data and IC model.
ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms7690
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&2015 Macmillan Publishers Limited. All rights reserved.
three-segment ‘local’ series and blocks (segment n¼3–28, sample
N¼2,166) (Supplementary Fig. 5a–f). Again, we found that the
middle segment or block averaged B1/3 (s
nþ1
¼0.343±0.014),
variance was significantly lower compared with adjacent
segments (Levene’s test, Po0.001) and there was an associated
tradeoff between any first (s
n
) and third (s
nþ2
) segment
proportion, regardless of position in the series (s
nþ2
¼0.91
s
n
þ0.63, r2¼0.879, Po0.001). Moreover, the segment ratios
were significantly correlated (that is, [s
nþ2
]/[s
n
]¼1.75[s
nþ1
]/
[s
n
]0.78, r2¼0.826, Po0.001), indicating that the sizes of any
first two segments were a highly significant predictor of the
subsequent third segment size. When we evaluated the compara-
tive data in a multivariate framework, we found that eigenvectors
from the comparative data were significantly better correlated
with the IC model predictions than with the alternative null
models (PC1 angle ¼1.49, r
v
¼0.9997, Fisher-z¼4.36, Po0.001)
(Fig. 4; Supplementary Tables 3).
Discussion
Our results demonstrate that the IC provides a common
explanatory framework for the generation of scale-free size
variation (that is, proportions) in a variety of segmented
structures in vertebrates. Previous work on this phenomenon
was limited to teeth14,24,25, and it was unclear whether the
activator interactions proposed in the IC also predicted ‘rules’
applicable to other sequentially forming structures. Given the
explanatory power of IC predictions for the results presented
here, this model may be generalizable to a range of other
structures and phylogenetically distant taxa. Importantly, this
mechanism also appears to impact both short-term responses
of population-level variation and long-term patterns of
macroevolutionary diversity to selection, and thus should help
explain variational bias in a range of structural phenomena.
The puzzle of this result is, given the potential ubiquity of a
relatively simple and common regulatory ‘logic’ and the
subsequent limits on variation it entails, how is evolutionary
diversity generated? In part this question results from the
disparity between perceived and measurable diversity, the latter
of which is substantially smaller than the former. That said, while
the IC biases variation in a predictable manner, there are number
of ways in which these ‘rules’ may be combined with other
developmental processes to produce more complex patterns.
These include: (1) the iterative use of simple segmentation rules
as ‘sub-routines’ within hierarchical modules (for example,
phalangeal segmentation occurs within limbs; and such mod-
ularity is also consistent with evolution of the mammalian
vertebral column26), (2) the shaping of cell number or volume
into alternative shapes and (3) the use of later developmental
events like growth to ‘fine tune’ outcomes on a regional basis
(Supplementary Fig. 6a–d). For example, while vertebrae vary in
size across regions and frequently alternate in size, evidence from
growth in a number of species suggests this results from later
differential growth27,28, consistent with earlier constraints on
somite-size patterning and proportions. We therefore hypothesize
that an IC mechanism provides the initial pattern of proportional
variation during segment formation, serving as a ‘foundation’ on
which later variation may add or subtract29. That said, while later
developmental processes such as differential growth may remodel
proportions, the signal of the earlier segmentation event is not
obliterated.
We propose that activator/inhibitor ratios, broadly defined, are
the mechanism for the evolutionary and developmental changes
observed in segmented structures on both local and global (whole
structure) scales. The shared developmental rules and quantita-
tive predictions of the IC model suggest underlying commonal-
ities that may help inform previous models of limb, digit and
somite formation by recasting them in an activator–inhibitor
framework. For example, more explicit reaction-diffusion models
of proximo-distal axis formation30,31 may be more accurate
than classic descriptions such as the ‘progress zone’, ‘early
specification’ or ‘two-signal’ models (discussed in ref. 15), which
propose that individual segments initially form as a function of
time balanced by inhibitory signals from the distal limb tip.
Somitogenesis has likewise been conceived of proceeding via a
‘clock’ that interacts with an inhibitory ‘wavefront’16, and newer
studies suggest that the clock period changes with shortening of
the unorganized (presomitic) mesoderm32 and is partly self-
organizing33. In both cases, the clock determining condensation
formation can be conceived of as an auto-regulatory activator
process that is balanced by an auto-regulatory inhibitory signal,
each of which presumably can be varied. Supporting this idea, we
note that up or downregulation of the inhibitory signal in
somitogenesis16 leads to localized changes in proportions of
individual segments that we would predict are quantitatively
consistent with the IC model.
Our results contribute to increasing evidence that
activator–inhibitor interactions are involved in limb, digit and
somite segmentation, and could reflect a universal design
principle4,30–35, but while confirmatory these results do not
clarify the identity of the molecule(s) or the exact developmental
mechanisms involved. We argue that the value of using the IC
model is that, while previous models describe how segments
form, they make no predictions about how they vary in size, and
imply that elements are either independently formed or that
segment proportions are largely the result of selection on later
developmental events such as growth. Here we show that earlier
events are crucial to the generation and patterning of
evolutionary diversity. Moreover, commonalities in proportional
outcomes indicate that knowledge of the specific molecules
involved is likely less important than how they interact within a
regulatory network. These results show how quantitative
outcomes from comparative and experimental data are
informative of the kinds of developmental interactions that are
possible, and provide explicit predictions that will help inform
future models of segment development and evolution.
Specifically, the IC may provide a common framework, in a
s1s3
s2
0.8
0.6
0.2
0.8
0.6
0.4
0.2
0.8
0.6
0.4
0.2
Digit
Limb
Somite/
vertebra
Figure 4 | Macroevolutionary diversity in phalanges, limb, somite and
vertebral segment proportions exhibit similar properties. Ternary diagram
showing comparative species-level variation in 2,000 þsegment
proportions in various structures reported in the text. Solid line shows the
multivariate regression with 95% confidence interval denoted by the
dashed lines.
NATURE COMMUNICATIONS | DOI: 10.1038/ncomms7690 ARTICLE
NATURE COMMUNICATIONS | 6:6690 | DOI: 10.1038/ncomms7690 | www.nature.com/naturecommunications 5
&2015 Macmillan Publishers Limited. All rights reserved.
variety of developmental contexts, for predicting both short-term
responses to selection in population-level variation and long-term
evolvability and patterns of macroevolutionary diversity.
Methods
Data.To test our model against as many examples as possible, we collected
segment size data from the limbs, phalanges, somites and vertebral columns of
laboratory specimens, museum collections and previously published data sets for
both limbs and digits. See Supplementary Data 1–11 for complete list of taxa,
segment proportions and source information. Segment proportions were assessed
using comparable proxies of size including: (i) length of the whole segments (for
example, arm/leg, forearm/shank and manus/pes), (ii) maximum length of the
skeletal elements (for example, ventral height of the vertebral body) or (iii) area/
volume of segments. The exception to these was data from pigeons, in which the
autopod measure did not include digit length, inflating stylopod and zeugopod
estimates (Supplementary Data 2). We note that although volume or cell number
may be the most appropriate measure of size for the developmental phenomena we
describe, variational properties and model predictions (for example, proximo-distal
(PD) tradeoff) are not affected, regardless of the size measure used. Digit data was
measured as the proportion of the proximal, middle and distal phalanx to total size
of the phalangeal series, using both length measures and area of bone in dorsal/
ventral view. For phalangeal chondrogenic condensation data, we collected normal
chicken embryos at the end of digit segmentation (D11), stained for cartilage using
Alcian blue and measured areas of segments in ImageJ. Alcian-stained chondro-
genic condensations were measured as above and compared among treatment
groups. We did not include the final phalanx (that is, ungual) in avians due to
evidence that this segment represents a separate module in which a distal sec-
ondary ossification centre of dermal origin fuses to the final phalanx, complicating
measures of initial size. This distal-most phalangeal segment, known as the ungual,
may also be derived due to its association with secondary dermal ossification
centres associated with claws and nails36,37. For total segment numbers of three or
four, we utilized species-averaged data for each limb or digital ray. We used
individual specimen data where total segments are 44. We considered forelimbs
and hindlimbs in the same species to be independent data points, as well as each
ray within a species autopod. For somite data, we collected avian embryos at HH8-
10, and stained
to improve visualization of the individual forming segments and measured
two-dimensional area in ImageJ.
Barrier experiment.Tantalum foil implants were inserted into nascent pre-
chondrogenic condensations of chick hindlimb digit IV on day 6–7. Embryos
were collected at D10–11, fixed and Alcian stained as described above. Wound
controls had foil barriers inserted and then removed about 1 min later. Area was
measured as above (Supplementary Data 1).
Developmental model.In a simplified IC model of activation and inhibition, the
size of a segment is predicted by the equation:
sn
½¼1þðaiÞ
i
hi
ðn1Þð1Þ
Where sis a segment (size or proportion), nis the number of the segment (from
proximal to distal), ais the activator strength and ithe inhibitor strength14.
We assume a linear effect of activator to inhibitor.
Solving this equation for a three-segment system yields segments sizes of:
[s
1
]¼1, s2
½¼a
i
and s3
½¼2a
i1

, and proportions are s1
½¼ i
3a

,s2
½¼1
3

and s3
½¼2ai
3a

(ref. 14). Because s2
½¼1
3
, then s1
½þs3
½¼2
3
and
s3
½¼1s1
½þ2
3
, and variance is predicted to be [s
1
]¼[s
3
] and [s
2
]¼0.
This equation can be similarly solved for any nsegments, and yields generalized
predictions for segment proportion variation (Supplementary Table 1;
Supplementary Figs 1 and 2). For example, in the case of four segments:
s1
½
¼i
6a2i,s2
½
¼a
6a2i,s3
½
¼2ai
6a2iand s4
½
¼3a2i
6a2i. Notably, equation (1)
generalizes for any three consecutive segments [s
n
]y[s
nþ2
], such that:
sn
½¼1þðaiÞ
i
hi
ðn1Þ
snþ1
½¼1þðaiÞ
i
hi
ðnÞ
snþ2
½¼1þðaiÞ
i
hi
ðnþ1Þ
In which case, total size of three consecutive segments is equivalent to:
sn
½þsnþ1
½þsnþ2
½¼1þðaiÞ
i
hi
ðn1Þþ1þðaiÞ
i
hi
ðnÞþ1þðaiÞ
i
hi
ðnþ1Þ
¼3þðaiÞ
i
hi
ðn1ÞþðnÞþðnþ1Þ½
¼3þ1þðaiÞ
i
hi
n
hi
And thus the proportion of the middle segment [s
nþ1
] equals:
snþ1
½
sn
½þsnþ1
½þsnþ2
½
¼1þðaiÞ
i
hi
n
31þðaiÞ
i
hi
n
hi
¼1
3
It follows that the proportions of the remaining segments (s
n
and s
nþ2
) account
for 2/
3
of series size and function as a tradeoff. As an example, when a four-segment
series (that is, [s
1
s
4
]) is analysed as two local series (that is, [s
1
s
2
s
3
] and
[s
2
s
3
s
4
]), each would be predicted to exhibit a middle segment proportion of 1/
3
with reduced variance relative to a proximal-distal tradeoff. The global relationship
would still be predicted to vary in a manner consistent with a four-segment series.
This nested relationship between series of different lengths implies that segments
interact locally with their direct neighbours, but because this effect is cumulative
(that is, a ‘ratchet’) there is a global effect on the whole series (Supplementary
Fig. 5a). Importantly, local and global effects enable the analysis of multi-
segmented structures as series of ‘blocks’ of varying effective size.
For global series of total segment number n, the average segment proportion
equals 1/n. If the first segment accounts for 42/nof total proportional size, the
ultimate segment is predicted to be negative, which implies a condensation cannot
form. Furthermore, the first and ultimate segment proportions are predicted to
tradeoff and exhibit equivalent variance. When plotted as a function of segment
number, normalized segment variance is parabolic, with exponents following a
power law relationship. In odd numbered segmental systems, the middle segment is
predicted to be invariant and account for 1/nof total proportions, where nis the
total number of segments. For example, in a five-segment system (n¼5), [s
3
]is
predicted to be B1/
5
,orB14.3%, of total size (Supplementary Fig. 2a,b).
Null models.For the null models, we modelled three different assumptions about
how segment sizes are generated and how proportions interact (Supplementary
Fig. 3a–o).At first, we assumed that individual segment sizes are independently
generated, thus we randomly generated vectors of length [1,n] in which segment
proportions were both unconstrained, uncorrelated, with a log normal distribution,
where the mean and normalized variance of each segment is equivalent. Second, we
utilized a ‘random relay’, in which we randomized the ratio of aand ibetween
segments14). In this case, covariance among segments still exists but is randomized
in its direction, reflecting an inhibitory effect that is dependent on the segments
involved rather than a constant function of the cascade. Third, we tested a simple
‘ascending–descending’ model in which segment proportions may be the same,
increase or decrease, but do not alternate. We reasoned that this case described a
general class of models in which segments interact in a constant direction (for
example, same, up or down), but the magnitude of the effect varies between any
given pair of segments. In this case, the IC model represents one specific set of
possibilities in which the interaction effect between activation and inhibition is
constant among all segments.
Linear estimation.We used reduced major axis to estimate linear parameters
because all variables are measured with error. Test statistics for hypotheses of slope
and elevation were based on modified ANCOVA for reduced major axis as
estimated in the smatr3 package38)inR39. We performed a centred log-ratio
transformation on proportional series and report descriptive statistics (center and
variance) for the compositional space40 using both CoDaPack v.2.01.14 (ref. 41)
and the Rpackage compositions42. We calculated the variance for each segment
series length (n¼3–7) for the comparative data, IC model and null predictions,
and normalized for the total variance of the series.
Principal components analysis.We performed a robust principal components
analysis (PCA) in a ternary compositional framework using the Rpackage rob-
Compositions43. A ‘robust’ PCA is similar to an ordinary PCA (that is, it is a method
of ordination and data simplification), but differs in that it is less sensitive to outliers,
thus increasing signal even in small sample sizes, which we justify due to the low
dimensionality. We note that use of eigenvectors from a classical PCA would not
alter the interpretation of results. ‘Ternary’ refers to the diagram utilized to represent
the data type (that is, composed of three terms). The ‘compositional framework’
refers to the fact that proportional data considered as a whole (a ‘composition’)
exhibit statistical properties that differs from classical measures due to the use of a
shared denominator. The raw data undergo a centre-log-transform to place them in
a new statistical ‘space’ before implementation of the robust PCA. We calculated the
angle between the observed eigenvectors and those predicted by the IC model and
the alternative null models, as well as the associated vector correlation (r
v
)and
Fisher-zscore (because correlations are not normally distributed). We tested the null
hypothesis that the observed-IC correlation was not higher than the observed-null
correlations by randomly generating null populations, calculating the associated
eigenvector and then calculating the number of times the observed-null z-score
exceeded that of the observed-IC using Monte Carlo simulation (10,000 bootstrap
replicates)44 implemented as a custom algorithm in R39.
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Acknowledgements
B. Hallgrı
´msson, R.F. Johnston, C. Rolian and M. Rose kindly provided access to pre-
viously published data used in this paper. The Kyoto University Primate Research Institute
provided computed-tomography scans of primate vertebral columns. The Museum of
Comparative Zoology at Harvard University and the British Museum of Natural History
provided specimens for radiographs. G. Wagner and J. Jernvall commented on the
manuscript. This research was funded in part by the Alberta Ingenuity Fund Grant
#200300516 (N.M.Y.) and the University of Massachusetts Dartmouth (K.K.).
Author contributions
N.M.Y. and K.K. conceived the project. S.T., B.W. and K.K. performed the experiments.
N.M.Y., S.T., B.W. and K.K. collected the data. N.M.Y. and K.K. performed all analyses
and wrote the paper.
Additional information
Supplementary Information accompanies this paper at http://www.nature.com/
naturecommunications
Competing financial interests: There are no competing financial interests.
Reprints and permission information is available online at http://npg.nature.com/
reprintsandpermissions/
How to cite this article: Young, N. M. et al. Shared rules of development predict patterns
of evolution in vertebrate segmentation. Nat. Commun. 6:6690 doi: 10.1038/
ncomms7690 (2015).
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... The inhibitory cascade model (ICM) proposes a developmental and genetic link underlying this suite of traits (Kavanagh et al. 2007). Under the strict form of the ICM as well as proposed modifications to the model, molar crown size proportions are related by the self-regulation of activator and inhibitor molecules influencing the final size of sequentially developing tooth germs, resulting in a mesiodistal trade-off in size (Kavanagh et al. 2007;Young et al. 2015). ...
... 3. How sensitive are estimates of the mean and error to changes in sample size? 4. Does the use of composite molar rows instead of complete molar rows change the estimated amount of variation or mean ratio for a species or population? Answers to these questions will help guide future research of covarying morphotypes, such as better understanding how well the ICM functions as a line of least resistance (Schluter 1996;Young et al. 2015). If the model meets the expectations of lines of least resistance, it may serve as a framework for connecting evolutionary observations at a microevolutionary (within species) scale to those at a macroevolutionary (between species or clades) scale. ...
... In its most specifically developed form, the ICM predicts the results of a relationship between activator and inhibitor where the effect of activator and inhibitor relative to each other is constant (Kavanagh et al. 2007;Young et al. 2015). That constant is summarized by the ratio of M2 crown size relative to that of M1 (ibid.). ...
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Mammalian molar crowns form a module in which measurements of size for individual teeth within a toothrow covary with one another. Molar crown size covariation is proposed to fit the inhibitory cascade model (ICM) or its variant the molar module cascade model (MMC), but the inability of the former model to fit across biological scales is a concern in the few cases where it has been tested in Primates. The ICM has thus far failed to explain patterns of intraspecific variation, an intermediate biological scale, even though it explains patterns at both smaller organ-level and larger between-species biological scales. Studies of this topic in a much broader range of taxa are needed, but the properties of a sample appropriate for testing the ICM at the intraspecific level are unclear. Here, we assess intraspecific variation in relative molar sizes of the cotton mouse, Peromyscus gossypinus, to further test the inhibitory cascade model and to develop recommendations for appropriate sampling protocols in future intraspecific studies of molar size variation across Mammalia. To develop these recommendations, we model the sensitivity of estimates of molar ratios to sample size and simulate the use of composite molar rows when complete ones are unavailable. Similar to past studies on primates, our results show that intraspecific variance structure of molar ratios within the rodent P. gossypinus does not meet predictions of the ICM or MMC. When we extend these analyses to include the MMC, one model does not fit observed patterns of variation better than the other. Standing variation in molar size ratios is relatively constant across mammalian samples containing all three molars. In future studies, analyzing average ratio values will require relatively small minimum sample sizes of 2 or more complete molar rows. Even composite-based estimates from four or more specimens per tooth position can accurately estimate mean molar ratios. Analyzing variance structure will require relatively large sample sizes of at least 40-50 complete specimens, and composite molar rows cannot accurately reconstruct variance structure of ratios in a sample. Based on these results we propose guidelines for intraspecific studies of molar size covariation. In particular, we note that the suitability of composite specimens for averaging mean molar ratios is promising for the inclusion of isolated molars and incomplete molar rows from the fossil record in future studies of the evolution of molar modules, as long as variance structure is not a key component of such studies.
... The discovery of general models and mechanisms that create the phenotypes of organisms is a major goal of evolutionary developmental biology [1][2][3][4][5]. Very few such fundamental growth patterns exist, including logarithmic spiral growth [6,7]. ...
... 0000C1206) [52] where permitted by institutions/individuals. 3 School of Mathematical Sciences, Monash University, Melbourne, Victoria 3800, Australia. 4 Biomedicine Discovery Institute, Monash University, Melbourne, Victoria 3800, Australia. ...
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Background A major goal of evolutionary developmental biology is to discover general models and mechanisms that create the phenotypes of organisms. However, universal models of such fundamental growth and form are rare, presumably due to the limited number of physical laws and biological processes that influence growth. One such model is the logarithmic spiral, which has been purported to explain the growth of biological structures such as teeth, claws, horns, and beaks. However, the logarithmic spiral only describes the path of the structure through space, and cannot generate these shapes. Results Here we show a new universal model based on a power law between the radius of the structure and its length, which generates a shape called a ‘power cone’. We describe the underlying ‘power cascade’ model that explains the extreme diversity of tooth shapes in vertebrates, including humans, mammoths, sabre-toothed cats, tyrannosaurs and giant megalodon sharks. This model can be used to predict the age of mammals with ever-growing teeth, including elephants and rodents. We view this as the third general model of tooth development, along with the patterning cascade model for cusp number and spacing, and the inhibitory cascade model that predicts relative tooth size. Beyond the dentition, this new model also describes the growth of claws, horns, antlers and beaks of vertebrates, as well as the fangs and shells of invertebrates, and thorns and prickles of plants. Conclusions The power cone is generated when the radial power growth rate is unequal to the length power growth rate. The power cascade model operates independently of the logarithmic spiral and is present throughout diverse biological systems. The power cascade provides a mechanistic basis for the generation of these pointed structures across the tree of life.
... Frequently, this variation is nonrandom. For example, in developmental processes that proceed segmentally along an axis, such as limbs and vertebrae, it has been demonstrated that an element's position in the developmental sequence can impact its phenotypic (and inferred genetic) variation (Young et al. 2015). Traits with more genetic variation are expected to evolve at a faster rate (i.e., be more "evolvable") than those with less variation (Wagner 1988), which suggests that developmentally biased variation could impact rates of evolution at a macroevolutionary scale. ...
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... Such a feature is not noted in mesosaurs, in which, conversely, the lack of independence among metatarsals and phalanges suggests that there might be a strong developmental linkage between the formation of successive phalanges in a growing digit, where there is a dramatic decrease in size from phalanx to phalanx (Eble et al. 2005;Kavanagh et al. 2013;Young et al. 2015). This pattern involves a low degree of differentiation/parcellation of existing elements, probably associated with an ancestral evolutionary pattern (Piñeiro et al. 2016). ...
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... Like other teeth, molars are serially repeated organs. Together with limbs, vertebrae, and phalanges, they constitute segmental series of the body whose proportions may be governed by similar developmental rules (Kavanagh et al. 2007; Green and Sharpe 2015;Young et al. 2015). The size of a given segment within these series tends to covary with that of adjacent segments, as proposed by the Inhibitory Cascade (IC) model for lower molars in mice (Kavanagh et al. 2007). ...
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