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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

½¼1þðaiÞ

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

½¼a

i

and s3

½¼2a

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

½¼ i

3a

,

s2

½¼1

3

, and s3

½¼2ai

3a

(see Methods)), the proximal and

distal segment proportions function as a tradeoff that accounts

for the remainder (that is, s

nþ2

¼1s

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

¼1.00 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

¼0.97 s

n

þ0.69, r2¼0.813, Po0.001; r¼0.063,

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

¼1.06 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 (t¼1.026, 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

¼1.24 s

1

þ0.67, r2¼0.45) and feral

groups (s

3

¼1.06 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

¼0.97 s

n

þ0.69, r2¼0.813, P¼0.000; r¼0.063, 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

¼1.01 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

¼1.00s

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

¼1.01s

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

¼1.05s

1

þ0.67, r2¼0.793, P¼0.000; digit: s

3

¼0.93s

1

þ0.65, r2¼0.671, P¼0.000) (Supplementary Fig. 4a–d), with

elevations statistically indistinguishable from the IC model (limb:

t¼0.035, 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 ¼1.08 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

¼0.91

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.

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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

½¼1þðaiÞ

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

½¼a

i

and s3

½¼2a

i1

, and proportions are s1

½¼ i

3a

,s2

½¼1

3

and s3

½¼2ai

3a

(ref. 14). Because s2

½¼1

3

, then s1

½þs3

½¼2

3

and

s3

½¼1s1

½þ2

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

½¼1þðaiÞ

i

hi

ðn1Þ

snþ1

½¼1þðaiÞ

i

hi

ðnÞ

snþ2

½¼1þðaiÞ

i

hi

ðnþ1Þ

In which case, total size of three consecutive segments is equivalent to:

sn

½þsnþ1

½þsnþ2

½¼1þðaiÞ

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

½þsnþ1

½þsnþ2

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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