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J.
Zool.,
Lond.
(1977)
183,
527-539
A
unity underlying the different zebra striping patterns
JONATHAN
B.
L.
BARD
Medical Research Council, Clinical and Population dytogenetics
Unit,
Western General Hospital, drewe Road, Edinburgh
(Accepted
12
April
1977)
(With
3
plates and
2
figures in the text)
Toelucidate the relationship between the complex striping patterns of the different species
of
zebras, a simple conceptual experiment has been performed. Using data from horse embryos,
the normal growth of the zebra from early foetus to adult has been reversed to see what
happens both to the spacing and to the orientation
of
the stripes. It turns out that for each
species, there is a point in time when
all
the body stripes would have been perpendicular to
the dorsal line and equally spaced. Moreover the spacing is roughly the same
(0.4
mm) for
the three main species of zebra at this time.
This
point is during the third week of develop-
ment for
E.
burchelli,
fourth week for
E.
zebra
and fifth week for
E.
grevyi.
As
striping only
appears at about the eighth month of foetal development, it seems that the pattern is
determined a long time before the cells actually lay
down
pigment. Further analysis of the
pattern
so
laid down
on
a rapidly-growing foetus shows how shadow and gridiron stripes
can arise. The reason why leg stripes are orthogonal to body stripes cannot however be
derived from this phenomenological approach. These results suggest that a single mech-
anism generating equi-spaced stripes of separation
0.4
mm could lay down the body stripes
of
zebras and that species differences arise from pattern formation occurring at different
times in embryogenesis.
Contents
introduction and hypotheses
Zebra patterns
....
Equine embryology
..
Matching and mapping
. .
Further features of pattern
Discussion
......
Summary
......
References
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Page
527
528
53
1
533
535
537
538
538
Introduction
and
hypotheses
There are three extant and one extinct species
of
zebra,
E.
burchelli,
E.
zebra,
E.
grevyi
and
E.
quagga
respectively ((Plate I(a)-(d)), Ewart (1899)
;
Allen (1909)
;
Ridgeway (1909)
;
Rau (1974); Short (1975)). There are differences in striping patterns among species,
subspecies, individuals and even between the two sides
of
a single zebra (Ewart, 1899;
Cabrera,
1936).
Moreover, stripe widths vary greatly on any one animal. Nothing is
known
of
the mechanisms by which this diversity
of
stripes is laid down in the foetus nor
of
when such
a
mechanism operates.
It
is, however, likely that the same underlying
pattern-formation system is
at
work in all zebra embryos. First, there is considerable
variation within a species and the patterns
of
E.
zebra,
E.
burchelli
and
E.
quagga
(Ewart,
527
528
J.
B.
L.
BARD
1899; Cabrera, 1936) can be seen as nearly-over-lapping regions on
a
continuum. Second,
horse-zebra hybrid patterns are often uncharacteristic of the zebra parent. For example
“Romulus” (Plate I(f)), Ewart’s
E.
burcheZZi-pony hybrid (1899) has a striping pattern
intermediate between that of
E.
zebra and
E.
grevyi.
In the belief that the same striping mechanism does generate all zebra patterns, this
paper puts forward one set of hypotheses that shows how the different patterns could
arise from a common mechanism, and makes
a
testable prediction as to how the species
differences arise. The hypotheses are: that there is in
all
zebra embryos a single pattern-
forming mechanism that generates stripes of uniform separation normal to the dorsal
line, that different patterns in the four species are produced by the operation of this
system during different temporal windows in embryogenesis, and that the range of stripe
separations seen on a single animal comes from differential growth in the foetus after the
stripes are laid down.
If this framework is correct, one may predict that there will be a point in embryogenesis
for each species when laying down equidistant stripes will, following normal growth,
produce the appropriate adult pattern. To test this prediction, we should like to study the
stripes on zebra embryos. There are two problems here: first, although overt striping
appears at around eight months (Plate l(e)), it is likely, for reasons given later, that stripe
determination occurs within the first two months of development. Thus direct investigation
of initial striping
is
impossible. Second, the only published observations on equine embryo-
logy have been on horse foetuses. If, however, we assume that there are no relevant differ-
ences between horse and zebra embryogenesis we can make use of studies
of
normal horse
development (Martin, 1890; Ewart, 1897; Stoss, 1940; Zeitchmann
&
Krolling, 1955;
Douglas
&
Ginther, 1975; Van Niekerk
&
Allen, 1975). Before discussing these, however,
I
will
describe zebra patterns in more detail.
Zebra patterns
The basic features of zebra stripes are determined
by
inspection (Plates I and 11). The
hair pattern appears as black stripes on
a
white background (the belly and unstriped leg
regions are white). The width of the stripes varies, being wide on the neck and narrow on
the head. The dorsal line of the animal from the forehead to the tail is the axis for such
symmetry as exists (Plate II(a)-(c)). From the mane to the tail this line
is
seen as the
dorsal stripe. From
this
axis, stripes extend ventrally except over the nose, where they are
drawn foreward to the nostrils, and around the rump where each species has
a
character-
istic pattern. Stripes stop at the belly and bifurcate above the forelegs (the shoulder stripe).
On
the legs, transverse bands are seen that may run around the leg, be incomplete or may
bifurcate. Neck stripes end on the central midline where they may or may not merge. The
striping pattern around the eye and lower jaw is complex. Ear stripes tend to be transverse
or blotchy rather than extend from the dorsal line. Tail stripes are diffuse (mainly due to
the long hairs) but are also transverse on all species.
The main differences between the species are in stripe number (Table I) and in rump
patterns. On
E.
grevyi, narrow haunch stripes are normal to the dorsal stripe and extend to
the thin, transverse leg stripes where they bend away to form
a
triradius (Plate II(a)).
E.
zebra has three wide, transverse, thigh bands. From its dorsal stripe thin “gridiron”
stripes extend to the top transverse band (Plate II(b)).
E.
burcheZZi sometimes has
P
PLATE
I.
(a)
E.
grevyi,
the Imperial zebra (photograph courtesy
of
Dr D. Mollison). (b)
E.
zebra,
the Mountain zebra (stuffed skin at
British Museum (Natural History)). (c)
E.
burchelli,
the Common zebra. This zebra, named “Matopo”, was the sire
of
the hybrid “Romulus”
(Plate
I(f)).
(d)
E.
quagga,
The Quagga (the drawing of Agasse (reversed); by kind permission
of
the President and Council
of
the Royal
College
of
Surgeons of England). (e) The head
of
a
whole zebra foetus preserved in spirits at the British Museum (Natural History). Note that
the body stripes are weak and only partially formed but that the mane (and also the unshown tail) hairs are clearly pigmented. This
embryo weighs
7
kg giving it an age of about 8 months (King, 1965). (Insert) An
E.
burchelli
head
(R.
Scottish Museum) showing that neck
stripes may meet
on
the ventral surface and that the ear stripes can be parallel to the dorsal line.
(f)
A
pony-E.
burchelli
hybrid “Romulus”
(Ewart, 1899). Note that the pattern is more similar to
E.
zebra
(Plate Xb)), than to its sire “Matopo” (Fig. l(c)). “Romulus” does, however,
have traces of shadow stripes on its haunch.
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530
J.
B.
L.
BARD
PLATE
11.
A DEVELOPMENTAL BASIS
FOR
ZEBRA
STRIPING
processes are now initiated: first, the
nose
starts to extend; second, the neck stretches,
presumably as the cervical vertebrae grow; third, the tail shortens relative to the rest of
the body as its anterior part appears to regress into the rump. From the fifth to eighth
week, the limbs lengthen, the haunch increases in width and the relative size of the head
decreases. By the end of the eighth week, the embryo is recognizable as a horse.
533
100
-
-
E
10-
-
I
2
4
6
8
Weeks
FIG.
1. A
graph showing how the length of the embryo and the limb buds increase with time. The data points are
measured from the embryos shown
in
Plate
I11
together with the
18
day embryos
of
Stoss
(1940).
The length
measured is not the normal distance from crown'to rump but the length
on
the dorsal surface from the fore-brain
to the end of the tail. This is the distance over which stripes would be expected
to
form (Fig.
2).
The only undated
embryo is that of Zeitchmann
&
Krolling
(1955)
and its position is marked with error bars.
Matching and mapping
In the light of the earlier hypothesis, suppose that the stripes, when they first form, are
all roughly the same width and are normal to the dorsal line. We can then look for
a
stage when each species, were it to reverse normal growth, would have equally-spaced
stripes at right angles to the dorsal line. If this is possible, it will give the time of develop-
ment when
a
pattern-forming process having such properties could generate adult patterns.
It is clear that, were stripes originally equispaced, wide stripes on the adult would originate
in areas of the embryo which later expand relative to the whole, and that narrow adult
stripes would first form on regions of the embryo that were relatively large.
Having thus dated stripe initiation for each species, we can then use the length of the
embryo and the appropriate number of adult stripes to calculate the mean stripe separation
on the embryo. In determining the appropriate number of stripes, we will exclude shadow,
534
J.
B. L.
BARD
gridiron and pseudo-gridiron stripes. The reason for this, as will be shown later, is that
they probably form after the main stripes.
Consider, first,
E.
grevyi
with its wide neck stripes, numerous fine rump stripes and thin
nose stripes drawn down
to
the nostrils. Contracting the neck stripes requires going
back to a point before the seventh week when the neck expands. Regularizing the nose
stripes demand returning to the fifth week when the nose extends. Expanding the
rump
FIG.
2.
Hypothetical striping prepatterns. (a) a tracing of a
21
day embryo with stripes
of
separation
0.4
mm on
the dorsal surface
(8
x).
(b)a tracing of an embryo aged approximately 3tweeks with stripes of separation 0.4mm.
Note that the posterior stripe is drawn as a caudal stripe. It is postulated that tail-bud extension after the stripe was
laid down is responsible for this anomalous stripe orientation
(8
x).(c) a tracing of
a
5
week embryo with equally-
spaced stripes
0.4
mm apart
(4
x).
(ai) The effect of 34 days growth
on
striping laid down by 21 days (Fig. 2(a));
note that the anterior stripes merely broaden while the back few stripes are dragged posteriorly by tail-bud
expansion. (aii) The effect
of
2 weeks growth on stripes laid down by
3
weeks (Fig. 2(a)). Note that the number
of stripes in each area
of
the body corresponds
to
the pattern on
E.
burehelli
while the pattern
of
stripes laid down
at
5
weeks (Fig. 2(c)) is much more characteristic
of
E.
grevyi.
The
3
week embryo is that
of
Ewart
(1915,
Fig.
8)
and the5 week embryo that
of
Ewart
(1897);
the intermediate embryo
is
that of Zeitzchmann Krolling
(1955).
This last embryo (b, ai) was undated and is about
4
mm shorter than its degree of development would suggest
(Fig.
1).
Consequently, there is room
for
only
34
stripes rather than the predicted
43.
I
have assumed that the drawn
scale on the original photograph is correct and that the specimen was unfixed. Were either
of
these assumptions
wrong, the embryo might well have its expected length
of
18-19
mm.
stripes to be proportionate takes
us
back to the fifth week when the tail is at its largest
relative to the rest of the body. At this point the fine stripes behind the triradius dis-
continuity on the haunch will come normally
off
the dorsal line. Stripe initiation much
earlier than the 5th week
is
excluded as there is little tail area over which equispaced stripes
can be laid down. The length of the embryo in the middle of the fifth week
is
about
32
mm;
E.
grevyi
has around
80
stripes. The initial stripe repeat is thus
of
the order of
400
pm
(Fig. 2(c)).
A
DEVELOPMENTAL BASIS
FOR
ZEBRA STRIPING
535
Next, consider
E.
zebra
which has
a
pattern similar to that of
E.
grevyi
except on the
rump where there is
a
gridiron and on the haunch where there are three broad stripes. The
relatively small number of rump stripes (if the gridiron is excluded) requires going back in
time to at least the fourth week when tail-bud expansion is at around the level of the hind
limb. This contraction will cause the caudal stripe to spread normally from the dorsal line.
Reversing limb growth to this time implies that the three large, haunch stripes on the
adult will contract to form normal-sized transverse stripes on the bud. The
34
week
embryo is about
14-19
mrn
long (see Plate 111, Fig.
1)
and
E.
zebra
has (excluding the
gridiron) around
43
stripes (Table I). The initial stripe repeat is thus
3401140
pm.
Finally consider
E.
burchelli
where the few, broad caudal stripes start at the centre
of
the belly. To account for this it is necessary to go back to the third week when the body is
extending. If the dorsal surface extends faster than the ventral surface, stripes that are
initially normal to the dorsal line
will
be pulled caudally. This suggests that, if equidistant
stripes are laid down on the embryo, the process occurs at around three weeks when the
embryo is
11
mm long. The adult
E.
burchelli
has
25-30
stripes again giving a mean separa-
tion on the embryo of around
400
pm (Table
I,
Fig. 2(a)).
The striping
on
E.
quagga
is
clearly
a
degenerate case of
E.
burchelli
as the head and neck
markings are similar in the two species. The absence of stripes on the limbs and on the
back half of the Quagga implies either that the striping mechanism operates for
a
short time
or that only the head and shoulders are competent for stripe formation.
To summarize, it appears possible to run the normal course of development backwards
to
a
different time for each species when all the body stripes could be normal to the dorsal
line. On each species, the presumptive stripes seem
to
be equispaced and to have
a
repeat
of
about
400
pm
(-20
cell diameters).
Further features
of
pattern
In the previous section, shadow and gridiron stripes were excluded from the calculation
of mean stripe separation as it was suggested that they formed after the main stripes. The
reasons for this suggestion emerge when one combines the geometric analysis with
a
consideration of how the growth of the embryo affects stripe formation. To do this it
is
necessary
to
make two assumptions about the
way
that the striping mechanism works:
first, that the tissue remains competent for a period longer than that required for stripe
determination, and, second, that stripes will form at some position if the local intensity of
the determining factor there exceeds some threshold.
Shadow
stripes
Consider a region of tissue which is partially determined: dark stripes are laid down but
light regions maintain competence. Assume, moreover, that there
is
a
natural spacing or
wavelength between dark stripes. Were growth of the embryo to increase stripe spacing
much beyond this wavelength, then a new peak of determination in the centre of the now-
large white stripe would be expected to arise. The area
of
the caudal stripes of
E.
burchelli
undergo just such growth; shadow stripes tend to be found between them. The further
apart growth forced the dark stripes, the further above threshold would be this peak and
the wider the intermediate stripe (Plate II(e)).
This explanation does not predict that
a
new stripe will be a “shadow” (i.e. lighter than
536
J.
B. L.
BARD
a normal dark stripe). There are two plausible explanations. First, significant growth may
occur towards the end of competence
so
that only some of the “white” cells can respond
to the new instruction. Second, the intermediate peak, when it forms, may be too near the
switching threshold
to
activate all cells. The fact that wider shadow stripes are darker than
narrow ones (Plate 2(e)) argues for the second alternative.
Gridiron stripes
We may examine gridiron and pseudo-gridiron stripes in the light of the growth that
occurs on the dorsal surface during the third to fifth week if we assume that new dorsal
tissue maintains competence. Suppose that dorsal growth takes the form of a wave of
mitosis moving caudally, causing the embryo to curl and ultimately generating the tail.
We now distinguish between two situations: stripe formation at some point occurring
before the wave passes that point and pattern formation occurring afterwards. In the first
case, growth will pull the extant stripes caudally leaving an unstriped gap (Fig. 2(ai), (aii))
still competent to generate new stripes that will fill this empty fan-shaped region between
dorsal-ventral and caudal stripes. If pattern formation occurs early, when the wave is in
the centre of the back, the pseudo-gridiron of
E.
burchelli
is formed (Plate II(a)).
If
the
wave has reached the hind limb-bud region
(3i
weeks) before pattern formation occurs
then the gridiron of
E.
zebra
will form (Plate II(b)). Such gridiron stripes were thus
excluded from earlier calculations as they were considered secondary stripes formed after
the original pattern.
In contrast, consider pattern formation occurring after the wave of growth has passed:
all the stripes will be normal to the dorsal line and there will be no caudal stripes. This
appears
to
be the case in
E.
grevyi
(Plate II(a)). Growth that occurs after competence will
merely widen extant stripes. In this regard compare
E.
zebra
and the
E.
burchelli-pony
hybrid (Plate I(b), (f)). Both have wide haunch stripes but the hybrid has traces of shadow
stripes whereas the mountain zebra does not. This difference could be explained
by
positing a shorter determination time in
E.
zebra
than in
E.
burchelli.
Hybrid patterns
Hybrids tend to have more stripes than their zebra parent, for example horse-E.
grevyi
hybrids have more than
100
stripes (Rzknicki,
1396).
The coat is often bay with dark
brown stripes which may
be
ill-defined. Where there is an
E.
burchelli
parent, the hybrid
pattern tends to be characteristic of the mountain zebra (see Ewart
(1899)
and Plate l(f)).
These differences would be expected if striping began later in the hybrid than in the
zebra parent, and if the same mechanism generated stripes on tissue now only partially
competent.
Leg patterns
The one aspect of zebra striping for which no explanation can be put forward is the
transverse striping on the legs: no plastic transformation can make these stripes normal
to the dorsal stripe. The reasons for this change in orientation are unknown, but there are
at least three possibilities: first, there is some axis on the leg that corresponds to the
dorsal stripe; second, the pattern-forming system on the leg is different from that on
the head and body; third, the geometrical differences between the cylindrical leg and
the planar flank makes the pattern mechanism generate transverse stripes.
A
DEVELOPMENTAL BASIS
FOR
ZEBRA
STRIPING
Discussion
The main conclusion presented in this paper
is
that the diverse striping patterns in the
various zebra species can be simply explained. One has to hypothesize, first, that there
exists in all embryos a single mechanism capable of generating vertical stripes of separation
about 0.4 mm (-20 cell diameters) on the body that become horizontal bands on the leg
and, second, that this mechanism operates at different times in the different species.
A
geometric analysis shows that this period is during the third week of development for
E.
burchelli,
fourth week for
E. zebra
and fifth week for
E. gretyyi,
and thus demonstrates
a unity underlying the different adult patterns.
While this analysis is certainly the simplest that can account for the diversity of patterns
and requires relatively little of an underlying mechanism, it is possible that more complex
postulates would provide a better framework for considering striping. One might suggest,
for example, that the pattern of each species
is
originally laid down on the embryo in its
final, adult form. Now, however, not only are there very stringent demands on the under-
lying mechanism but it also becomes difficult to find
a
relationship between the different
species, to understand how hybrid patterns arise and
to
show how caudal stripes are
formed. Furthermore, such a framework gives no clue as to when determination of stripes
occurs in the different species.
The analysis given here, on the other hand suggests that pattern formation occurs
between three and five weeks after fertilization. In embryological development, this period
is between tail-bud extension and growth after the main anatomical features have been
formed.
It
is certainly some time after closure of the neural fold and likely to be well after
migration
of
the neural crest cells, the potential pigment-forming cells. By five weeks of
development, neural crest migration will have been completed for some time (by analogy
with chick and amphibian development; Weston, 1970). This suggests that the mechanism
for striping affects differentiation of melanoblasts rather than their migration. This
contrasts with the study of Twitty
(1945)
on the formation
of
the single anterior-posterior
stripe on the amphibian
Triturus torosus
but
is
in accord with the way in which pigment
cells in black and white barred chicken feathers become determined (Nickerson, 1944).
In this case melanoblasts from white regions
of
the feather can produce melanin when
removed from their normal environment. Unfortunately, determination in feathers occurs
as the growing rudiment passes through an inductive zone and therefore no further
insights into zebra striping can be obtained from this system.
The only experimental studies on mammalian stripe formation have been made on mice.
Here, clonal growth seems responsible for the relatively few large, diffuse body bands
(Mintz, 1971
;
Lyons, 1970; Wolpert
&
GingeI1, 1970) but the studies provide no due as
to how the range
of
zebra stripes form. In cat embryos, Goldschmidt (1938) and Toldt
(1912) noted that riges were present on cat embryos where stripes might later be expected.
They viewed “growth tensions” as the source
of
such
ridges but did not discuss how
growth might cause them
nor
when they would first
be
observed. In zebra stripe formation,
it seems likely that determination occurs at about three to five weeks of development while
the stripes themselves appear much later (Fig. l(e)). This means that only a pre-pattern is
laid down by the striping mechanism at this early stage.
The basis of the pattern-formation system still remains completely obscure. One
suggestion has been put forward by Searle (1968); he hypothesized that there could be a
chemical system whose concentration variation over the embryo would determine striping,
537
538
J.
B.
L. BARD
and he pointed to the potential of Turing mechanisms (Turing,
1952;
Bard
&
Lauder,
1974)
for generating such patterns. The demands that any mechanism put forward will
have to satisfy are, however, very strict. The theory will have to explain not only vertical
striping on the body and horizontal bands
on
the leg but also the formation of triradii and
branching as well as dorsal stripes, shadows and gridirons. It will also have to account
for the fact that no two zebras are identical and that spots may occasionally arise on
zebras (King,
1965)
and are frequently seen on hybrids (Ewart,
1899,
1900).
It would thus
be of use to know at least
a
little more about how the stripes are actually laid down in the
embryo.
While nothing is actually known about the process of pattern formation there are several
obvious possibilities: the stripes might just appear or spots might be generated on the
dorsal line and be extended by an inductive wave moving ventrally; alternatively, stripes
could be laid down, initially
at
the head, by a wave of competence moving posteriorly
generating stripes as it went. The methodology of this paper would only differentiate
between these and other options were a particular mechanism to make some geometric
prediction. For example, consider that a wave of striping moved posteriorly: if the stripes
were equally-spaced
when$rst
laid
down,
then, by the time a slow-moving wave had laid
down the tail stripes, the head could have grown and its stripes become wider. In this case,
reversing development
in
the manner of the earlier section would show this. It turns out,
in fact, that the embryonic data is just not good enough to make such distinctions and
therefore it has not been possible to obtain any information on how the stripes are laid
down.
In terms of the mechanistic
basis
of
pattern formation, however, the main result
of
this
paper is to give
a
set of necessary and possibly sufficient properties that the generating
mechanism must have. In another sense the morphological analysis shows that the problem
ofzebra striping is tractable. Were it not possible to show that body stripes could originally
have been equi-spaced then one would have had to look for a physico-chemical mechanism
that generated stripes whose spacing
on
even the flank was a function
of
embryological
time and anatomical position. Neither the geometry nor the development would impose
any constraints at all
on
the physico-chemical mechanism.
Summary
Analysis
of
zebra striping and equine embryo morphology shows how
a
single mechan-
ism forming stripes with
a
spacing of about
20
cells can,
by
operating at different times in
embryogenesis, generate the different zebra patterns. The analysis yields some properties
of the underlying striping mechanism.
I
thank Dr J. Jewel1 and Mr
A.
Redfern of
the
British
Museum (Natural History) and Dr
A.
Clarke of the Royal Scottish Museum for help with material and Mr Alexander Bruce
for
photo-
graphic assistance.
I
am grateful to Mr
G.
Mitchison, Mr
I.
Lauder and Dr
F.
Wasoff for
discussions and to Dr R.
V.
Short for information and for commenting on the paper. Finally
I
thank Ms
E.
G.
Bard for her critical reading
of
the manuscript.
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A.
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Mammals from British East Africa, collected
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Bull.
Am.
Mus.
nat.
Hist.
N.Y.
26:
147-175.
A DEVELOPMENTAL BASIS FOR ZEBRA STRIPING 539
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J.
B. L.
&
Lauder,
I.
(1974). How well does Turing’s theory
of
morphogenesis
work?
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theor. Biol.
45:
Cabrera, A. (1936). Subspecific and individual variation in the Burchell zebras.
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Mammal.
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89-1 12.
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H.
&
Ginther,
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(1975). Development
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