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The distribution of seafloor ages determines fundamental characteristics of Earth such as sea level, ocean chemistry, tectonic forces, and heat loss from the mantle. The present-day distribution suggests that subduction affects lithosphere of all ages, but this is at odds with the theory of thermal convection that predicts that subduction should happen once a critical age has been reached. We used spherical models of mantle convection to show that plate-like behavior and continents cause the seafloor area-age distribution to be representative of present-day Earth. The distribution varies in time with the creation and destruction of new plate boundaries. Our simulations suggest that the ocean floor production rate previously reached peaks that were twice the present-day value.
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DOI: 10.1126/science.1219120
, 335 (2012);336 Science et al.N. Coltice
Floor
Dynamic Causes of the Relation Between Area and Age of the Ocean
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(where ris the dislocation density) for the hot-
pressed and the compressively deformed specimens
for the representative 12- and 101-s oscillation
periods, which intercept the Q
1
axis at ~ 0.035
and 0.07 respectively, reflect contributions from
intergranular relaxation processes, such as grain-
boundary sliding, in the fine-grained (3 to 6 mm)
polycrystalline olivines of this study. The additional
dissipation, attributable to dislocation damping, was
approximately Q
1
= 0.024 × r(mm
2
) at a 101-s
period for the compressively pre-deformed mate-
rials. Thus, dislocation damping may account for
about 25% of the dissipation measured in the fine-
grained (3.1 mm) hot-pressed specimen 6585.
In order to assess the relative contributions of
these two dissipation mechanisms for the larger
grain sizes expected of Earths mantle, we used
the previously mentioned JF model (16), describ-
ing the behavior of undeformed, essentially dry
and melt-free polycrystalline olivine (including
H6585), of average dislocation density ~0.1 mm
2
.
This model, evaluated under laboratory conditions
of 0.2 GPa and 1100°C and at the experimental
periods near 12 and 101 s for representative upper-
mantle grain sizes of 1 and 10 mm, yields values
of Q
1
between 0.0065 and 0.0115 (Fig. 3, inset).
Such dissipation is largely due to intergranular re-
laxation rather than dislocation damping. For com-
pressively pre-deformed olivine tested at a 101-s
period, comparable levels of dissipation would
be expected from dislocation damping alone for
upper-mantle dislocation densities of 0.3 to
0.5 mm
2
. The torsionally pre-deformed speci-
men (T0436) of the present study, with a popula-
tion of dislocations similarly favorably oriented for
glide, displayed much higher levels of dislocation
damping than did compressively pre-deformed
materials of comparable dislocation density. We
conclude therefore that dislocation damping asso-
ciated with typical upper-mantle dislocation den-
sities (~0.01 to 0.1 mm
2
)(10,23) may contribute
comparably with grain-boundaryrelated dissipa-
tion (with associated shear wave dispersion), es-
pecially in regions of Earths upper mantle that
are subject to relatively high prevailing (or fossil)
deviatoric stress sand consequently high dis-
location density (11), and for shear waves with
propagation/polarization directions that provide
high resolved shear stress for dislocation glide.
Deformation in and beneath the oceanic litho-
sphere spreading away from a mid-ocean ridge in-
volves simple shear in the vertical plane parallel
to the spreading direction. This shear, if accom-
plished by glide on the dominant [100](010) slip
system of olivine, will tend to result in rotation
of the (010) planes of individual olivine crystals
toward the horizontal so that [100] is preferen-
tially aligned with the spreading direction. A
crystallographic preferred orientation of this type,
commonly measured in mantle xenoliths, provides
the accepted explanation of the azimuthal anisot-
ropy of compressional (P
n
) wave speed (6,24,25).
This fabric provides favorable average V
SH
>V
SV
(V
SH
, shear wave velocity with horizontal polar-
ization; V
SV
, shear wave velocity with vertical
polarization) in transversely isotropic seismolog-
ical wave speed models (26) that account for the
discrepancy between Rayleigh and Love surface
wave velocities (27). This fabric offers optimal av-
erage resolved shear stress for [100](010) dislo-
cation glide for the geometry of the simple shear
stress field controlling ongoing tectonic deforma-
tion beneath the oceanic plate. The same stress
field applies to vertically travelling shear waves
polarized parallel to the direction of plate motion
direction. Accordingly, we predict that these seis-
mic waves should be most strongly attenuated by
dislocation glide in the suboceanic mantle.
Our data demonstrate that strain-energy dis-
sipation (and shear modulus dispersion) associ-
ated with grain-boundary relaxation phenomena
are augmented by the effects of dislocation re-
laxation. The relaxation strength is expected to
vary linearly with the dislocation density, and in
turn with the magnitude of the fossil/prevailing
stress field as rºs
2
(11). However, only in rel-
atively cool parts of the lithosphere is a high dislo-
cation density, reflecting a high fossil stress, likely
to survive the process of static dislocation recovery.
Under these circumstances, the relevant tectonic
settings of high potential for dislocation damping
will be regions in the lower lithosphere and as-
thenosphere, where olivine is or was deformed via
(steady-state) dislocation creep. These regions in-
clude suboceanic mantle, deep-lithosphere shear
zones, and the material immediately above and
beneath an actively subducting slab.
References and Notes
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Acknowledgments: We thank H. Kokkonen, C. Saint, H. Miller,
and F. Brink for experimental help and D. Kohlstedt for
allowing us to use his laboratory at the University of
Minnesota. The Australian government (an Endeavor
International Postgraduate Research Scholarship), a Mervyn
and Katalin Paterson Fellowship (Research School of Earth
SciencesAustralian National University), and NASA grant
NNX11AF58G supported this work. We thank three anonymous
reviewers for helping to improve the manuscript. The raw data
are available in the supplementary materials.
Supplementary Materials
www.sciencemag.org/cgi/content/full/336/6079/332/DC1
Materials and Methods
Figs. S1 to S4
Databases S1 to S5
References (2937)
22 December 2011; accepted 20 March 2012
10.1126/science.1218318
Dynamic Causes of the Relation Between
Area and Age of the Ocean Floor
N. Coltice,
1,2
*T. Rolf,
3
P. J. Tackley,
3
S. Labrosse
1,2
The distribution of seafloor ages determines fundamental characteristics of Earth such as sea
level, ocean chemistry, tectonic forces, and heat loss from the mantle. The present-day distribution
suggests that subduction affects lithosphere of all ages, but this is at odds with the theory of thermal
convection that predicts that subduction should happen once a critical age has been reached. We used
spherical models of mantle convection to show that plate-like behavior and continents cause the
seafloor area-age distribution to be representative of present-day Earth. The distribution varies in time
with the creation and destruction of new plate boundaries. Our simulations suggest that the ocean
floor production rate previously reached peaks that were twice the present-day value.
The distribution of ages of the ocean floor is
a first-order observation that determines
the evolution of Earths surface and inte-
rior (1). Because heat flow and bathymetry direct-
ly depend on the age of the ocean floor (2), a shift
in the area-age distribution profoundly modifies
Earths cooling (3), sea level (4,5), and conse-
quently global climate (6,7). The characterization
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of the age of the ocean floor has shown that its
present-day area per unit age decreases roughly
linearly with increasing age (8,9), defining a
function triangular in shape (Fig. 1A) for which a
common expression is
dAðtÞ
dt ¼C01
t
tmax
ð1Þ
where A(t) is the area of ocean floor that is
younger than age t,C
0
is the rate of generation
of new ocean floor, and t
max
is the age of the
oldest seafloor [where present-day C
0
and t
max
are 3.01 km
2
year
1
and 180 million years (My),
respectively, and C
0
(t
max
/2) is the total oceanic
surface].
If such a distribution were to define a steady
state, it would result from a constant production
of ocean floor for the past 180 My combined with
a consumption of seafloor, with a probability in-
dependent of its age (1,10). However, an evolv-
ing crustal production could explain the variance
of the data equally well (11) and one-dimensional
(1D) models provide a good fit to the present-day
observations as long as spreading rates have varied
(12). Indeed, seafloor spreading reconstructions
have shown variations of ocean floor production,
essentially through creation of mid-ocean ridges
after the breakup of Pangea (1315). As a conse-
quence, the distribution has differed from the
triangular shape we observe today (12,15).
The dynamic origin of the area-age distribu-
tion is a subject of debate, because subduction of
young and buoyant seafloor seems at odds with
the principles of convection that predict insta-
bilities of the top boundary layer occurring for
old and cooled material only. Continents may
geometrically impose subduction of seafloor in-
dependently of the age (3), but other mechanisms
could also reduce the dependence of subduction
on seafloor age. Most of them involve rheolog-
ical complexities of plates such as plate bending
(16) and dehydration stiffening (17). However,
simulations of mantle convection have never pre-
dicted any consistent triangular area-age distri-
bution, thereby failing to satisfy an elementary
geological constraint on mantle dynamics.
We performed 3D spherical mantle convec-
tion simulations introducing minimal complexity
to study the causes of the triangular area-age
distributions (18). In the following models, we
varied the number of continents (for a constant
surface fraction of 30%) and the rheology (iso-
viscous or inducing plate-like behavior). In these
simulations, we calculated synthetic ages for the
ocean floor from the computed local heat flow by
means of the half-space cooling approximation
(18), which is a very good approximation for a
mantle convection model (3). However, the synthet-
1
Laboratoire de Géologie de Lyon, Université Lyon 1; Ecole
Normale Supérieure de Lyon; Université de Lyon; CNRS, 69100
Villeurbanne, France.
2
Institut Universitaire de France.
3
In-
stitute of Geophysics, ETH Zürich, 8092 Zürich, Switzerland.
*To whom correspondence should be addressed. E-mail:
nicolas.coltice@univ-lyon1.fr
0 40 80 120 160 200
Age (Ma)
0
1
2
3
4
5
6
Area per unit age (km2 yr-1)
40 80 120 160 200
Age (Ma)
0
5
10
15
20
Plates
Continent
40 80 120 160 200
Age (Ma)
0
1
2
3
4
5
6
6 continents
6 continents
3 continents
1 continent
+plumes
ABC
Fig. 1. (A) Distribution of area versus age (Ma, millions of years ago) of the ocean floor on the present-day
Earth from (9). (B) Time-averaged distribution computed in 3D spherical simulations implementing
continents (red) or plate-like behavior (black) over 5 billion years. (C) Time-averaged distribution computed
in 3D spherical simulations implementing continents (their cumulative area is 30% of the total) and plate-
like behavior. The model with plumes (purple) has 15% of core heating generating hot plumes. The straight
dashed line in each panel represents the best triangular fit for the present-day distribution. The error bars
show the standard deviation of the distribution.
0306090120150
Area-age distributions Isochron maps
0 40 80 120 160 200
A
g
e (Ma)
0
1
2
3
4
5
6
7
0 40 80 120 160 200
Age (Ma)
0
1
2
3
0 40 80 120 160 200
Age (Ma)
0
1
2
3
4
AB
CD
EF
Area per unit age (km2 yr-1)Area per unit age (km2 yr-1)Area per unit age (km2 yr-1)
Fig. 2. Snapshots of the distribution of the area versus age of the ocean floor along with the cor-
responding best triangular fit in dashed lines (left) and maps of synthetic isochrons (right) computed in
the 3D spherical convection models. The gray areas on the maps represent the continents, the white lines
are the positions of the downwellings, and the age contours are plotted at 10-My intervals. (Aand B)An
example corresponding to a triangular distribution (with three continents covering respectively 15%,
10%, and 5% of the surface). (Cand D) An example for a flat distribution (one supercontinent). (Eand F)
An example for a skewed distribution (six continents covering 5% of the surface each).
20 APRIL 2012 VOL 336 SCIENCE www.sciencemag.org
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ic ages can be biased in regions of downwellings
and in diffuse zones of extension or compression
where heat transport is more complex.
Convection simulations integrated over 5 bil-
lion years generated time-averaged distributions
of the area versus synthetic age of ocean floor.
For the model with six continents (each covering
5% of the surface area) but without plate-like
behavior (i.e., the viscosity is constant for each
material), the synthetic area-age distribution is
not triangular but the area decreases with age
faster than exponentially (Fig. 1B). As previously
observed, this is typical of internally heated con-
vection (3,19). The area-age distribution for the
model without continents but with plate-like be-
havior is also not triangular (Fig. 1B); it displays
a skewed plateau. The plateau expresses the fact
that young and hot material is not entrained in
subduction and only the lithosphere that has
reached a certain age (here, around 60 My) can
be subducted. These distributions are consistent
with those already computed in models without
continents and in cartesian geometry (3).
When plate-like behavior and continents are
combined, the average area-age distribution is
close to a triangular shape with an approximately
linear decrease of the area with increasing age
and a present-day production of seafloor slightly
larger than the observed present-day value (Fig.
1C). The averaged synthetic distributions given
by the convection models with continents and
plate-like behavior are in good agreement with
the observed triangular distribution for the present-
day Earth and with a 1D distribution correspond-
ing to a model with a subduction probability
depending on the square root of age (12). Simu-
lations with different numbers and sizes of con-
tinental blocks, with and without a reasonable
amount of core heating (15% of the total heat
flow), yield results with very little differences.
Within the course of a simulation, the area-age
distribution is mostly triangular but evolves with
the birth of new plate boundaries and the vanish-
ing of others. When the distribution is triangular
(Fig. 2A), ridge-like structures with youngocean
floor end at triple junctions and regions of trans-
form motion (Fig. 2B). The downwellings here
are mostly located on the edges of the continents.
Several of the ridge-like structures are cut by down-
wellings, highlighting the sinking of youngma-
terial in these models. Here, continents seem to act
as a geometrical constraint that imposes the location
of downwellings at the continent-ocean boundary.
A first type of nontriangular distribution (Fig.
2C) is relatively flat with a smaller value for the
production of new ocean floor (t
max
is about the
same as for the triangular shape), where down-
wellings are not all located on the edges of the
continents (Fig. 2D). Such a distribution is more
likely encountered in simulations with few con-
tinents (one or two), rather than with many. This
distribution is close to that observed with plate-
like behavior and without continents described
above. Hence, a flat distribution could occur when
the geometrical influence of the continents on the
location of downwellings is minimal and when the
flow is self-organized so that ocean floor is free to
reach a critical buoyancy before starting to sink.
A second type of nontriangular distribution,
observed in all the simulations at times where new
plate boundaries are generated (Fig. 2E), has two
characteristics: a large production of new ocean
floor (here almost twice the time-averaged one)
and a relative skewness. In this snapshot, ridge-
like structures dominate and are very irregular.
Fig. 4. (Aand B) Evolution of the average spectral heterogeneity of the temperature field in (A) the
supercontinent case and (B) the six-continent case, corresponding to the evolution depicted in Fig. 3.
Shown are powers of the first six harmonic degrees in a logarithmic scale, depth-averaged over the upper
mantle. For each point in time, the spectrum is normalized separately with the maximum spectral power
occurring at this time. The color scale corresponds to the normalized power.
0
2
4
6
8
10 1 continent
6 continents
0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
Elapsed time (My)
25
30
35
40
45
50
Production rate of
new ocean floor (km2 yr -1)Oceanic heat flow (TW)
Fig.2E
Fig.2C
Fig. 3. Production rate of new ocean floor (top) and oceanic heat flow (bottom) as a function of elapsed
time in models with the supercontinent covering 30% of the surface (black) and with six continents each
covering 5% of the surface (red). The average productions are 4.91 km year
1
with one continent and
4.55 km year
1
with six continents, with standard deviations of 1.59 km year
1
and 0.97 km year
1
,
respectively. The transit time t
s
of 85 My is used for the scaling (18). The averages of the heat flow are
38.2 TW with one continent and 39.3 TW with six continents, with standard deviations of 4.8 TW (12%)
and 2.8 TW (7%), respectively. The vertical dashed lines illustrate the points in time represented in Fig. 2C
and Fig. 2E. The distributions computed over the time period give the average distributions in Fig. 1C.
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They are formed in response to the onset of new
cold instabilities. They develop and a reorganization
of the flow takes place to progressively produce a
more triangular distribution. Variations in the shape
of the distribution with time are consistent with
reconstructions for the past 150 My (12,14,15).
The shape of the distribution may have evolved
from flat-like, when Pangea was barely splitting,
to a skewed distribution after the birth of new
ridges (15), ultimately transforming to the present-
day triangular shape with dispersed continents.
Like the shape of the area-age distribution,
the rate of production of new ocean floor (youn-
ger than 10 My) in the mantle convection mod-
els varies with time (Fig. 3). Fluctuations are
moderate32% and 21% of the mean value
for the supercontinent and six-continent cases,
respectivelybut they can reach 100% at times,
doubling or halving the production of new ocean
floor. The strongest variations occur on a time
scale of 500 million years, which corresponds to
the time scale of flow reorganization through the
onset of new plate boundaries. The peaks of pro-
duction are generally correlated with the gener-
ation of new plate boundaries and peaks in heat
flow (like the configuration in Fig. 2F). The fluc-
tuations are stronger with one continent than with
six continents. Many small continents make the
flow adopt a smaller wavelength, so that a change
in plate organization has a smaller contribution
to the total (Fig. 4). The smaller wavelength im-
poses a higher time-averaged heat flow than for
the supercontinent case (20). The magnitudes
and time scales of the computed variations of
the production of new ocean floor are compara-
ble to those extracted from seafloor spreading
reconstructions (12,13).
Our models provide a fundamental basis for
realistically simulating Earths mantle convection.
Although they have relatively low Rayleigh num-
bers and simplified parameters for the interior of
the mantle, they show that plate-like behavior and
the presence of continents are the two necessary
ingredients to build a model in which young
seafloor is subducted like on Earth. Continents
constrain the location and geometry of the down-
wellings that cool Earths mantle. When subduc-
tion is confined at an ocean-continent boundary,
convection forces the subduction of very young
seafloor. Such a situation is favored by continen-
tal growth and dispersal. The distribution of sea-
floor age is a primary observation that should
be used as a diagnostic when simulating Earths
mantle, predicting the long-term cooling of Earth,
the fluctuations of sea level caused by tectonics
(21) that ultimately condition climate change on
geological time scales.
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Acknowledgments: We thank R. D. Müller and T. W. Becker
for fruitful reviews. Supported by Institut Universitaire de France
and ANR grant DynBMO (Dynamique de locéan de magma
basal) ANR-08-JCJC-0084-01 (N.C. and S.L.) and by Crystal2Plate,
a FP-7 funded Marie Curie action under grant agreement
PITN-GA-2008-215353 (T.R.). Supercomputing resources were
provided by ETH and the Swiss Supercomputer Centre (CSCS).
Supplementary Materials
www.sciencemag.org/cgi/content/full/336/6079/335/DC1
Materials and Methods
Data File and Codes
References (2227)
13 January 2012; accepted 21 March 2012
10.1126/science.1219120
A Segmentation Clock with
Two-Segment Periodicity in Insects
Andres F. Sarrazin,*Andrew D. Peel,Michalis Averof
Vertebrate segmentation relies on a mechanism characterized by oscillating gene expression. Whether
this mechanism is used by other segmented animals has been controversial. Rigorous proof of cyclic
expression during arthropod segmentation has been lacking. We find that the segmentation gene
odd-skipped (Tc-odd) oscillates with a two-segment periodicity in the beetle Tribolium castaneum.By
bisectingembryosandculturingthetwohalvesover different time intervals, we demonstrate that
Tc-odd cycles with a period of about 95 minutes at 30°C. Using live imaging and cell tracking in green
fluorescent proteinexpressing embryos, we can exclude that cell movements explain this dynamic
expression. Our results show that molecular oscillators represent a common feature of segmentation in
divergent animals and help reconcile the contrasting paradigms of insect and vertebrate segmentation.
Many animals generate body segments se-
quentially from a posterior region known
asthegrowthzone(1,2). Whether there
are common mechanisms underlying this process of
segmentation in disparate segmented animals, such
as vertebrates, annelids, and arthropods, has been
intensely debated (38). A role for molecular os-
cillators in segmentation was initially proposed
on theoretical grounds by Cooke and Zeeman (9).
Their clock and wavefrontmodel explained how
the temporal periodicity of a clock could be trans-
lated into a repetitive spatial pattern during sequen-
tial segmentation. Subsequent studies showed that
oscillating patterns of gene expression sweeping
through the growth zone play a key role in verte-
brate segmentation (1013).
A number of studies have indicated that an
equivalent segmentation clock may operate in the
presegmental zone of arthropods (35,14,15).
These studies revealed changing patterns of gene
expression in the presegmental zone of an insect,
a centipede, and a spider. They also showed that
disrupting Notch signaling, which is an important
element of the vertebrate segmentation clock
(13,16), leads to defects in segmentation in some
of these species. These results have been inter-
preted by some researchers as evidence that a
common mechanism for segmentation was in-
herited by vertebrates and arthropods from a
segmented common ancestor.
However, several doubts remain regarding
this interpretation. First, Notch signaling is known
to be involved in many other developmental pro-
cesses, such as specification of the presegmental
zone. These diverse functions may provide al-
ternative explanations for segmentation defects
(8,17,18). Second, cycling expression patterns
have been inferred from in situ hybridization
stainings on fixed embryos and comparison of
similarly staged embryos. However, embryo-to-
embryo variation and difficulty in accurately
staging embryos (relative to the speed of segment
formation) limits the reliability of this approach.
Moreover, it has not yet been proven that these
dynamic expression patterns reflect intracellu-
lar changes in gene expression, rather than cell
movements. Thus, there is no rigorous demon-
stration that cyclic waves of expression are sweep-
ing through the growth zone of arthropods. We use
embryo culture and live imaging in the insect
Tri bo lium ca sta ne um to address these issues.
Institute of Molecular Biology and Biotechnology (IMBB),
Foundation for Research and Technology Hellas (FORTH),
Nikolaou Plastira 100, GR-70013 Heraklio, Crete, Greece.
*Present address: Instituto de Química, Pontificia Universidad
Católica de Valparaíso, Casilla 4059, Valparaiso, Chile.
These authors contributed equally to this work.
To whom correspondence should be addressed. E-mail:
averof@imbb.forth.gr
20 APRIL 2012 VOL 336 SCIENCE www.sciencemag.org338
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