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The dynamics of architectural complexity on coral reefs
under climate change
YVES-MARIE BOZEC
1,2
, LORENZO ALVAREZ-FILIP
3
and PETER J. MUMBY
1,2
1
Marine Spatial Ecology Lab, ARC Centre of Excellence for Coral Reef Studies, School of Biological Sciences, University of
Queensland, St. Lucia, Qld 4072, Australia,
2
College of Life Sciences, University of Exeter, Exeter EX4 4PS, UK,
3
Unidad
Acad
emica de Sistemas Arrecifales, Instituto de Ciencias del Mar y Limnolog
ıa, Universidad Nacional Aut
onoma de M
exico,
Puerto Morelos, Quintana Roo 77580, M
exico
Abstract
One striking feature of coral reef ecosystems is the complex benthic architecture which supports diverse and abun-
dant fauna, particularly of reef fish. Reef-building corals are in decline worldwide, with a corresponding loss of live
coral cover resulting in a loss of architectural complexity. Understanding the dynamics of the reef architecture is
therefore important to envision the ability of corals to maintain functional habitats in an era of climate change. Here,
we develop a mechanistic model of reef topographical complexity for contemporary Caribbean reefs. The model
describes the dynamics of corals and other benthic taxa under climate-driven disturbances (hurricanes and coral
bleaching). Corals have a simplified shape with explicit diameter and height, allowing species-specific calculation of
their colony surface and volume. Growth and the mechanical (hurricanes) and biological erosion (parrotfish) of car-
bonate skeletons are important in driving the pace of extension/reduction in the upper reef surface, the net outcome
being quantified by a simple surface roughness index (reef rugosity). The model accurately simulated the decadal
changes of coral cover observed in Cozumel (Mexico) between 1984 and 2008, and provided a realistic hindcast of
coral colony-scale (1–10 m) changing rugosity over the same period. We then projected future changes of Caribbean
reef rugosity in response to global warming. Under severe and frequent thermal stress, the model predicted a dra-
matic loss of rugosity over the next two or three decades. Critically, reefs with managed parrotfish populations were
able to delay the general loss of architectural complexity, as the benefits of grazing in maintaining living coral
outweighed the bioerosion of dead coral skeletons. Overall, this model provides the first explicit projections of reef
rugosity in a warming climate, and highlights the need of combining local (protecting and restoring high grazing) to
global (mitigation of greenhouse gas emissions) interventions for the persistence of functional reef habitats.
Keywords: bleaching and hurricanes, habitat loss, hindcast and forecast simulation, mechanical stress, parrotfish erosion, struc-
tural complexity
Received 5 May 2014; revised version received 17 July 2014 and accepted 25 July 2014
Introduction
One striking feature of coral reef ecosystems is the devel-
opment of three-dimensional (3-D) limestone structures
that enhance living and refuge space for a multitude of
organisms. Complex reef architectures typically support
diverse and abundant biological communities (reviewed
by Graham & Nash, 2013) by facilitating the survival of
organisms through the mediation of critical ecological
processes, including recruitment, predation and
competition (e.g. Jones, 1991; Hixon & Beets, 1993; Syms
& Jones, 2000). While the reef architecture is an impor-
tant driver of the reef community structure, complex
architectures are often observed on reefs with an exten-
sive cover of live corals (Alvarez-Filip et al., 2011; Gra-
ham & Nash, 2013), especially when complex (e.g.
branching) or large massive coral life-forms dominate
(Rogers et al., 1982; Steneck, 1994; Alvarez-Filip et al.,
2011). Yet reef-building corals are in decline worldwide
(Gardner et al., 2003; Bruno & Selig, 2007; De’ath et al.,
2009) and a general loss of architectural complexity has
been reported in the Caribbean in the past four decades
(Alvarez-Filip et al., 2009a).
Central to the creation of the reef relief is the growth
and calcification of hard corals that constitute the
structural units of the superficial reef framework (e.g.
Hubbard et al., 1998; Perry et al., 2008), even though
the accretion of reefs over geological time scales incor-
porates many other factors (Shinn et al., 1982; Perry
et al., 2008). While coral skeletons extend the reef sur-
face through carbonate accretion and cementation, a
number of biological and physical agents lead to the
erosion of the upper carbonate framework (Hutchings,
Correspondence: Yves-Marie Bozec, Marine Spatial Ecology Lab,
School of Biological Sciences, University of Queensland, St. Lucia,
Qld 4072, Australia, tel. +61 7 33 651 671, fax +61 7 33 651 655,
e-mail: y.bozec@uq.edu.au
1©2014 John Wiley & Sons Ltd
Global Change Biology (2014), doi: 10.1111/gcb.12698
Global Change Biology
1986; Glynn, 1997; Tribollet & Golubic, 2011). The bal-
ance between these constructive (accretion) and
destructive (erosion) processes determines the ability
of the reef surface to grow through net carbonate
accretion (Stearn et al., 1977; Perry et al., 2008, 2012).
Yet, recent carbonate budgets of Caribbean reefs have
revealed significant reductions in their ability to sus-
tain a net reef accretion (Kennedy et al., 2013; Perry
et al., 2013). Considering the importance of corals in
the production of reef carbonate, and the predicted
impacts of climate change on coral growth and calcifi-
cation (Hoegh-Guldberg et al., 2007; Anthony et al.,
2011; Frieler et al., 2012), there is a growing concern
over the ability of coral reefs to maintain functional
habitat structures in the future (Hoegh-Guldberg et al.,
2007; Kennedy et al., 2013). A failure of reefs to main-
tain a positive carbonate budget will likely lead to a
decline in many ecosystem services including biodiver-
sity, fisheries productivity and recreational value
(Done et al., 1996).
While a negative carbonate budget implies a net loss
of reef framework, it gives little indication of the conse-
quences for the quality of the reef habitat structure (i.e.
the complexity of its superficial architecture), which has
a functional impact on reef-associated organisms. The
complexity of the reef habitat is typically captured by
its topography (McCormick, 1994; Jones & Syms, 1998),
yet little is known about the rate of loss of topographi-
cal complexity associated with a negative reef carbonate
budget. Habitat is a multi-scale concept but commu-
nity-based studies have mostly investigated topograph-
ical patterns at the scale of metres (from 1 to 10s of
metres). At this scale, processes shaping reef topogra-
phy are those affecting the growth of living and erosion
of dead coral skeletons, and such processes operate at
relatively short (as opposed to geological times) tempo-
ral scales (e.g. <100 years, Perry et al., 2008). The
response of coral-scale (1–10 m) topographical com-
plexity to erosion likely depends (1) on species-specific
rates of coral mortality in response to disturbances,
such as bleaching and hurricanes, and (2) the loss of
complexity caused by the erosion of structurally differ-
ent carbonate skeletons. Therefore, quantifying the con-
tribution of each coral species to the reef surface
topography, through the complexity of their skeleton
during both the accreting (live) and eroding (dead)
phases is key for estimating the degradation of colony-
scale habitat complexity on net eroding reefs. Predicting
the dynamics of reef structural complexity is of particu-
lar importance to envision the future functioning of
reefs and their ability to support ecosystem services
(Pratchett et al., 2014; Rogers et al., 2014).
Here, we develop and test a mechanistic model of
reef topographical complexity for contemporary
Caribbean reefs. The model describes the dynamics of
corals and other benthic taxa under the control of
multiple disturbances (hurricanes and coral bleach-
ing), and is calibrated using observed changes on the
reef benthic structure in Cozumel (Mexico) on decadal
time scales. Providing corals have a simplified shape
with explicit diameter and height, the model calcu-
lates carbonate accretion and erosion at the scale of a
coral colony, simulating changes in coral volume and
surface and their impact on the reef topographical
complexity. Model simulations are used to investigate
possible scenarios of change in reef topographical
complexity in response to global warming under dif-
ferent hurricane and local management (i.e. parrotfish
protection) regimes.
Materials and methods
Model overview
A mechanistic model of reef topographical complexity was
developed by extending a two-dimensional (2-D) model of
coral populations (Mumby, 2006; Mumby et al., 2006, 2007;
Edwards et al., 2011) to quantify the contribution of the 3-D
structure of coral colonies to the extension of the reef surface.
The 2-D model is designed to simulate coral-algae dynamics
in a regular square lattice of 400 cells, each approximating
1m
2
of a typical mid-depth (5–15 m) Caribbean forereef. Indi-
vidual cells can be occupied by multiple coral colonies of dif-
ferent species and patches of cropped algae (a mixture of
coralline algae and short turf) or macroalgae (Dictyota pulchel-
la,Lobophora variegata). Each coral colony is defined by its
cross-sectional (circular) basal area on the square lattice. Start-
ing from a given size structure and absolute cover area, coral
colony sizes (in cm
2
) are updated every 6 month following
systematic and probabilistic rules which reflect processes of
coral population dynamics (recruitment, colony growth, pre-
dation and natural mortality), macroalgal populations (growth
and grazing from herbivores) and coral-algae interactions
(competition for space). As a result, coral populations grow if
the grazing pressure is high enough to maintain macroalgae
in a cropped state (short turf) so that space is freed for coral
growth and recruitment (Mumby, 2006). However, coral pop-
ulations in the model are subject to bleaching and hurricanes
that can occur either randomly or following a predefined sche-
dule, both disturbance regimes being able to impair the persis-
tence of a coral-dominated state (Edwards et al., 2011; Mumby
et al., 2013). A full description of model components, rules,
parameters and assumptions is provided in Appendix S1.
Model implementation of topographical complexity
Reef topographical complexity is commonly assessed in the
field using the chain-and-tape method (Risk, 1972) where a
fine chain is draped over the reef bottom surface along short
(from 3 to 20 m, Knudby & LeDrew, 2007; Alvarez-Filip
et al., 2009a) transect lines. Dividing the chain length by the
©2014 John Wiley & Sons Ltd, Global Change Biology, doi: 10.1111/gcb.12698
2Y.-M. BOZEC et al.
horizontal distance it covers produces an index of surface
roughness or rugosity (Luckhurst & Luckhurst, 1978; McCor-
mick, 1994). The rugosity index approximates how much the
3-D reef surface departs from its 2-D projection on an horizon-
tal plane: the higher the ratio, the greater the deformation of
the reef bottom. As a result, high rugosity values (i.e. >2.5) are
typically found in rich coral areas dominated by complex life-
forms, such as the large branching acroporids, whereas low
rugosity values (i.e. <1.5) are characteristics of coral-depauper-
ate reefs or reefs dominated by diminutive coral forms (Rogers
et al., 1982; Steneck, 1994; Alvarez-Filip et al., 2011).
Assuming that the extension of the reef surface is primarily
driven by coral growth and calcification, corals can be consid-
ered as building blocks that successively generate the forma-
tion of 3-D carbonate structures. Here, corals are stylised by
circular paraboloid volumes, i.e. solids of revolution obtained
by rotating a parabola around their axis of symmetry (Fig. 1a).
Like the 2-D grid model, coral growth is modelled by the
cross-sectional basal area of coral colonies (i.e. their planimet-
ric projection on the grid lattice) which grows laterally at a rate
that is species-specific (listed in Appendix S1, Table S1). For
every radial increment, colony height is calculated from
empirical relationships derived from field data (see parametri-
zation below), so that coral colonies can grow vertically over
time (Fig. 1b). Designing a regular solid shape for corals facili-
tates the calculation of colony surface area and volume
through the use of standard geometric formula, based on
diameter and height (see Appendix S1, Eqns S1 and S2). As a
result, the volume and actual surface area of living colonies
increase over time as the colonies grow in three dimensions.
When an entire colony dies, its skeletal structure becomes a
new substrate covered by short algal turf, thus extending the
reef framework surface that can be colonised by corals and
macroalgae. Here, dead corals are a new class of object
enabling the representation of the upper carbonate framework
of the reef. Like living corals, the spatial arrangement of dead
corals is not explicit, but skeletal material accumulates within
the cell (Fig. 1c). Dead skeletons are subject to external erosion
driven by excavating parrotfish and it is assumed that urchin
abundance is functionally absent, including Echinometra. The
total volume of carbonate that is eroded at every time step is
fixed for the whole reef grid. Colony volume after external
erosion is used to recalculate the height of dead skeletons
(Eqn S2) based on the simplifying assumption that basal col-
ony diameter is kept constant during grazing erosion (Fig. 1b).
As such, external bioerosion is directed towards the top of
coral colonies in conformity with the observation that excavat-
ing parrotfish preferentially erode convex surfaces (Bellwood
& Choat, 1990; Bruggemann et al., 1996; Ong & Holland,
2010). As a result, grazing erosion flattens individual dead
skeletons, thus reducing reef substrate area at every time
increment. Erosion by infaunal bioeroders (e.g. sponges, bival-
ves, worms and cyanobacteria, Tribollet & Golubic, 2011) is
assumed not to affect the shape of coral skeletons; rather,
internal erosion increases skeletal porosity, and, consequently,
susceptibility to storm-induced breakage (see details below).
The model tracks the individual production/erosion of car-
bonate skeletons which drives the pace of extension/reduction
of the reef surface. Surface and planimetric areas of dead colo-
nies are combined (Eqn S3) to estimate the surface area of the
dead carbonate framework (hereafter referred to as “reef sub-
strate”) in every grid-cell. As a result, the reef substrate area is
changing over time depending on the extent of coral mortality
and erosion. One implication is that transient changes in reef
substrate area dynamically influence spatial ecological pro-
cesses such as grazing intensity and competition between cor-
als and algae (see details in Appendix S1).
Both dead and living coral colonies contribute to the topo-
graphical complexity of a reef. At every time step, the actual
surface area of the reef bottom is estimated by combining the
surface and planimetric areas of living corals with the reef
H
D
C
Live coral Dead coral
(a)
(b)
(c)
Fig. 1 Model assumptions for the representation of the 3-D
structure of the reef bottom: (a) geometry of a circular parabo-
loid as a proxy of coral colony shape (D: diameter, H: height, C:
contour); (b) morphological changes of living (left panel) and
dead (right panel) coral colonies over time: coral growth
extends colony diameter and height, whereas external erosion
decreases colony height of dead corals; (c) schematic illustration
of the reef bottom built from the accumulation of dead (white
paraboloids) and living (grey paraboloids) corals within a
model grid cell. The exact position of coral colonies within a cell
is actually unknown.
©2014 John Wiley & Sons Ltd, Global Change Biology, doi: 10.1111/gcb.12698
DYNAMICS OF REEF RUGOSITY 3
substrate area (Eqn S5). A surface-to-area ratio is then calcu-
lated (Eqn S6) for the whole reef grid by dividing the surface
area of the reef bottom by its planimetric projection (i.e. the
horizontal area of the reef grid). The higher the ratio, the
greater the deformation of the reef bottom thus providing an
index of surface roughness for the modelled reef. Here, sur-
face roughness is not a strict equivalent to the rugosity index
assessed in the field, the latter capturing only the deformation
of the reef bottom based on its vertical (2-D) profile. However,
we assume the two indices of topographical complexity are
proportional, in a similar manner to the surface-to-area and
contour-to-linear ratios relationships at colony scales. An
empirical relationship between reef rugosity and surface
roughness was derived from the systematic analysis of 3-D
and 2-D morphometrical ratios of paraboloids of increasing
diameter and height (see details in Appendix S1). This rela-
tionship allowed us to convert reef surface roughness into a
field-relevant rugosity index at any time step of the model.
Parametrization of colony shape: observed coral
morphology
Coral morphometric data collected on reefs in south-western
Cozumel (Mexican Caribbean) in April 2009 were used to
derive empirical relationships between colony diameter and
colony height and to test the assumption that the shape of
massive and submassive coral colonies can be approximated
by a circular paraboloid. Coral colonies were randomly sam-
pled at middepth (7–14 m) in four sites and the following
measurements were taken: (1) maximum horizontal extension
(~colony diameter); (2) maximal vertical extension (~colony
height) and (3) the contoured length measured along the maxi-
mum horizontal extension (~colony contour). As for the simu-
lation model, we assume that the sampled colonies can be
represented by regular disks on the horizontal plane, with
a diameter equal to the maximum horizontal extension
measured.
Colony height (H) was modelled using linear regression
with colony diameter (D) as predictor for the seven most
represented species: Agaricia agaricites (n=73), Porites astreo-
ides (n=51), Siderastrea siderea (n=42), Montastraea cavernosa
(n=35), Orbicella faveolata (n=24), Orbicella annularis
(n=22) and Porites porites (n=19). For every species, Hand
Dwere square root transformed to meet the assumption of
normality, and linear models were designed with forced
zero intercepts. This produced seven empirical relationships
that were used in the simulation model to update the height
of living corals for every radial increment specified by the
species growth rates.
To validate our assumption of paraboloid coral colonies, we
calculated the contour (C) of every sampled coral colony using
its observed Dand predicted H. The contoured length of a cir-
cular paraboloid corresponds to the length of the parabolic arc
and is given by (Stine & Geyer, 2001):
^
C¼D2
8
^
Hln 4
^
H
Dþffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
4
^
H
D
!
2
þ1
v
u
u
t
2
6
43
7
5þD
2ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
4
^
H
D
!
2
þ1
v
u
u
tð1Þ
For each coral species, predicted and observed Cwere com-
pared using the Spearman’s rank correlation coefficient, high
correlations indicating that the paraboloid shape is an accept-
able proxy of actual coral colony shape.
Model calibration: Cozumel reef data (1984–2008)
The model was calibrated using historical benthic surveys of
the leeward reefs in south-western Cozumel, compiled from
literature and published reports (Appendix S2, Table S3). We
selected data on benthic cover reported on middepth (5–20 m)
inner reefs and shelf-edge reefs, where sand cover did not
exceed 25%. The unit of observation is a reef site according to
the definition of a reef in the simulation model (20 920 m).
When available, within-site samples (i.e. transects) were aver-
aged to produce a site-level estimate of benthic cover, and
every record was assigned to the appropriate season as
defined in the simulation model (summer: July to December;
winter: January to June). The resulting data series runs for
twenty-four years (August 1984–May 2008). Site description
and selection are detailed in Appendix S2.
Coral cover. Model initialization was set up with a 31% coral
cover, which corresponds to the average reported during the
period 1984–88 (n=25 reefs) before hurricane Gilbert hit the
coast of Cozumel in September 1988. Based on the description
of coral composition (Appendix S2, Table S4), initial coral
cover was distributed among the same seven coral species
used in the parametrization phase (% relative cover): A. agari-
cites (53%), P. porites (24%), O. annularis (7%), O. faveolata (7%),
M. cavernosa (4%), P. astreoides (3%), S. siderea (2%). In the
model, A. agaricites included the polymorph A. tenuifolia which
was the most common coral on the tops of the shelf-edge reefs
in the mid 1980s. P. porites includes P. furcata which has a
similar digitate morphology. As a result, those seven species
represented 90% and 95% of the total coral cover surveyed in
1984–1988 and 2005, respectively. For each model initializa-
tion, coral species covers were randomized following a normal
distribution (see details in Appendix S1) to reproduce the vari-
ability (22–49%) observed on total coral cover in 1984–1988.
Parametrization of other benthic covers (i.e. macroalgae,
sponges and ungrazable cover) is detailed in Appendix S2.
Topographical complexity. Unfortunately, the only available
data for topographical complexity were collected in 2007–2008
(Alvarez-Filip et al., 2011). At this time, reef rugosity was 1.5
on average and strongly correlated with total coral cover
(Appendix S2). Initial reef rugosity was therefore derived
from the initial coral cover (31%) using Alvarez-Filip et al.
(2011)’s empirical relationship between reef rugosity and total
coral cover, assuming the two metrics exhibited the same rela-
tionship at the start of the time-series. From this relationship
we extrapolated an average rugosity value of 1.9 which was
further randomised following a normal distribution (see
details in Appendix S1).
Parrotfish grazing and bioerosion. Reefs in south-western
Cozumel have been protected since 1980 (Fenner, 1988) and
©2014 John Wiley & Sons Ltd, Global Change Biology, doi: 10.1111/gcb.12698
4Y.-M. BOZEC et al.
currently support high parrotfish abundances and biomasses
(LAF and PJM, pers. obs.), especially Sparisoma viride and Sca-
rus vetula which are very efficient grazers. Therefore, maximum
grazing impact (Appendix S1) was set to 40% of the actual sur-
face of the reef substrate grazed, which is representative of a
reef with unfished parrotfish populations (Mumby, 2006).
Parrotfish bioerosion in the Caribbean is mainly due to
S. viride and large individuals of S. vetula (Frydl & Stearn,
1978; Bruggemann et al., 1996). In the absence of detailed data
on the size composition of parrotfish assemblages in Cozumel,
we simulated different bioerosion rates falling into the range
of published grazing erosion values (0.01–7.62 kg CaCO
3
m
2
yr
1
, (Bruggemann et al., 1996; Mallela & Perry, 2007;
Perry et al., 2012). Each tested value of parrotfish erosion was
scaled to the dimension of the model grid (20 920 m), then
converted into a total volume (cm
3
) of carbonate to be
removed from the grid every 6 month, assuming a standard
density of 1.7 g cm
3
for carbonate skeletons (Perry et al.,
2012). Parrotfish bioerosion was concomitant with grazing, so
that the eroded surface of dead skeletons equalled the area
grazed, and the cumulated volume eroded in every cell
matched the volume specified at the reef scale (see details in
Appendix S1).
External disturbances: hurricanes and bleaching. Modelled
reefs were subject to the actual regime of major category hurri-
canes (i.e. category 3 and higher on the Saffir-Simpson scale)
that occurred between 1984 and 2008 in Cozumel: hurricanes
Gilbert in 1988 (category 5), Roxanne in 1995 (category 3), and
Emily (category 4) and Wilma (category 4) in 2005. We
allowed for two hurricanes during summer 2005 to represent
the cumulative damages caused by Emily and Wilma. Because
patterns of reef damages caused by hurricanes are typically
patchy (e.g. Woodley et al., 1981; Rogers et al., 1982), the
occurrence of a scheduled hurricane was further randomized
for each replicate simulation. For a simulated reef, the proba-
bility to be impacted by a scheduled hurricane (Appendix S1)
was derived from the observed proportion of Cozumel reef
sites that were significantly damaged by hurricanes Gilbert
(Fenner, 1991) and Emily-Wilma (Alvarez-Filip et al., 2009b).
When occurring, hurricanes cause whole-colony (dislodge-
ment) and partial (fragmentation) coral mortalities due to
mechanical stress. Similar to (Edwards et al., 2011), colony
breakage is a function of hurricane category and colony size,
but here rates of breakage were further adapted to each coral
species based on species-specific losses reported in Cozumel
(Appendix S1). While the fragility of recently dead skeleton is
likely similar to that of living colonies, susceptibility to break-
age after death may either increase with internal bioerosion
(i.e. macro- and microboring) or decrease with cementation by
binding agents (i.e. calcareous encrusters). Because the extent
and timing of these processes are unknown, we simply
assumed that the probabilities of breakage of dead skeletons
were proportional to those of their living counterparts, with a
magnitude factor to be determined by fitting the model to
Cozumel observations. This was implemented using a global
multiplier of coral mortalities (hereafter referred to as break-
age susceptibility relative to live corals), identical for all
species of dead corals and varying from 0 to 2. In this way, the
net effects of cementation and internal erosion are encapsulated
implicitly in the probability of breakage without requiring a
complex and highly uncertain parametrization. Dislodged col-
onies and fragments (dead and alive) were removed from the
model grid assuming transport and dispersion off the reef.
We also allowed for bleaching events to occur based on
Cozumel waters thermal climatology for the period 1984–2008.
Weekly based sea surface temperatures (SST) recorded by
NOAA at Cozumel were converted into Degree Heating
Weeks (DHWs) similar to (Edwards et al., 2011). DHWs
allowed the calculation of coral mortality (see details in
Appendix S1) following the empirical data of Eakin et al.
(2010). Bleaching did not occur if a hurricane had occurred
that year.
Model performance. A total of 100 model simulations were
run over 48 seasonal time steps (from summer 1984 to winter
2008) to compare the simulated coral cover and reef rugosity
with observations from Cozumel. Model performance was
assessed through its ability to meet three objectives: (1) repro-
duce the observed average and variability in total coral cover
over time; (2) reproduce the relative cover of the dominant
species (A. agaricites,P. porites and O. annularis) as observed
before and after the 2005 hurricane season (Alvarez-Filip et al.,
2009b); (3) reproduce the relationship between total coral
cover and rugosity as observed in 2007–2008 (Alvarez-Filip
et al., 2011). Considering the high uncertainty associated with
parrotfish bioerosion and susceptibility of dead skeletons to
breakage caused by hurricanes, different values of these two
parameters were tested until the agreement between simula-
tions and observations, based on visual judgement, were rea-
sonably good. No statistical procedure was applied for
optimising simulations, considering that a better fit to obser-
vations will not increase confidence in the adjusted parameter
values of mechanical and biological erosion. However, we
report the relative influence of the two erosion rates on model
outputs (final coral cover and rugosity) for a critical evaluation
of erosion and its relative importance on model performance,
given the uncertainty of observations.
Model application: future scenarios of topographical
complexity
The model was finally used to explore long-term (40 years)
scenarios of changing rugosity for a Caribbean reef submitted
to future thermal stress and different regimes of hurricanes.
Bleaching events were scheduled according to future SST as
predicted by the UK Hadley Centre Global Environmental
Model HadGEM1 (Johns et al., 2006) following the Representa-
tive Concentration Pathway (RCP) 8.5 trajectory for green-
house gases (GHG), a warming scenario which considers
high, “business as usual” GHG emissions (Riahi et al., 2011).
The simulated scenarios used the Caribbean basin mean SST
(Edwards et al., 2011) calculated monthly from 2010 to 2050 to
calculate degree heating weeks which determine the probabil-
ity of coral bleaching (Appendix S1). We therefore assumed
that the response of corals to bleaching is dominated by the
©2014 John Wiley & Sons Ltd, Global Change Biology, doi: 10.1111/gcb.12698
DYNAMICS OF REEF RUGOSITY 5
intensity of acute thermal stress and not modified by acclima-
tion/adaptation. Hurricanes occurred randomly with a low
(0.05) and high (0.2) probability to contrast the effects of differ-
ent hurricane regimes (one every 20 years vs. one every
5 years on average) on reef rugosity. When a hurricane occurs,
its strength (Saffir-Simpson categories 1–5) is determined ran-
domly with an equal chance for each category.
Model simulations were used to estimate the average time
for a present-day Caribbean reef to lose its topographical com-
plexity. For the two scenarios of hurricane frequency, the
model was initialized with increasing total coral cover (from 2
to 25% by increments of 1%) and rugosity (from 1.3 to 2 by
increments of 0.05) to explore a wide range of reef architec-
tures. Total coral cover at initial step was distributed across
the seven coral species with the same relative covers used to
reconstruct Cozumel reef trajectories. For each coral/rugosity
combination we calculated the average time step at which reef
rugosity falls below 1.2 based on a minimum of 40 replicate
simulations. A threshold of 1.2 was chosen because it repre-
sents the Caribbean average at the end of a recent meta-analy-
sis of reef rugosity on Caribbean reefs (Alvarez-Filip et al.,
2009a). The two hurricane scenarios were run for a high (40%)
and medium (20%) grazing impact for evaluating the effects
of managed (fully protected) vs. unmanaged (fished) parrot-
fish populations on the future predictions of reef rugosity. Par-
rotfish bioerosion was reduced proportionally to grazing
impact to balance the indirect, positive effects of parrotfish
grazing on the persistence of corals with the direct, negative
effects of parrotfish erosion on topographical complexity.
Results
Coral colony morphometrics
The analysis of in situ morphometric measurements
showed that colony height is linearly related to colony
P. porites
O. faveolata
S. siderea
O. annularis
M. cavernosa
P. astreoides
A. agaricites
Colony diameter (cm)
Colony height (cm)
050100150
0
50
100
150
Fig. 2 Linear regressions of colony height as a function of col-
ony diameter for the seven coral species based on Cozumel in
situ measurements (see Appendix S3, Fig. S4 for detailed rela-
tionships and related statistics).
P. astreoidesA. agaricites S. siderea M. cavernosa
O. faveolata O. annularis P. porites
Observed contour (cm) Observed contour (cm) Observed contour (cm)
Predicted contour (cm)
Observed contour (cm)
Predicted contour (cm)
ρ = 0.844 ρ = 0.892 ρ = 0.953 ρ = 0.962
ρ = 0.955 ρ = 0.981 ρ = 0.915
0
10
20
30
40
50
60
70
30 30
0
10
20
30
40
50
60
60
0
20
40
60
80
100
0
50
100
150
200
0 10 20 40 50 60 70 0 10 20 40 50 60 0 20 40 80 100 050100
150 200
0
50
100
150
200
250
150
300
0 50 100 0 50 100 150
200 250 200 250 300
0
10
20
30
40
50
60
01020
30 40 50 60
0
50
100
150
200
250
Fig. 3 Relationship between predicted and observed colony contours (full circles) for the seven coral species. Empty circles indicate
outliers (details in Appendix S3, Fig. S4). The Spearman’s rank correlation coefficient (q) is significantly non null at P<0.001 for every
coral species. Solid lines represent a 1 : 1 relationship.
©2014 John Wiley & Sons Ltd, Global Change Biology, doi: 10.1111/gcb.12698
6Y.-M. BOZEC et al.
diameter for the seven coral species (Fig. 2; Appen-
dix S3, Fig. S4). Colony height increased more quickly
with diameter (i.e. steeper slope) for the three mound-
like species, M. cavernosa,O. faveolata and O. annularis.
These species also included coral colonies with the larg-
est diameter (up to 100 cm). Species departing from a
mound-like shape, such as A. agaricites (weedy/
encrusting colonies) and P. astreoides (boulder/encrust-
ing colonies) exhibited the weakest, although signifi-
cant, relationship.
To test for the ability of paraboloids to approximate
coral colony shapes, we calculated the expected con-
toured lengths of in situ coral colonies under a parabo-
loid model (Eqn 1), based on their observed diameter
and predicted height (i.e. as estimated by the empirical
relationships). Expected colony contours were highly
correlated with the contours measured in situ for all
coral species (Fig. 3), with highest correlations obtained
for boulder and mound-like coral shapes (S. siderea,M.
cavernosa,O. faveolata and O. annularis). As a conse-
quence, the contour indices (i.e. the ratio of the con-
toured length to the largest diameter) calculated from
in situ colonies were very similar to those expected
under a paraboloid model (Appendix S3, Fig. S5 and
Table S5).
Historical trajectories of reefs in Cozumel
Model simulations between 1984 and 2008 closely
matched the observations of total coral cover reported
in Cozumel (Fig. 4a), except for the 1996–1997 observa-
tions where average coral cover has been estimated at
around 30–40% while simulations predicted a 25%
average at this time. In 25 years, coral populations have
declined from a cover of ~31% to ~16%. Simulations
and observations per coral species (Fig. 5) suggested
that this decline was mostly due to losses in the cover
of A. agaricites (from 18% to 5%) and P. porites (from 8%
to 0.5%). Model and data indicated that coral losses
were due to mortalities induced by hurricanes (10%
after hurricane Gilbert in 1988, 11% after hurricanes
Emily-Wilma in 2005). Just before the 2005 hurricane
season, P. porites populations had recovered the cover
exhibited before hurricane Gilbert (~8%). In contrast,
the A. agaricites population in 2005 failed to recover its
(a)
(b)
(c)
Fig. 4 Reconstructed trajectories of total coral cover (a) and reef
rugosity (b) between 1984 and 2008 on south-western Cozumel
reefs, and relationship (c) between simulated reef rugosity and
total coral cover at the start (green dots) and at the end (red
dots) of the modelled period. Grey lines and red lines in (a) and
(b) represent, respectively, the individual and average reef tra-
jectories of coral cover and rugosity predicted by the model.
Black dots represent the observed site averages and open dots
the global averages for a given season. Regression equations in
(c): 2007–2008 observations, y=1.072 +0.027 x(R
2
=0.85,
P<0.001, N=16); 2007 predictions, y=0.914 +0.037 x
(R
2
=0.37, P<0.001, N=100).
©2014 John Wiley & Sons Ltd, Global Change Biology, doi: 10.1111/gcb.12698
DYNAMICS OF REEF RUGOSITY 7
prehurricane (Gilbert) level (~18% before summer 1988
vs. ~9% before summer 2005). According to the model,
SST anomalies may have lead to marginal bleaching
mortalities (absolute losses <5% for each bleaching
event).
Predicted rugosity in 2007–2008 (Fig. 4b) was similar
to observations and correlated with the predicted total
coral cover (Fig. 4c). The observed and predicted coral-
rugosity relationships had comparable intercepts (AN-
COVA, P=0.077) but slight differences between slopes
(ANCOVA, P=0.038). With an hypothetical average
rugosity of 1.9 in 1984, the model predicted two acute
reductions in architectural complexity related to the
1988 and 2005 hurricane seasons, followed by recovery
periods.
The present model fits (Figs 4 and 5) were obtained
using a rate of parrotfish erosion of 0.5 kg CaCO
3
m
2
yr
1
and a susceptibility of dead skeletons to hur-
ricanes of 1 (i.e. the probability of breakage of a dead
skeleton is the same as its living counterpart). How-
ever, other reasonable fits to Cozumel observations
were obtained for different combinations of values of
bioerosion and breakage susceptibility of dead skele-
tons, the respective effects of the two erosion parame-
ters being negatively correlated (Appendix S4, Fig. S6).
With lower probabilities of breakage for dead skeletons
compared to live corals (i.e. breakage susceptibility rel-
ative to live corals <1), possible values of bioerosion
rates (conditional to an acceptable fit to observations)
extended from 0 to 4 kg CaCO
3
m
2
yr
1
. For higher
probabilities of breakage (i.e. breakage susceptibility
>1), only bioerosion rates below 1 kg CaCO
3
m
2
yr
1
provided an acceptable fit.
Future scenarios of topographical complexity
Model scenarios of future global warming (RCP8.5
business-as-usual GHG emissions) for different hurri-
cane frequencies and local management interventions
(Fig. 6) predicted that reef rugosity is likely to respond
negatively to future losses of coral cover caused by
bleaching. Setting a threshold of rugosity =1.2 for a
nearly flat reef, the model estimated the average time
by which different reef topographies may become flat
given their present-day amount of corals. Under a sce-
nario of parrotfish management (grazing impact =40%,
bioerosion =0.5 kg CaCO
3
m
2
yr
1
), low complexity
reefs (i.e. present-day reef rugosity between 1.3 and 1.5)
may become flat (rugosity <1.2) by 2040 in Caribbean
environments subjected to a low hurricane regime
(Fig. 6a). The same low complexity reefs, this time in a
more severe hurricane environment, may flatten in less
than 20 years (i.e. by 2030). Even high complexity reefs
(rugosity between 1.8 and 2) may significantly lose
structure by 2040. A relatively rich coral cover (i.e.
>20%) offers little resistance to a decline of habitat
structure driven by global warming, regardless of the
hurricane regime. Under a scenario of no management
of parrotfish populations (grazing impact =20%,
bioerosion =0.25 kg CaCO
3
m
2
yr
1
), the deleterious
effects of global warming on reef rugosity (Fig. 6b)
exceeded those predicted on managed reefs, despite a
net reduction in parrotfish erosion associated with
reduced grazing.
Discussion
Simulating the dynamics of the reef architectural com-
plexity is challenging because it requires the explicit
modelling of mechanisms linking physical processes
(those driving the deformation of the reef surface) to
biological processes (those controlling the dynamics of
the coral reef-builders). Central to a reliable represen-
tation of the coral-scale reef topography is the geome-
try of coral skeletons and their changing surface/
volume during the accreting and eroding phases.
Mean 2007-08Nov 2005May 2005Mean 1984-86
Coral cover (%)
Aa Pa Ss Mc Of Oa Pp Aa Pa Ss Mc Of Oa Pp Aa Pa Ss Mc Of Oa Pp Aa Pa Ss Mc Of Oa Pp
10
5
15
20
0
10
5
15
20
0
10
5
15
20
0
10
5
15
20
0
Fig. 5 Comparison of the species (average) absolute per cent cover between in situ observations (grey bars) and model predictions
(black dots) at different time steps between 1984 and 2008. Error bars indicate standard deviations around the observed (dotted line)
and simulated (thick line) averages. Aa =A. agaricites, Pa =P. astreoides, Ss =S. siderea, Mc =M. cavernosa,Of=O. faveolata,Oa=O.
annularis,Pp=P. porites.
©2014 John Wiley & Sons Ltd, Global Change Biology, doi: 10.1111/gcb.12698
8Y.-M. BOZEC et al.
Here, using simple morphometrical rules to describe
the evolution of massive coral shapes, we developed
a mechanistic model of reef rugosity driven by ecolog-
ical and physical processes. The model simulates the
accretion/erosion of the carbonate framework through
explicit changes in live/dead coral volumes and
actual surface areas, allowing calculation of reef sur-
face roughness similar to the field-based rugosity
index. Under reasonable assumptions (i.e. consistent
with field observations), the model reproduces the
long-term trend of the benthic structure observed on
Cozumel reefs. Critically, the model forecasts a gen-
eral loss of rugosity under climate change scenarios in
the Caribbean. Under realistic rates of parrotfish ero-
sion, simulations suggest that protecting parrotfish
locally may dampen rather than accelerate the nega-
tive impacts of climate-driven disturbances on the reef
architecture.
One major assumption of the model is that processes
shaping the reef surface are mostly those affecting the
surface of live and dead coral skeletons. Hence, coral
growth was considered as the primary constructional
process of the upper reef framework, ignoring other
constructive agents (i.e. encrustation and cementation)
that consolidate coral material (Scoffin, 1992; Hubbard
et al., 1998; Perry et al., 2008). While it is reasonable to
assume that encrustation by secondary framebuilders
(e.g. coralline algae and epibiont animals, Scoffin, 1992)
do not significantly affect reef topography at the scale it
is commonly assessed, simulations did not account for
the carbonate sediments and fragments that progres-
sively fill the gaps between coral skeletons. Here, coral
Parrotfish
management
No parrotfish
management
Average year at which reef rugosity drops below 1.2
>
<
Initial rugosityInitial rugosity
Initial coral cover (%) Initial coral cover (%)
(a)
(b)
Low frequency hurricanes High frequency hurricanes
2020 2025 2030 2035 2040 2045 2050
1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.01.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0
1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.01.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0
10
15
20
25
5
5
10
15
20
25
10
15
20
25
5
5
10
15
20
25
Fig. 6 Future projections (2010–2050) of reef rugosity in the Caribbean under the RCP8.5 global warming scenario, for reefs (a) with
and (b) without protection of parrotfish populations from fishing, and low (~every 20 years, left panels) and high (~every 5 years, right
panels) frequency of hurricanes. Surface plots display the average year (see key) for a Caribbean reef structure to be critically eroded
(rugosity <1.2) given its present-day (2010) coral cover (y-axis) and reef rugosity (x-axis). Dark green contours indicate a reef rugosity
that did not fall below 1.2 by 2050.
©2014 John Wiley & Sons Ltd, Global Change Biology, doi: 10.1111/gcb.12698
DYNAMICS OF REEF RUGOSITY 9
fragments generated by storm were assumed to be
transported off the reef whereas it is likely that a signif-
icant proportion enter into the constitution of the inter-
locking framework (Blanchon et al., 1997; Rasser &
Riegl, 2002), not only decreasing rugosity but also
consolidating the primary carbonate framework thus
increasing its resistance to hydrodynamic forces.
Moreover, parrotfish grazing is not the only agent of
carbonate degradation and many boring organisms sig-
nificantly erode carbonate skeletons, potentially at simi-
lar rates (Tribollet & Golubic, 2011; Perry et al., 2012)
but with unknown consequences for the shape of coral
skeletons. However, the balanced effects of cementation
and internal erosion are accounted for implicitly in the
probability of skeletal breakage due to mechanical ero-
sion. The integration of all the constructive and destruc-
tive agents of coral reef early diagenesis will require
complex and uncertain assumptions, and it is unlikely
that an overly complex model based on insufficient
knowledge will improve our ability to predict future
changes of reef topography. Overall, this model must
be regarded as a simplification of the early diagenesis
of the upper reef framework, and is obviously not suit-
able for describing the process of vertical reef accretion
over geological times nor for calculating the full carbon-
ate budget of a reef.
Model simulations of coral populations in Cozumel
were in close agreement with in situ observations,
despite discrepancies among survey protocols (Appen-
dix S2). Model and data indicated an overall 50% loss
of coral cover on middepth (5–15 m) reefs in south-
western Cozumel in a 25 years time interval. Our study
suggests that storms were the main driver of decadal
variations of coral cover. Predicted coral bleaching was
low, in conformity with the marginal coral mortalities
reported along the Mexican coast after the recent mass-
bleaching events (McField et al., 2005; Eakin et al.,
2010). The presence of very strong currents over the
shelf of Cozumel (Muckelbauer, 1990; Alvarez-Filip
et al., 2009b) may have protected corals from strong
temperature anomalies.
With a disturbance regime dominated by frequent
hurricanes (four in 25 years with a minimum category
3), Cozumel reefs appeared to be quite resilient as sug-
gested by the recovery of coral cover (+0.5% per year)
between the 1988 and 2005 hurricane damages. The
studied period is representative of the hurricane regime
recorded in Cozumel over a longer timeframe (one
every 7 years on average in the period 1851–2013,
Landsea et al., 2014). In addition, resilience to hurri-
canes is confirmed by the early coral recoveries
observed after hurricanes Gilbert (Fenner, 1991) and
Emily-Wilma (Alvarez del Castillo-Cardenas et al.,
2008). While branching Acropora spp. have been uncom-
mon in the recent history of Cozumel (Jord
an, 1988;
Muckelbauer, 1990; Fenner, 1991), most of the reported
loss was due to A. agaricia and P. porites, two coral spe-
cies with a delicate skeleton (Fenner, 1991). We expect
the recovery could have been higher without the (lim-
ited) coral losses caused by hurricane Roxanne (1995)
and the successive episodes (1998, 1999) of minor coral
bleaching predicted by the model. Other examples of
long-term coral recovery in the Western Atlantic are
unfortunately uncommon (Roff & Mumby, 2012).
Slightly faster recovery rates (+1% per year) have been
reported in the US Virgin Islands at St Croix (Bythell
et al., 2000) and St John (Edmunds, 2002) for compara-
ble time intervals (7–11 years) and similar reef struc-
tures (i.e. moderate to high coral cover dominated by
nonbranching corals). In the absence of the fast-grow-
ing Acropora spp., it is probably unrealistic to expect fas-
ter recovery rates on present-day Caribbean coral reefs.
Without historical data on topographical complexity
(i.e. earlier than 2007), the variations of reef rugosity
predicted by the model are speculative. First, the recon-
structed trajectory of rugosity is dependent on the 1984
rugosity average, which is unknown. The most parsi-
monious assumption was to set initial rugosity to the
value (1.90) observed for a similar average coral cover
(31%) on the same reefs in 2007–2008, that, like the 1984
sites, lacked Acropora (i.e. for Orbicella-dominated reefs
of similar health). Second, an acceptable fit to observa-
tions was provided by different values of mechanical
(hurricane-driven) and biological (parrotfish-driven)
erosion. The rate of breakage of dead skeletons is diffi-
cult to parametrize: whether dead skeletons are more
or less susceptible to mechanical stress compared to
live coral colonies depends on factors not accounted by
the model, such as rates of internal erosion vs. cementa-
tion. Higher rates of framework breakage (i.e. breakage
susceptibility relative to live corals >1) require rates of
parrotfish bioerosion below 0.5 kg CaCO
3
m
2
yr
1
,
but such low bioerosion rates would lead to unrealistic
high levels of rugosity for reefs that were not damaged
by hurricanes. Inversely, lower rates of breakage (rela-
tive susceptibility <1) would result in higher bioerosion
rates (0.5–4 kg CaCO
3
m
2
yr
1
) with the risk of exces-
sive erosion of reef rugosity. Our choice of a grazing
erosion value of 0.5 kg CaCO
3
m
2
yr
1
falls within
the upper range of values commonly reported in the
Caribbean for similar depths (0.01–0.69 kg CaCO
3
m
2
yr
1
; (Stearn & Scoffin, 1977; Frydl & Stearn, 1978;
Bruggemann et al., 1996) although higher values have
been recently estimated [1.75–2.17 kg CaCO
3
m
2
yr
1
;
(Perry et al., 2012)]. However, starting simulations with
a different rugosity value would require different rates
of erosion to match the mean rugosity estimated in
2007–2008.
©2014 John Wiley & Sons Ltd, Global Change Biology, doi: 10.1111/gcb.12698
10 Y.-M. BOZEC et al.
Despite inevitable model limitations, the historical
reconstruction of topographical complexity in Cozumel
matched the trend observed at the scale of the Carib-
bean region (Alvarez-Filip et al., 2009a). Hence, an ini-
tial rugosity of 1.90 is in the range of values reported
for Orbicella-dominated reefs in the early 1980s. More-
over, the model predicted reef mean rugosity in 1998 to
be 1.76, a value very similar to the estimated regional
average (1.75) at the same date. After the 1998 mass-
bleaching event, Caribbean reef complexity has
declined continuously to reach unprecedented low lev-
els (~1.2). Today, Cozumel reefs remain in the upper
range of Caribbean reef rugosity, and this may be due
to the low incidence of coral bleaching combined with
the ability of coral populations to recover from hurri-
canes. Model simulations thus predicted a recovery of
reef rugosity after hurricane Gilbert (Sept. 1988), the
regeneration of coral cover being fast enough to offset
the erosion of the carbonate framework. This indicates
that the carbonate budget of Cozumel reefs may have
been positive (i.e. net accreting) during the period
1984–2005, meaning the reef architecture was resilient
to severe damages caused by hurricanes.
Our analysis also provides a first approximation of
the rate of change in Caribbean reef rugosity in a warm-
ing climate, based on coral population dynamics under
an intensified bleaching regime and simplified rates of
erosion. Although model projections remain uncertain,
our findings generate hypotheses about the possible
responses of reef topographical complexity to global
warming. Under severe and frequent thermal stress
caused by business-as-usual GHG emissions, low and
medium rugosity (<1.7) reefs may lose structure in the
next three decades. Under high frequency hurricane
regimes, the same reef habitats may be critically
degraded over shorter timescales (<20 years). Coral
mortalities due to bleaching disrupted the development
of complex architectures and compromised their ability
to recover from hurricane damages. It is noteworthy
that model forecasts ignored the possible reduction in
coral calcification due to chronic warming and acidify-
ing seas. However, some corals may have the ability to
acclimate or adapt to elevated temperatures (Palumbi
et al., 2014), and it is unclear what would be the
response of the other organisms involved in the cemen-
tation/erosion of the primary carbonate framework. In
addition, the effects of ocean warming and acidification
are less well recognized for benthic taxa competing
with corals and may lead to complex outcomes (Mum-
by & van Woesik, 2014). While our ability to forecast
reef responses to climate change will continually be
improved as new data become available, more reliable
projections may be achieved by linking the dynamics of
the reef topography to a comprehensive carbonate
budget. Further developments will also require extend-
ing the model to other reef habitats, particularly by
depth (e.g. reef flat, shallow forereef and deeper reefs)
since the rates of erosion are likely to vary with the hab-
itat preferences of the different eroding organisms.
Under a “business-as-usual” scenario of GHG emis-
sions (RCP 8.5), the ability of Caribbean reefs to main-
tain functional reef habitats in the short term may
depend on the efficiency of local management in sus-
taining high grazing. As a result, model simulations
suggest that with realistic rates of parrotfish bioerosion,
high levels of grazing would benefit the reef habitat
structure rather than accelerating its degradation
(Fig. 6). Protecting or restoring parrotfish grazing may
help corals recovering from moderate bleaching and
hurricanes (Mumby et al., 2014) thus maintaining
carbonate production at levels that will offset skeletal
erosion (Kennedy et al., 2013). Rates of bioerosion of
depleted parrotfish stocks, although being much lower
than for healthy parrotfish populations, became detri-
mental to reef rugosity when skeletal production was
dramatically reduced. Our results thus support the
view of the importance of combining aggressive mitiga-
tion of GHG emissions with local interventions aiming
at favouring a net coral growth.
Forecasting the quality of the reef architecture is cru-
cial to envision the future provision of reef habitats. By
simulating an explicit reef habitat structure, the present
model offers new perspectives for the projection of
coral reef futures under warming scenarios. For
instance, it may be possible to forecast the responses of
ecosystem function and services to gradual changes in
the reef architecture, providing simple relationships
between topographical complexity and the diversity,
density or biomass of the associated motile fauna (Gra-
ham et al., 2006; Wilson et al., 2010; Graham & Nash,
2013; Nash et al., 2013; Rogers et al., 2014). Here, reef
architectural complexity was modelled by simulating
the extension/reduction in the reef bottom, the net out-
come being quantified by a simple ratio between the
reef surface area and its horizontal projection. Such a
ratio gives little indication about the actual shape of the
reef surface which determines the quality of the habitat
structure (e.g. the relative proportion of convex vs.
concave surfaces, the size of holes and crevices or the
presence of overhangs). However, the same limitation
affects field-based rugosity measurements: the “chain-
and-tape” method is not able to discriminate the shape
and size of the structural elements of the reef substrate
(McCormick, 1994; Shumway et al., 2007) because dif-
ferent textures (or profiles) can produce similar surfaces
(or contours). While model developments are required
to improve the simulation of the reef architecture (e.g.
by integrating the growth and erosion of complex coral
©2014 John Wiley & Sons Ltd, Global Change Biology, doi: 10.1111/gcb.12698
DYNAMICS OF REEF RUGOSITY 11
shapes), further empirical data are needed to support
model parametrization and calibration. This includes a
better quantification of topographical complexity and
the production of time-series through repeated sam-
pling of the reef architecture. In this regard, fine-scale
bathymetric reconstructions created from underwater
imagery (e.g. Friedman et al., 2012) appear as a promis-
ing support for model development. Such methods
may also improve reef monitoring, because a gradual
loss of habitat structure may go unnoticed until detri-
mental effects on reef-associated organisms become evi-
dent. Clearly, more precise data and models will
benefit the monitoring and the management of reef-
associated services by focusing intervention on the
maintenance of functional reef habitats.
Acknowledgements
The research leading to these results has received funding from
the European Union 7th Framework programme (P7/2007-
2013) under grant agreement No. 244161 (FORCE project), a
NERC grant and ARC Laureate Fellowship to PJM. We thank D.
Fenner, E. Jord
an-Dahlgren and G. Muckelbauer for providing
information related to early surveys on Cozumel reefs. Coral
morphometric data were collected with the permission and sup-
port of the Parque Nacional Arrecifes de Cozumel and the Com-
isi
on Nacional de
Areas Naturales Protegidas of M
exico. We
also thank I. Chollett for formatting the historical SST time-ser-
ies of Cozumel, P. Halloran for providing the SST forecasts for
the climate change scenarios, and G. Roff and J.C. Ortiz for fruit-
ful discussions.
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Supporting Information
Additional Supporting Information may be found in the
online version of this article:
Appendix S1. Model description and parametrization.
Appendix S2. Cozumel coral reef data 1984–2008.
Appendix S3. Additional results of the analysis of coral
morphometrics.
Appendix S4. Model fits to Cozumel data for different ero-
sion values.
©2014 John Wiley & Sons Ltd, Global Change Biology, doi: 10.1111/gcb.12698
DYNAMICS OF REEF RUGOSITY 13
