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Local overfishing patterns have regional effects on health of coral, and
economic transitions can promote its recovery
Russell Milnea,∗
, Chris Baucha,b, Madhur Ananda,b
aDepartment of Applied Mathematics, University of Waterloo
bSchool of Environmental Sciences, University of Guelph
Abstract
Overfishing has the potential to severely disrupt coral reef ecosystems worldwide, while harvesting at
more sustainable levels instead can boost fish yield without damaging reefs. The dispersal abilities
of reef species mean that coral reefs form highly connected environments, and the viability of reef
fish populations depends on spatially explicit processes such as the spillover effect and unauthorized
harvesting inside marine protected areas. However, much of the literature on coral conservation
and management has only examined overfishing on a local scale, without considering how different
spatial patterns of fishing levels can affect reef health both locally and regionally. Here, we simulate
a coupled human-environment model to determine how coral and herbivorous reef fish respond to
overfishing across multiple spatial scales. We find that coral and reef fish react in opposite ways
to habitat fragmentation driven by overfishing, and that a potential spillover effect from marine
protected areas into overfished patches helps coral populations far less than it does reef fish. We
also show that ongoing economic transitions from fishing to tourism have the potential to revive
fish and coral populations over a relatively short timescale, and that large-scale reef recovery is
possible even if these transitions only occur locally. Our results show the importance of considering
spatial dynamics in marine conservation efforts, and demonstrate the ability of economic factors to
cause regime shifts in human-environment systems.
Keywords: Coral reefs, overfishing, transient dynamics, human-environment model, habitat
fragmentation
Introduction
Coral reefs are home to very high levels of biodiversity [1, 2, 3], and provide vital services to
humans such as harvesting of reef fish and ecotourism [4]. Overfishing has long been known to
be a major stressor of reefs [5, 6, 7], due to its ability to shift areas from a coral-dominated to a
macroalgae-dominated state [6, 8]. Such shifts, when considered on a regional scale, can disrupt5
connectivity on a reef and give rise to fragmented rather than connected habitats. This has been
shown to alter the composition of species present [9, 10], although the overall effects of fragmentation
are ambiguous [11]. Additionally, as the economies of reefside communities transition from being
based on fishing to tourism, areas that were previously overfished may see a regime shift in the
∗Corresponding author
Email address: r2milne@uwaterloo.ca (Russell Milne)
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opposite direction, back to coral dominance. However, the speed of such a shift, as well as whether10
one can happen regionally due to local-scale economic transitions, is yet to be seen. Here, we use
a spatially explicit coral reef model using a coupled human-environment framework to investigate
these multi-scale processes, and to determine their implications for the future viability of both coral
reefs and the communities that depend on them.
Overfishing of reef fish has been cited as one of the most prominent threats to the livelihood of15
coral reefs (e.g. [5, 6, 7]). This is due to the fact that many commercially valuable species of reef
fish, and especially parrotfish, are predators of macroalgae [12, 13], which can overgrow coral and
outcompete it for available space. Fishing pressure on heavily-harvested coral reefs in the Pacific
has been estimated at or above 50 percent of organisms from many different commercially viable
species per year [14, 15]. Many of the species surveyed were being fished above levels predicted20
to be sustainable, including half of all parrotfish species in Hawaii [14], and harvesting rates in
general were often far above the rates associated with a shift to a macroalgae-dominated state
according to past modelling results [8, 16]. Further complicating matters is the fact that other
coral reef stressors, such as nutrient loading, have interacting effects with overfishing that increase
the propensity of an overfished system for a regime shift even further [17, 18].25
While overfishing is known to have deleterious effects on coral reefs, including causing regime
shifts, fishing can safely be performed at lower rates without these risks. Harvesting rates asso-
ciated with small-scale subsistence fishing, which have previously been estimated at one tenth of
commercial rates [19], have been found to be between one seventh and one third of the estimated
upper limits for sustainability of coral populations [20]. Many communities situated adjacent to30
coral reefs are in the process of transitioning from economies based around commercial fishing to
those more heavily based around tourism, including those in the Pacific [21, 22] and the Caribbean
[21, 23]. After this transition, fishing operations would typically be on a smaller scale; the wide
gap between commercial and subsistence fishing rates suggests the possibility that these economic
transitions could drive regime shifts. In particular, this raises the question of how quickly a reef35
that has previously been under very high fishing pressure can recover following such an economic
transition. In addition to this, as commercial fishing is an important industry both in terms of
how much revenue it generates [4, 24, 25] and how many people depend on it for food [6, 24], it is
necessary to balance the needs of the fishing and tourism industries as well as the coral reef itself.
Ideally, a reefside community should have a healthy reef as well as sustainable fishing and tourism40
industries; therefore, finding conditions for the coexistence of these is imperative.
In addition to featuring a wide array of trophic interactions such as the linkages that cause
coral to be harmed by overfishing, coral reef ecosystems are also very complex spatially. Part of
this is due to their sheer size. The Great Barrier Reef is the largest marine protected area in the
world [26], and the Caribbean Sea similarly features a large network of reefs offshore of various45
islands. Reefs within a given region are also incredibly heterogeneous in their internal composition,
with sites dominated by coral, macroalgae, and algal turf all being present [27]. Similarly, different
reefs, and different areas of a reef, are highly connected due to the dispersal of coral larvae [28, 29],
fish [30, 31, 32] and nutrients, and these dispersal processes themselves have different effects across
different spatial scales [29]. Therefore, damaging one part of a reef also should have farther-reaching50
effects on areas that it is connected to. However, most modelling of overfishing and other coral reef
stressors has been done strictly at local scales (see review in [33]). Because of this, an increased
focus on multi-scale effects of overfishing has the potential to uncover many new insights.
Owing to coral reefs’ size and complexity, concepts pertaining to nonlocal processes are often
seen in field and theoretical literature related to reefs. For instance, previous models considering55
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connectivity between coral reef habitats implicitly [34] and explicitly [35] have emphasized the
importance of the spillover effect, where dispersal of coral larvae or fish from relatively undisturbed
reefs into adjacent fished areas can help counteract the degradation caused by overfishing. A
potential counteracting effect is large-scale and commercial harvesting in areas that are nominally
protected, as seen with many species associated with coral reefs [36, 37, 38]. Fishing boats routinely60
travel sizable distances away from their home ports [39, 40], and outside fishers often employ overly
damaging fishing techniques against marine protected area (MPA) regulations [36]. Hence, an MPA
without enforced boundaries is liable to have substantial fishing pressure from adjacent areas outside
it. In light of this, it is important to understand how processes such as nonlocal fishing pressure
and the spillover effect can interact to affect reef health over broader spatial scales.65
Echoing the spatial heterogeneity present in coral reef ecosystems, the debate over the best
conservation strategy for coral is also spatial in nature. Habitat connectivity has been cited as
important for the design of marine protected areas (MPAs) on coral reefs [41, 42, 28], as it also has
with other types of marine ecosystems [43], and its prominence in the literature has been steadily
increasing over time [44]. However, the debate over the importance of connectivity is not closed, as70
it rests on the distances that the species being protected can disperse. One recent paper concluded
that the dispersal abilities of Caribbean reef fish are insufficient to traverse the gaps between current
MPAs [32], whereas other work has found that marine species disperse over such great distances that
the importance of connectivity in designing MPAs is minimal [45]. Because of these discrepancies
in the literature, and given the importance of establishing sound conservation strategies for coral75
reefs, more research on the optimal configuration of MPAs is needed.
Analogous to the debate over connectivity of MPAs is that over the relative threats posed by
habitat loss and habitat fragmentation. Again, this is underpinned by the dispersal abilities of the
species that would be protected. Although habitat fragmentation is a great concern in terrestrial
ecosystems, marine species generally have greater dispersal ability and are therefore affected less80
by it. Fragmentation has been shown to have highly variable effects on the functioning of coral
reefs and other marine ecosystems [11], including on abundance and biodiversity of reef fish [10],
and the effects of habitat fragmentation via degradation due to overfishing may also be countered
by mechanisms such as the spillover effect. Recent calls have been made for more research on
the variety of responses that marine communities have to fragmentation, especially research that85
integrates dynamics over both local and regional scales [11]. Hence, it is necessary to build a robust,
multi-scale theory around how important connectivity and fragmentation are for the viability of
the many species that inhabit coral reefs.
In this paper, we use a coupled human-environment model to determine the effects of overfishing
on coral reefs across both local and regional scales, and provide policy solutions for managing90
overfished reefs. We identify how economic transitions can lead to regime shifts from macroalgae to
coral dominance, and show that these transitions, when occurring locally, can promote both healthy
reefs and a sustainable economy with fishing and tourism both being viable. We test the ability of
coastal communities to stop coral decline via temporarily subsidizing the tourism industry, and find
that such short-term subsidies can drive long-term coral recovery. We contrast the spatial effects95
of fish and coral dispersal with those of nonlocal harvesting inside MPAs, and show the importance
of strict enforcement of MPA boundaries. We also determine that coral and herbivorous fish have
very different responses to habitat fragmentation, with the implication that MPA design needs to
take into account divergent needs of multiple species.
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Methods100
Model formulation
To simulate the dynamics of a coral reef, we adapted a dynamical system model of Spiecker
et al. [35] featuring herbivorous fish, coral, macroalgae, nutrients and detritus. We chose this
model because it is mechanistic and based around recruitment and mortality rates (as opposed to
state transition models, e.g. [46]), which is important as the regional-scale dynamics we investigate105
strongly involve processes like the production and dispersal of coral larvae. In order to be able to
capture the dynamics in many different areas of a reef habitat, we simulated a linear network of
patches along a coastline, interconnected via dispersal of the model’s components. This is similar
to the integro-differential equation approach used in [35], although we assumed a patchy rather
than continuous landscape in order to capture the effects of overfishing within a certain area rather110
than at a single point. In order to perform an in-depth examination of overfishing, especially as
it relates to economic transitions between fishing-based and tourism-based economies, we added a
novel differential equation to the model representing the proportion of economic activity in each
patch related to tourism (rather than fishing), with change over time driven by the relative economic
utility gained from these strategies. We also introduced a dynamic fish harvesting rate that depends115
on economic strategies in each patch and incorporates harvesting by fishing boats outside their local
patch. Our full human-environment model is below:
dHi
dt =rHiMi
kHi+MiHi−mHiHi−ξiHi+gHi
dCi
dt = (1 −Mi−Ci)gCi−mCiCi
dMi
dt = (1 −Mi−Ci)gMi−mMiMi−rHiMi
kHi+MiHi
dDi
dt =mHiHi+mCiCi+mMiMi−γiDi+gDi
dNi
dt =qi−iNi+fiγiDi−rMiNi
kMi+NiMi+gNi
dzi
dt = (1 −zi)κizi(czi+kTCi−kFhHiHi)
(1)
The dispersal functions in the model are below. For coral and macroalgae, this is part of
their growth rate, whereas for the other components this is mathematically equivalent to passive
dispersal.120
gMi(t) = P
jNj
kMj+NjrMjMjθMj(i)
gCi(t) = P
j
rCjCjθCj(i)
gI(t) = −Ii(t) + P
j
IjθIj(i), I ∈ {H, D, N }
(2)
The dynamic harvesting rate is below:
ξi(t) = X
j
hHj(1 −zj)θBj(i) + ˜
hHjzjθBj(i)(3)
Within the model, there are five biological components. Each one represents a certain functional
group or abiotic factor rather than focusing on individual species, an approach also used in e.g.
[46, 47]. These are herbivorous fish H, coral C, macroalgae M, detritus Dand nutrients N. Coral
and macroalgae compete for space offshore, and therefore their total abundance is restricted in the125
model, i.e. M+C≤1. Any space not colonized by coral or macroalgae is assumed to be covered
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by algal turf or bare rock. The herbivorous fish population has been normalized to be on the same
scale as coral and macroalgae, and hence is expressed in terms of its density over an arbitrary area.
(Scaling constants with units of area−1are therefore omitted due to being equal to 1).
In the model, herbivorous fish are assumed to eat macroalgae using a Holling Type II functional130
response, represented as a mathematically equivalent Hill function with maximum growth rate rH
and half-saturation constant kH. The fish reproduce at the rate at which they eat macroalgae,
die of natural causes at a rate mH, and are harvested at a variable rate (detailed below). Coral
and macroalgae reproduce via the dispersal of larvae and propagules [34], so their growth rate is
nonlocal. Coral larvae are created in each patch at a rate rC. This is constant in [35], but we took it135
to vary temporally, since coral reproduction events happen at specific times during the year [48] and
to allow for a mechanism for macroalgae to overgrow coral. Macroalgae propagules are created in
each patch at a rate depending on the available nutrients, which is governed by a saturation function
with maximum growth rate rMand half-saturation constant kM. At each time step, the new coral
larvae and macroalgae propagules are distributed among patches according to their distances from140
whichever patch the larvae and propagules originated in. Dispersal of new larvae and propagules
out of each patch is governed by a Gaussian dispersal kernel centred on that patch that has been
discretized (see e.g. [49]), and the intrinsic growth rate for coral or macroalgae in one patch is the
sum of the larvae or propagules created anywhere that disperse into that patch. This rate is scaled
down by the factor (1 −M−C) for both, to represent their shared carrying capacity. Coral die of145
natural causes at a rate mC, while macroalgae die of natural causes at a rate mMand are eaten
by fish as detailed above. Detritus is formed by organisms that die of natural causes at one-to-one
rates, and decays into nutrients at a rate gD. Nutrients are formed from detritus at the same rate,
scaled by a conversion constant fN, and are uptaken by macroalgae as mentioned above. Nutrients
also enter the system via inorganic processes (e.g. river outflows) at a rate qNand leave it (e.g. by150
ocean currents) at a rate eN. These processes can be seen in a schematic of the local dynamics of
the model (Fig. 1).
In addition to their local dynamics, fish, detritus and nutrients are assumed to undergo passive
dispersal between patches. The dispersal rates for these are governed by Gaussian dispersal kernels
in the same way as coral and macroalgae reproduction are. Adult coral and macroalgae are assumed155
not to move. We chose baseline values of the standard deviations of each kernel to be 1. This
represents relatively large ability for fish, coral larvae and macroalgae propagules to disperse outside
of their home patches. The standard deviations for detritus and nutrients are the same as those for
fish, coral larvae and macroalgae propagules since dispersal by the latter groups is dependent on
physical factors such as tides and ocean currents, which also drive dispersal by the former groups.160
A Gaussian dispersal kernel is also used to quantify the amount of time that fishing boats from
any given patch spend in each patch in the system (including their own), and hence the nonlocal
fishing pressure in each patch; this is denoted σB.
We complemented the biological components of the model by adding a state variable zen-
compassing local economic strategies, in a format similar to that used previously for quantifying165
support for conservation [50]. Specifically, we considered two economic strategies, namely fishing
and ecotourism, and let zibe the proportion of economic agents in patch iengaging in ecotourism.
In our model, zchanges according to the relative utility of both strategies. zincreases when a
large amount of coral is present (and hence ecotourism is more profitable), and it decreases when
large quantities of fish are available to be harvested (measured by the quantity hHiHi). We use170
the parameters kTand kFto scale how strongly support levels for tourism and fishing, respec-
tively, depend on the underlying biological conditions, and we define czas the degree to which one
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strategy is more profitable than the other due to external factors. Additionally, zchanges due to
social pressure using the replicator dynamics found in [50], under the assumption that economic
agents in a patch will be more likely to use a particular strategy if their neighbours are also using175
(and profiting from) it. We take κto be the base rate at which economic agents can switch their
strategies. zis coupled back into the model via the dynamic fishing rate, as only economic agents
engaging in fishing are assumed to fish at the higher commercial rate. This can be seen in the local
schematic (Fig. 1).
Model parametrization180
To obtain the kinetic rates for herbivorous fish growth, we surveyed the doubling times of all
parrotfish species in FishBase [51], the same method as that used in previous modelling papers (e.g.
[16, 50]). We took rH= 0.7 yr−1and kH= 0.5, since the majority of species were categorized as
having doubling times less than 15 months and nearly all of the rest were in the category of having
doubling times of 1.4 to 4.4 years. Our values produce a reproduction rate similar to the linear185
rates used in previous work [16, 50] when macroalgae cover is at its maximum of M= 1. Coral
reproduction rate for different species has been estimated at annual doubling [52], an average of
5.7 larvae per colony per year [53], and ten eggs per polyp in a yearly spawning session [54]. We
took rC= 5 yr−1, a value in the middle of this range. Macroalgae are known to grow very quickly,
and tenfold yearly growth under optimal conditions has been reported [55]. Spiecker et al. deemed190
a value of 15 for macroalgae growth rate to be biologically plausible, and their sensitivity analysis
found most state variables to be minimally responsive to changes in it, so we took rMto be the
slightly lesser value of 12 yr−1. We kept the value of mC= 0.44 yr−1from previous studies [50],
and used the low natural mortality rate of 0.1 yr−1for herbivorous fish and macroalgae.
When considering nutrient dynamics on coral reefs, we looked specifically at nitrogen. This195
was done because macroalgae and other primary producers on pristine coral reefs have shown
N-limitation, but those closer to developed areas are often saturated with nitrogen due to anthro-
pogenic input and therefore are P-limited instead [56, 57, 58]. Coral reefs have high rates of nutrient
exchange with the surrounding oceanic water [59] and short residence times [60], so we took to be
a high rate of 0.6. Nutrient input into coral reefs and other marine ecosystems has been estimated200
as on the order of 100 to 1000 kg N km−2yr−1in most areas [61, 26], with higher values for
areas of dense human settlement, and nitrogen concentration of water entering wetlands adjacent
to the Great Barrier Reef has been measured at 200 µg N L−1under flood conditions [62]. We
therefore considered values of qranging from 20 to 120 kmol N yr−1, representing the total amount
of nitrogen exported into a patch of approximately 1 km2. We took γto be 1 yr−1under the205
assumption that all detritus would decompose within a year [63, 64], and used a value of 20 kmol N
for fas nutrient input from detritus decomposition was expected to be an order of magnitude less
than input from external loading [65]. We used a half-saturation constant for nutrient uptake by
macroalgae (kM) of 80 kmol N yr−1, close to the median of the values reported in previous studies
[66, 67] after adjusting units to make kMon the same scale as N. This choice also meant that210
nitrogen availability was close to saturation at the upper ranges of qthat we tested, as expected.
We used a baseline of 0.5 for the commercial fishing rate hH; this value has been used in prior
human-environment modelling work on coral reefs [50] and is consistent with available data for
reef fish harvesting [14, 15]. We took the subsistence fishing rate ˜
hHto be 0.05, one tenth of the
baseline commercial rate [19]. Unless we were simulating economic transitions or the effects of215
tourism subsidies (see below), we took czto be zero, indicating no external economic pressure in
favour of fishing or tourism. We fit the other social parameters (κ,kT,kF) by simulating the system
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for different orders of magnitude of these parameters, and choosing values for which zconverged
to equilibrium at 0 or 1 after a plausible length of time following a shock. We ultimately took
κ=kT=kF= 1.220
Numerical methods
In order to investigate local dynamics and check when regime shifts are expected to take place,
we simulated a one-patch version of the model while varying harvesting rate (hH) and nutrient
loading rate (q). This allowed us to determine how the ability of overfishing to push coral reefs
into a macroalgae-dominant regime is mediated by nutrient loading. For each run of the model, we225
determined the post-transient average values of coral and macroalgae cover, as well as herbivorous
fish abundance. We defined different regimes as discrete regions of parameter space (harvesting
rate vs. nutrient loading rate) with qualitatively similar dynamics.
To evaluate whether overfishing-driven habitat loss or fragmentation is more detrimental to coral
and herbivorous fish, we simulated a network of 25 patches in which a fixed number of patches were230
heavily overfished (hH= 0.8) and the rest were fished at subsistence levels (hH= 0.05). We varied
both the number of overfished patches (to test the effects of habitat loss) and their configuration
(to test the effects of habitat fragmentation). Configurations that we used included one where
all overfished patches formed a contiguous area in the middle of the simulated landscape, with
large contiguous areas of non-overfished patches on either side, and several where overfished and235
non-overfished patches alternated in a repeating pattern. Each of these patterns involved taking
specifying a certain number of patches to be overfished and taking the rest to be non-overfished,
and spacing groups of overfished patches evenly throughout the system (where each group consisted
of a fixed number of patches). For each run of the model, we took the average post-transient values
of coral cover and herbivorous fish abundance across the landscape as a whole, in overfished patches240
and in non-overfished patches. This allowed us to easily separate the local and regional effects in
each scenario. We also took different values of σBto control for the effects of nonlocal harvesting,
using values of 0.25 (for a system in which fishing is almost entirely done locally) and 1 (for a system
in which substantial amounts of harvesting takes place outside of fishing boats’ local patches).
To determine the relative effects of the spillover effect and fishing across MPA boundaries, we245
determined the average equilibrium values of herbivorous fish and coral in a 25-patch system while
varying their dispersal abilities (σHand σC) and the amount of time fishing boats spend locally
(represented by the mean value of the discretized Gaussian distribution generated by σB). In the
simulated system, approximately half of the patches (13 of 25) were overfished (hH= 0.5) and the
rest were fished at subsistence rates. The overfished patches were either located in a contiguous250
stretch in the middle of the simulated area (the ”contiguous case”) or alternating one-to-one with
non-overfished patches (the ”fragmented case”).
To determine the long-term effects of economic transitions between a fishing-based economy
and a tourism-based one, as well as check conditions for the coexistence of fishing and tourism,
we ran simulations that treated czas a time-dependent function, rather than its static baseline255
value of zero. We ran different simulations to represent long-term economic trends and temporary
subsidization of the tourism industry. For long-term trends, we made czincrease linearly from 0 to
a maximum value of 5 over a span of five years. For short-term subsidization, czwas initialized at
a positive constant value (taken to be integer values from 1 to 5), held there until a time ˜
t(taken
to be integer values from 1 to 15), and then reset to 0. As above, we used a 25-patch system. In260
the long-term trend scenario, we altered czin a varying number of connected patches (1 to 25) in
the middle of the simulated area to test the effects of both local and regional economic shifts.
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In both long-term and short-term scenarios, we initialized the system using initial conditions
representative of the macroalgae-only regime, and determined the amount of time taken before the
overfished patches shifted back to a coral-dominated state (defined as over 50 percent coral cover)265
and healthy fish population levels (fish density of 1). These values were chosen to represent typical
average coral and fish levels in the coral-dominated regime (see Results section), and to be high
enough that the systemwide average attaining these levels would indicate a regional-scale recovery.
We also checked the long-term average coral cover in these systems, to test whether recovery was
temporary or permanent. The initial conditions that we used in overfished patches were 90-99270
percent macroalgae cover with the rest of the seabed covered by coral, fish density equal to the
amount of coral cover, fishing being 99 percent of the economic activity, and detritus and nutrients
being at their average steady-state levels reached under these conditions. We also took hHas the
constant value of 0.5 in each patch to preclude the possibility of natural recovery.
Results275
Local dynamics and regime shifts
We found three distinct regimes that the system’s local dynamics can take (Fig. 2). The
first of these featured cyclical dynamics, with coral dominant most of the time and macroalgae
always present. In this regime, tourism eventually composed all economic activity (Fig. 3), as
zrose and fell depending on the relative abundances of coral and fish but was always higher at280
the end of a cycle than at its beginning. Due to the lack of fishing pressure, the herbivorous
fish and macroalgae populations followed oscillatory boom-bust patterns similar to those found
in the Rosenzweig-MacArthur model. The second regime featured stable, nonzero levels of coral,
macroalgae and herbivorous fish. Here, macroalgae was dominant over coral, with coral cover of
the seabed typically above 10 percent but below 30 percent. Economic activity converged to a285
state where only fishing was viable, although very long transients were possible depending on the
social parameters (Fig. 3). However, fish populations were higher in this regime than they were in
the cyclical coral-dominant regime. The third regime was characterized by local extinction of both
coral and herbivorous fish, with macroalgae taking up all available space on the seabed. Economic
activity tended towards the all-fishing equilibrium while there were still fish available to catch.290
However, after a certain point in time, changes in economic behaviour became minimal as coral
and fish populations were both roughly zero and no economic utility could be gained from either of
them.
The boundaries between the different regimes are sharp, and transitions between the regimes
can be driven by both overfishing and excessive nutrient loading (Fig. 2). Both the macroalgae-295
dominant and macroalgae-only regimes occur when economic activity converges to the fishing-only
equilibrium, while the coral-dominant regime is coterminous with the area of parameter space in
which economic activity converges to the tourism-only equilibrium. This indicates that in the
macroalgae-dominant regime, some coral survived despite the fact that coral-related ecotourism
was not economically viable.300
Spatial effects of local overfishing
We found that herbivorous fish and coral responded in opposite ways to the two patterns of
local overfishing that we tested (Fig. 4). Herbivorous fish abundance was lower on average when
overfished patches were contiguous (i.e. they were harmed more by habitat loss than fragmentation).
In fact, the case where overfished patches alternated with non-overfished ones saw no decrease in305
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average herbivorous fish abundance compared to the baseline. In contrast, coral had greater declines
in the alternating-patch scenario, corresponding to habitat fragmentation as a result of overfishing.
There, coral cover was uniformly low across the system, whereas in the contiguous-patch scenario
large amounts of coral survived in the patches away from the stressed area.
Increasing the proportion of patches that were overfished resulted in the expected linear decline310
in systemwide coral cover, as patches shifted one by one from being in the coral-dominant regime
to the macroalgae-only regime. However, this masked nonlinear effects on coral in the overfished
and non-overfished patches (Fig. 5). In the scenario where overfished patches were contiguous,
coral cover fell off sharply in them but remained almost constant in the non-overfished ones. When
overfished and non-overfished patches formed an alternating pattern, the decline in coral cover was315
steeper and was linear in both kinds of patches, and coral was completely extirpated at a ratio of
two overfished patches for every one non-overfished one.
As with habitat fragmentation, we found that the combination of nonlocal harvesting and the
spillover effect had very different impacts on coral and herbivorous fish 7. For the case with
contiguous strings of overfished and non-overfished patches, increasing fish dispersal ability (and320
hence the strength of any potential spillover effect) caused an increase of average fish density across
the system by over 20 percent (Fig. 7b). This held regardless of how much time fishers spent locally.
In the case where overfished and non-overfished patches alternated, and therefore any overfished
patch could receive some spatial subsidies from an adjacent MPA, average fish density was higher
than in the contiguous case (Fig. 4, Fig. 7b) with little dependence on fish dispersal ability in325
most cases. Coral dispersal ability had almost no effect on the abundance of fish or coral, with the
exception of when both coral and fishing boats were almost entirely confined to their local patches.
In contrast, we found that unauthorized fishing across MPA boundaries could lower coral cover by
significant amounts, especially in the fragmented case (Fig. 7a) where we found losses of over thirty
percent.330
Economic transitions
When we simulated systemwide transitions from a fishing-based to a tourism-based economy, we
found that herbivorous fish returned to healthy levels after about 15 to 20 years, with the system
returning to a coral-dominated state after an additional 10 years (Fig. 6). This was dependent
on the degree to which coral was previously extirpated, as expected. Local economic transitions335
resulted in systemwide fish recovery when they occurred in as little as 12 percent of patches (Fig.
6b), and systemwide coral recovery happened when at least 56 percent of patches transitioned (Fig.
6a). (This meant that under some conditions, herbivorous fish were predicted to recover but coral
was not.) The recovery times for fish and coral following these local transitions were typically longer
by a few years than they were when the entire system transitioned, although the recovery times340
increased nonlinearly as the number of patches decreased towards the minimum number for which
a recovery would take place, indicating the possibility of a bifurcation.
In our simulations involving short-term subsidization of the tourism sector in a heavily over-
fished system, we found that depending on how much tourism was subsidized and for how long,
four different outcomes were possible (Fig. 8). In increasing order of subsidy length or amount,345
these were the status quo (macroalgae dominance), a temporary recovery of the herbivorous fish
population, a temporary recovery of both fish and coral, and a permanent shift to a tourism-based
economy with healthy fish and coral populations. When fish and/or coral recovered, temporarily
or permanently, this happened after the tourism subsidies had finished, indicating that tourism
subsidies set off a positive feedback loop in terms of fish and coral populations.350
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Discussion
We found that habitat fragmentation (via overfishing and subsequent shift to conditions more
favourable to macroalgae) strongly affected both coral and herbivorous fish. However, the effects of
habitat fragmentation on these two functional groups were opposite to one another. When holding
constant the percentage of patches that were overfished, coral cover was higher when long strings of355
non-overfished patches were adjacent to each other. In contrast, herbivorous fish populations were
highest when overfished patches alternated with non-overfished ones, This is consistent with the
results of Bonin et al. [10], who found that habitat fragmentation had only a temporary negative
effect on reef fish, and when disentangled from habitat loss its long-term effects were neutral or
even positive.360
In a similar vein, we found that dispersal ability of herbivorous fish had much different effects
on their abundance in contiguous and fragmented habitats. We found that the abundance of
herbivorous fish was strongly dependent on their dispersal ability in scenarios where there were
long stretches of overfished patches that could potentially receive spillover, although this saturates
when MPAs and overfished patches alternate with each other and form a fragmented pattern. In365
these areas, herbivorous fish always exhibited a strong spillover effect, elevating the fish population
size and hence the potential fish catch regardless of their dispersal ability (as there was always a
place outside of any MPA for them to disperse into).
Our results suggest that a strategy of placing MPAs in the middle of overfished areas [68] would
be effective in maximizing both fishing yield and standing fish populations, potentially by even more370
than the 20 percent increase predicted by Cabral et al. Our results also recommend the enforcement
of MPA boundaries by requiring fishing operations to harvest mostly locally (above 75 percent in
their home patches), as doing so is predicted to greatly boost coral populations while maintaining
increased fish yield from the spillover effect. Although it has recently been shown that more mobile
species show increased spillover tendencies and that some spillover is present regardless of whether375
habitats are fragmented or not [69], we believe that our study is the first to look at the interaction
between these two factors.
The differing responses of coral and herbivorous fish to habitat fragmentation and dispersal
ability can be explained by their different life history traits. When coral larvae disperse into an
adjacent patch, if that patch is completely occupied by macroalgae, the coral larvae will be much380
less able to establish themselves. This can be seen in Fig. 7, where we found that coral larval
dispersal ability has minimal effect on system coral cover. Our results here are in accordance with
field results showing that the presence of macroalgae can inhibit both coral larval settlement and
coral recruit survival after settlement [70, 71]. Hence, overfishing can cause coral to decline not
just by removing predation pressure on faster-growing algae, but also by preventing colonization385
by coral larvae. This feedback loop can drive a shift to the macroalgae-dominant regime, and its
presence explains why we found sharp regime boundaries (Fig. 2).
In the case when overfishing took place in a contiguous area, coral reacted very differently to an
increase in the proportion of overfished patches depending on the local fishing rate. The average
coral cover in overfished patches saw a steep dropoff after only a small number of patches became390
overfished, due to the breakdown of spatial subsidies. However, coral cover in the non-overfished
patches (representing MPAs or areas fished at small-scale subsistence rates) remained at reasonably
high levels, even when most patches were overfished and nonlocal harvesting was prevalent. This
indicates the possibility of a conservation trap, in which a conservation-dependent species (in this
case coral) is maintained via costly human intervention even though shifting the system to a more395
sustainable state would require less money and effort [72].
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Given the predicted high discrepancy between coral health in overfished and non-overfished
patches (or outside and inside MPAs) in the contiguous case, a manager could reasonably believe
that only by implementing strict conservation measures can the coral be protected. However, we
found two alternatives that may be considered if maintaining an MPA is not financially feasible.400
Firstly, the regime we found with high fish populations and stable coral cover (Fig. 2) features z
converging to the fishing-only equilibrium, indicating that the coral population is not conservation-
dependent. This is achievable for harvesting rates between 20 and 30 percent per year, similar
to what has been seen in a previous model [50]. Secondly, we found that promoting ecotourism
can shift a system back to a coral-dominated state over an appreciable timeframe, even if such405
promotion is temporary (Fig. 8) or spatially limited in scope (Fig. 6). These additional options
allow coral reef managers more choice in the strategies they have for reef protection.
We found that following a large-scale economic transition that reduced fishing pressure on
previously degraded reefs, fish could be expected to return to healthy levels after 14 to 20 years,
with coral following about 10 years afterward. This is comparable to measured recovery times of410
reef ecosystems following other disturbances. For example, a recent long-term study on resilience
of Caribbean coral and parrotfish populations found that percentage coral cover had risen from
36 to 47 percent, in line with pre-disturbance levels, seven years after a 2010 coral bleaching
event [73]. Extending this rate of recovery of slightly less than two percent cover per year to the
scenarios that we tested, which had much lower initial conditions for coral, yields recovery times415
very similar to what we found (Fig. 6). The same study found that parrotfish recovery after the
disturbance, when assisted by a law enacted the same year that banned their harvesting, happened
at a greater magnitude than coral recovery, echoing our findings that herbivorous fish recovery
during an economic transition serves as a leading indicator for coral recovery.
Another long-term study found no significant increase in coral cover from low starting points420
(about 10 and 20 percent cover) in the six years following a period of disturbances [74], in accordance
with our result that recovery from such levels should not be expected within that timeframe. Shifts
to macroalgae-dominated regimes taking 14 years, about half the length we found for a shift in
the other direction, have been observed in the field [18]; the difference can be explained by factors
such as macroalgae’s ability to inhibit coral larval settlement (Fig. 7) and its higher intrinsic425
growth rate. Additionally, prior modelling results suggest that coral is able to recover after major
hurricanes that happen once every 20 years, provided other environmental conditions are favourable
[46, 75], which is also comparable to our results. This correspondence between our socially-driven
transitions and the biologically-driven ones seen in previous field and modelling work helps validate
the social component of our model, and indicates that coupled social-environmental interactions430
will be a useful addition to coral research going forward.
In addition to the spatial dynamics of coral and herbivorous fish, our results also show that
different economic strategies (fishing and tourism) can coexist at a regional level. Specifically, we
found that economic transitions from fishing to tourism along some parts of a reef can result in
herbivorous fish populations rebounding across the system, enough so that fishing remains viable435
where the economic transitions did not take place. Our findings are supported by recent mod-
elling results showing that fishing and tourism can coexist in the same area [76], as well as field
observations that different economic strategies in marine communities have complex, overlapping
distributions [77]. Similarly, our results suggest that reef health and fish catch can be effectively
balanced by using strategies that we identified, such as selecting local areas in which tourism would440
be temporarily subsidized or annual harvesting rates would be limited to intermediate levels. As
economic models of fishing that both take into account marine protected areas and are spatially
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explicit have only been put forward recently [78, 76], we believe that spatial modelling of economic
strategies on coral reefs is an area ripe for future research.
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Tables675
Parameter Value Units Description
rH0.7 yr−1Herbivorous fish maximum intrinsic
growth rate
kH0.5 unitless Half-saturation constant for herbivo-
rous fish growth
mH0.1 yr−1Mortality rate for herbivorous fish from
natural causes (i.e. non-harvesting)
hH0.05 −0.5−0.8 yr−1Commercial fish harvesting rate
˜
hH0.05 yr−1Subsistence fish harvesting rate
rC5 yr−1Coral intrinsic growth rate
mC0.44 yr−1Coral mortality rate
rM12 yr−1Macroalgae intrinsic growth rate
kM80 kmol N yr−1Half-saturation constant for macroal-
gae growth
mM0.1 yr−1Macroalgae mortality rate
γ1 yr−1Detritus decomposition rate
q20 −60 −120 kmol N yr−1Nitrogen loading rate
0.6 yr−1Nitrogen flushing rate
f20 kmol N Scaling constant for conversion of detri-
tus into nutrients
κ1 yr−1Rate at which economic agents can
switch strategies
cz0−0−5 unitless Economic utility for tourism (as com-
pared to fishing) from external sources
kT1 unitless Scaling constant for how strongly
tourism utility varies due to coral cover
kF1 yr Scaling constant for how strongly fish-
ing utility varies due to fish catch
Table 1: Parameters, their units, and their associated values in this paper
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Figures
Figure 1: Schematic showing local interactions between model components. Red lines represent economic interactions,
blue ones represent trophic and competitive ones, and black ones represent cycling of materials.
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(a)
(b)
Figure 2: Levels of coral cover (Fig. 2a) and herbivorous fish density (Fig. 2b) in one patch as a function of harvesting
rate and nutrient loading rate, showing three distinct regimes. Values taken are the equilibrium value or the average
over one limit cycle.
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Figure 3: Time series showing coral cover, fish density and percentage of economic agents engaging in tourism for
different values of κand hH, within a single patch. The top two graphs show dynamics in the cyclic coral-dominant
regime, while the bottom two show transient dynamics in the high-fish regime.
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(a)
(b)
Figure 4: Coral cover (Fig. 4a) and fish density (Fig. 4b) in each of 25 patches, on a scale from red (low) to green
(high), showing variation between contiguous and fragmented reefs. Here, 12 of 25 patches are overfished (arranged
in groups of 1, 2, 3 and 4), and σB= 0.25. Averages of coral cover and fish density for the entire system are also
provided for each configuration.
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(a)
(b)
Figure 5: Average coral cover (Fig. 5a) and fish density (Fig. 5b) across a 25-patch system as a function of percentage
of patches overfished, showing cases where overfished patches are contiguous and dispersed throughout the system.
Values are shown for the system as a whole as well as for both overfished and non-overfished patches. Here, σB= 1.
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(a)
(b)
Figure 6: Time taken for average coral cover in a 25-patch system to return from a degraded state to 50 percent
(Fig. 6a) and average fish density to return to 1 (Fig. 6b), following long-term economic transitions from fishing
to tourism. Black boxes indicate that coral or fish was not observed to recover to the stated thresholds within 200
years.
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(a)
(b)
Figure 7: Average coral cover (Fig. 7a) and fish density (Fig. 7b) in a 25-patch system for different values of σH,
σCand σB. Here, 13 of the 25 patches were overfished. Note the differences in scale on the vertical axes.
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Figure 8: State reached by an overfished, macroalgae-dominated system after temporary subsidies to ecotourism.
The four states shown differ in their transient and steady-state behaviour.
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