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Local overfishing patterns have regional effects on health of coral, and
economic transitions can promote its recovery
Russell Milne1,2, Chris T. Bauch1,2, Madhur Anand1,2
1Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, Canada
2School of Environmental Sciences, University of Guelph, Guelph, Ontario, Canada
* Corresponding author. Email address: r2milne@uwaterloo.ca
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
Statements and Declarations
This research was funded by NSERC Discovery Grants awarded to Chris T. Bauch and to Madhur
Anand. The authors declare that no competing interests exist.
Data and code availability
There is no primary data in the paper. We have made the code for simulating the model available
on Zenodo (DOI: 10.5281/zenodo.5534958).
1
Author contributions
Russell Milne: Conceptualization, formal analysis, investigation, methodology, software, visualiza-
tion, writing – original draft preparation, writing – review and editing. Chris T. Bauch: Concep-
tualization, funding acquisition, project administration, supervision, writing – review and editing.
Madhur Anand: Conceptualization, funding acquisition, pro ject administration, supervision, writ-
ing – review and editing.
2
Introduction
Coral reefs are home to very high levels of biodiversity [Bellwood and Hughes, 2001, Veron et al., 2009,
Berumen et al., 2013], and provide vital services to humans such as harvesting of reef fish and eco-
tourism [Costanza et al., 1997]. Overfishing has long been known to be a major stressor of reefs
[Roberts, 1995, McManus et al., 2000, McClanahan et al., 2008], due to its ability to shift areas5
from a coral-dominated to a macroalgae-dominated state [McManus et al., 2000, Blackwood et al., 2010].
Such shifts, when considered on a regional scale, can disrupt connectivity on a reef and give rise
to fragmented rather than connected habitats. This has been shown to alter the composition of
species present [Caley et al., 2001, Bonin et al., 2011], although the overall effects of fragmentation
are ambiguous [Yeager et al., 2020]. Additionally, as the economies of reefside communities transi-10
tion from being based on fishing to tourism, areas that were previously overfished may see a regime
shift in the opposite direction, back to coral dominance. However, the speed of such a shift, as well
as whether 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 viability15
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
of coral reefs (e.g. [Roberts, 1995, McManus et al., 2000, McClanahan et al., 2008]). This is due
to the fact that many commercially valuable species of reef fish, and especially parrotfish, are
predators of macroalgae [Mantyka and Bellwood, 2007, Ferrari et al., 2012], which can overgrow20
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 [Nadon, 2017, Lennox et al., 2019]. Many of the species surveyed were being
fished above levels predicted to be sustainable, including half of all parrotfish species in Hawaii
[Nadon, 2017], and harvesting rates in general were often far above the rates associated with a25
shift to a macroalgae-dominated state according to past modelling results [Blackwood et al., 2010,
Blackwood et al., 2011]. 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 [Zaneveld et al., 2016, Arias-Gonz´alez et al., 2017].
While overfishing is known to have deleterious effects on coral reefs, including causing regime30
shifts, fishing can safely be performed at lower rates without these risks. Harvesting rates as-
sociated with small-scale subsistence fishing, which have previously been estimated at one tenth
of commercial rates [Dalzell, 1996], have been found to be between one seventh and one third of
the estimated upper limits for sustainability of coral populations [Kuster et al., 2005]. Many com-
munities situated adjacent to coral reefs are in the process of transitioning from economies based35
around commercial fishing to those more heavily based around tourism, including those in the Pa-
cific [Birkeland, 1997, Fabinyi, 2020] and the Caribbean [Birkeland, 1997, Diedrich, 2007]. After
this transition, fishing operations would typically be on a smaller scale; the wide gap between com-
mercial 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 reef that has previously40
been under very high fishing pressure can recover following such an economic transition. In addi-
tion to this, as commercial fishing is an important industry both in terms of how much revenue
it generates [Costanza et al., 1997, Grafeld et al., 2017, Ngoc, 2019] and how many people depend
on it for food [McManus et al., 2000, Grafeld et al., 2017], it is necessary to balance the needs of
the fishing and tourism industries as well as the coral reef itself. Ideally, a reefside community45
3
should have a healthy reef as well as sustainable fishing and tourism 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 area50
in the world [McKergow et al., 2005], and the Caribbean Sea similarly features a large network
of reefs offshore of various 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 [ ˙
Zychaluk et al., 2011]. Similarly, different reefs, and different areas of a reef, are highly
connected due to the dispersal of coral larvae [Storlazzi et al., 2017, Thomson et al., 2021], fish55
[Abesamis et al., 2017, Almany et al., 2017, Beltr´an et al., 2017] and nutrients, and these dispersal
processes themselves have different effects across different spatial scales [Thomson et al., 2021].
Therefore, damaging one part of a reef also should have farther-reaching 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 [Blackwood et al., 2018]). Because of this, an increased focus60
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 of-
ten seen in field and theoretical literature related to reefs. For instance, previous models con-
sidering connectivity between coral reef habitats implicitly [Elmhirst et al., 2009] and explicitly
[Spiecker et al., 2016] have emphasized the importance of the spillover effect, where dispersal of65
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 commer-
cial harvesting in areas that are nominally protected, as seen with many species associated with
coral reefs [Camargo et al., 2008, Jupiter et al., 2012, Jacoby et al., 2020]. Fishing boats routinely
travel sizable distances away from their home ports [Fabinyi, 2010, Cabral et al., 2017], and out-70
side fishers often employ overly damaging fishing techniques against marine protected area (MPA)
regulations [Camargo et al., 2008]. 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 under-
stand how processes such as nonlocal fishing pressure and the spillover effect can interact to affect
reef health over broader spatial scales.75
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 [Almany et al., 2009,
Botsford et al., 2009, Storlazzi et al., 2017], as it also has with other types of marine ecosystems
[Laurel and Bradbury, 2006], and its prominence in the literature has been steadily increasing over80
time [Balbar and Metaxas, 2019]. However, the debate over the importance of connectivity is not
closed, as it rests on the distances that the species being protected can disperse. This is also related
to the spillover effect. Reef species that are capable of long-range dispersal will have stronger
spillover effects, so populations in MPAs that are geographically far apart will be able to reinforce
one another. In contrast, the spillover effect will be weaker when considering species with less85
capability to disperse, so MPA connectivity is a more important consideration for the conservation
of these species. One recent paper concluded that the dispersal abilities of Caribbean reef fish are
insufficient to traverse the gaps between current MPAs [Beltr´an et al., 2017], whereas other work
has found that marine species disperse over such great distances that the importance of connectivity
in designing MPAs is minimal [Costello and Connor, 2019]. Because of these discrepancies in the90
literature, and given the importance of establishing sound conservation strategies for coral reefs,
4
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 terrestrial95
ecosystems, marine species generally have greater dispersal ability and are therefore affected less
by it. Fragmentation has been shown to have highly variable effects on the functioning of coral
reefs and other marine ecosystems [Yeager et al., 2020], including on abundance and biodiversity
of reef fish [Bonin et al., 2011], 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 been100
made for more research on the variety of responses that marine communities have to fragmentation,
especially research that integrates dynamics over both local and regional scales [Yeager et al., 2020].
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 overfishing105
on coral reefs across both local and regional scales, and provide policy solutions for managing
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 find110
that such short-term subsidies can drive long-term coral recovery. We contrast the spatial effects
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.115
Methods
Model formulation
To simulate the dynamics of a coral reef, we adapted a model of Spiecker et al. [Spiecker et al., 2016]
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 transition120
models, e.g. [Mumby et al., 2007]), which is important as the regional-scale dynamics we investigate
strongly involve processes like the production and dispersal of coral larvae. In [Spiecker et al., 2016],
an integro-differential system is used to capture the dynamics in many different areas of a reef
habitat, with nonlocal processes such as organismal dispersal being spatially continuous. Since
our aim was to capture the effects of overfishing within specified areas rather than at individual125
points, we converted this system into a metacommunity version by simulating a linear network of
patches along a coastline, interconnected via dispersal of the model’s components. We kept the
assumption made in [Spiecker et al., 2016] that dispersal from one patch to another would follow a
Gaussian pattern, declining with increasing distance between the two patches in question. In order
to perform an in-depth examination of overfishing, especially as it relates to economic transitions130
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 depends on economic strategies
5
in each patch and incorporates harvesting by fishing boats outside their local patch. The biological135
components of our human-environment model are below, for ithe index of a given patch:
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−eiNi+fiγiDi−rMiNi
kMi+NiMi+gNi
(1)
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.
[Mumby et al., 2007, Babcock et al., 2016]. These are herbivorous fish H, coral C, macroalgae M,
detritus Dand nutrients N. Coral and macroalgae compete for space offshore, and therefore their140
total abundance is restricted in the model, i.e. M+C≤1. Any space not colonized by coral or
macroalgae is assumed to be covered 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).145
In the model, herbivorous fish are assumed to eat macroalgae using a Holling Type II functional
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 [Elmhirst et al., 2009], so their150
growth rate is nonlocal; these dynamics are explained below. Coral die of 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 γ. Nutrients are formed from detritus at the same rate, scaled by a conversion
constant f, and are uptaken by macroalgae as mentioned above. Nutrients also enter the system155
via inorganic processes (e.g. river outflows) at a rate qand leave it (e.g. by ocean currents) at a
rate e. These processes can be seen in a schematic of the local dynamics of the model (Fig. 1).
The functions in the model representing dispersal between patches are below. For coral and
macroalgae, these are part of their growth rates, whereas for the other components these are
mathematically equivalent to passive dispersal.160
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)
Coral larvae are created in each patch at a rate rC. This is constant in [Spiecker et al., 2016],
but we took it to vary temporally, since coral reproduction events happen at specific times during
the year [Szmant, 1986] 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 each165
time step, the new coral larvae and macroalgae propagules are distributed among patches according
6
to their distances from 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. [Lindeberg, 1990]), and the intrinsic growth rate for coral
or macroalgae in one patch is the sum of the larvae or propagules created anywhere that disperse170
into that patch. This rate is scaled down by the factor (1 −M−C) for both, to represent their
shared carrying capacity.
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 assumed175
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.180
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 quantifying
support for conservation [Thampi et al., 2018]. The differential equation governing zis below, for
ithe patch index:
dzi
dt = (1 −zi)κizi(czi+kTCi−kFhHiHi) (3)
When formulating z, we considered two economic strategies, namely fishing and ecotourism,185
and let zibe the proportion of economic agents in patch iengaging in ecotourism. In our model, z
changes 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, where hHiis the commercial fishing
rate in patch i). We use the parameters kTand kFto scale how strongly support levels for tourism190
and fishing, respectively, depend on the underlying biological conditions, and we define czas the
degree to which one strategy is more profitable than the other due to external factors. Additionally,
zchanges due to social pressure using the replicator dynamics found in [Thampi et al., 2018], under
the assumption that economic agents in a patch will be more likely to use a particular strategy if
their neighbours are also using (and profiting from) it. We take κto be the base rate at which195
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). This dynamic fishing rate is as follows, for ithe patch index:
ξi(t) = X
j
hHj(1 −zj)θBj(i) + ˜
hHjzjθBj(i)(4)
In each patch, the dynamic fishing rate is set to be the weighted average of two different rates:200
hH, the commercial rate, and ˜
hH, a background subsistence rate. This is due to the assumption
that any economic agents engaging in fishing (i.e. 1 −z) would harvest according to the commercial
rate, and that the dynamic fishing rate in any given patch would approach the subsistence rate if
economic activity in that patch approached 100 percent tourism. A Gaussian dispersal kernel is
used to quantify the amount of time that fishing boats from any given patch spend in each patch205
7
in the system (including their own), and hence the nonlocal fishing pressure in each patch; this is
denoted σB.
Model parametrization
To obtain the kinetic rates for herbivorous fish growth, we surveyed the doubling times of all
parrotfish species in FishBase [Froese and Pauly, 2021], the same method as that used in previ-210
ous modelling papers (e.g. [Blackwood et al., 2011, Thampi et al., 2018]). 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 linear rates used in previ-
ous work [Blackwood et al., 2011, Thampi et al., 2018] when macroalgae cover is at its maximum215
of M= 1. Coral reproduction rate for different species has been estimated at annual doubling
[Abbiati et al., 1992], an average of 5.7 larvae per colony per year [Santangelo et al., 2007], and ten
eggs per polyp in a yearly spawning session [Heyward and Collins, 1985]. 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 [Ruesink and Collado-Vides, 2006]. Spiecker et220
al. deemed 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
[Thampi et al., 2018], and used the low natural mortality rate of 0.1 yr−1for herbivorous fish and
macroalgae.225
When considering nutrient dynamics on coral reefs, we looked specifically at nitrogen. This
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 [Lapointe et al., 1987, Fourqurean and Zieman, 2002,
Lapointe et al., 2019]. Coral reefs have high rates of nutrient exchange with the surrounding oceanic230
water [Lowe and Falter, 2015] and short residence times [Nelson et al., 2011], so we took eto be
a high rate of 0.6. Nutrient input into coral reefs and other marine ecosystems has been es-
timated as on the order of 100 to 1000 kg N km−2yr−1in most areas [Vitousek et al., 1997,
McKergow et al., 2005], with higher values for areas of dense human settlement, or equivalently
between 0.3 and 10 kmol N km−2yr−1per capita depending on the flow rates of local rivers235
[Smith et al., 2003]. Nitrogen concentration of water entering wetlands adjacent to the Great Bar-
rier Reef has been measured at 200 µgNL−1under flood conditions [Adame et al., 2019]. 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 km2with low to intermediate population den-
sity (i.e. areas most likely to contain pristine reefs). We took γto be 1 yr−1under the assumption240
that all detritus would decompose within a year [Enr´ıquez et al., 1993, Chidami and Amyot, 2008],
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 [Voss et al., 2013]. We used a
half-saturation constant for nutrient uptake by macroalgae (kM) of 80 kmol N yr−1, close to the me-
dian of the values reported in previous studies [Pedersen and Borum, 1997, Mart´ınez et al., 2012]245
after adjusting units to make kMon the same scale as N. This choice also meant that 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 [Thampi et al., 2018] and is consistent with
8
available data for reef fish harvesting [Nadon, 2017, Lennox et al., 2019]. We took the subsistence250
fishing rate ˜
hHto be 0.05, one tenth of the baseline commercial rate [Dalzell, 1996]. Unless we
were simulating economic transitions or the effects of 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 for different orders of magnitude of these
parameters, and choosing values for which zconverged to equilibrium at 0 or 1 after a plausible255
length of time following a shock. We ultimately took κ=kT=kF= 1.
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 reefs260
into a macroalgae-dominant regime is mediated by nutrient loading. For each run of the model,
i.e. for each deterministic pair of values (hH, q), we 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. We did not encounter bistability for any parameter values within the ranges that265
we tested, and therefore each regime corresponds to one specific set of long-term model behaviour.
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 were
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 configuration270
(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 and
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,275
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 patches
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,280
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, we
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 locally285
(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 contiguous
stretch in the middle of the simulated area (the ”contiguous case”) or alternating one-to-one with
non-overfished patches (the ”fragmented case”).290
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 baseline
9
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 to295
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. In
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.300
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)
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 high305
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 90-99
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 nutrients310
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.
Results
Local dynamics and regime shifts
We found three distinct regimes that the system’s local dynamics can take (Fig. 2). The first315
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 at 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-320
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 a 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-dominant325
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. 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.330
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-
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 the335
macroalgae-dominant regime, some coral survived despite the fact that coral-related ecotourism
10
was not economically viable.
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 over-340
fished 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 in av-
erage 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 scenario345
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 decline
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,350
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 was
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 the355
spillover effect had very different impacts on coral and herbivorous fish (Fig. 6). For the case with
contiguous strings of overfished and non-overfished patches, increasing fish dispersal ability (and
hence the strength of any potential spillover effect) caused an increase of average fish density across
the system by over 20 percent (Fig. 6b). This held regardless of how much time fishers spent locally.
In the case where overfished and non-overfished patches alternated, and therefore any overfished360
patch could receive some spatial subsidies from an adjacent MPA, average fish density was higher
than in the contiguous case (Fig. 4, Fig. 6b) with little dependence on fish dispersal ability in
most cases. Coral larval 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 coral365
cover by significant amounts, especially in the fragmented case (Fig. 6a) where we found losses of
over thirty percent.
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 system370
returning to a coral-dominated state after an additional 10 years (Fig. 7). This was dependent
on the degree to which coral was previously extirpated, as expected. Local economic transitions
resulted in systemwide fish recovery when they occurred in as little as 12 percent of patches (Fig.
7b), and systemwide coral recovery happened when at least 56 percent of patches transitioned (Fig.
7a). (This meant that under some conditions, herbivorous fish were predicted to recover but coral375
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 times
increased nonlinearly as the number of patches decreased towards the minimum number for which
11
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-380
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,
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, temporarily385
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.
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 of390
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
of 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. [Bonin et al., 2011], who found that habitat fragmentation had only a395
temporary negative effect on reef fish, and when disentangled from habitat loss its long-term effects
were neutral or even positive.
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 were400
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. In
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).405
Our results suggest that a strategy of placing MPAs in the middle of overfished areas [Cabral et al., 2020]
would be effective in maximizing both fishing yield and standing fish populations, potentially by
even more 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 while410
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 whether habitats are fragmented or not [DiLorenzo et al., 2020], 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 dispersal415
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 much
less able to establish themselves. This can be seen in Fig. 6, 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 and420
coral recruit survival after settlement [Kuffner et al., 2006, Webster et al., 2015]. Hence, overfishing
can cause coral to decline not just by removing predation pressure on faster-growing algae, but also
12
by preventing colonization 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 an425
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 became
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. This430
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 more
sustainable state would require less money and effort [Cardador et al., 2015].
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 believe435
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.
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 to440
what has been seen in a previous model [Thampi et al., 2018]. Secondly, we found that promoting
ecotourism can shift a system back to a coral-dominated state over an appreciable timeframe, even
if such promotion is temporary (Fig. 8) or spatially limited in scope (Fig. 7). 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 on445
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 of
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 event450
[Steneck et al., 2019]. 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
times very similar to what we found (Fig. 7). 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 fish455
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 points
(about 10 and 20 percent cover) in the six years following a period of disturbances [Houk et al., 2014],
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 found460
for a shift in the other direction, have been observed in the field [Arias-Gonz´alez et al., 2017]; the
difference can be explained by factors such as macroalgae’s ability to inhibit coral larval settlement
(Fig. 6) and its higher intrinsic 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 [Mumby et al., 2007, Mumby and Hastings, 2007], which465
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 com-
ponent of our model, and indicates that coupled social-environmental interactions will be a useful
13
addition to coral research going forward.
In addition to the spatial dynamics of coral and herbivorous fish, our results also show that470
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 viable
where the economic transitions did not take place. Our findings are supported by recent modelling
results showing that fishing and tourism can coexist in the same area [Falc´o and Moeller, 2021], as475
well as field observations that different economic strategies in marine communities have complex,
overlapping distributions [Ruiz-Frau et al., 2013]. 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 would be temporarily subsidized or annual harvesting rates would be limited
to intermediate levels. As economic models of fishing that both take into account marine protected480
areas and are spatially explicit have only been put forward recently [Xuan and Armstrong, 2018,
Falc´o and Moeller, 2021], we believe that spatial modelling of economic strategies on coral reefs is
an area ripe for future research.
When determining the strength of the spillover effect and the differing responses of fish and coral
to habitat fragmentation, we took cz= 0, which assumes that the relative profitability of fishing485
and tourism depends solely on environmental conditions. Although this eliminated a potential
confounding factor in these analyses, it also represents a simplification compared to real-life systems,
and our results on reef recovery via economic transitions indicate that variation in czcan have a
significant environmental impact. This opens the door for future research on how changing economic
conditions could lead to more or less fragmented reefs (and hence alter species composition). Based490
on our results (see for instance Figs. 2 and 8), we predict that positive values for czwould boost
coral growth, while negative values could increase fish populations or lead to macroalgae dominance,
depending on the underlying biological conditions. (Hence, having a variety of local-scale values
for czcould provide another way to generate a fragmented system.) Since the ecosystem shifts we
found when czwas temporarily increased occurred a few years after the changes were made, we495
also predict that periodically varying czcould result in complex patterns of coral and macroalgae
dominance, and potentially a decoupling between coral cover and the preferences of economic actors.
In our simulations regarding fishing-to-tourism transitions, we started all patches at the same
low values for coral cover and fish density, and assumed that hHhad the systemwide value of
0.5. As indicated by our results, the spatial configuration of overfished areas and MPAs makes500
a big difference in the abundance of each reef species, and hence considering how heterogeneous
initial conditions affect the transition to a healthy reef would be useful. We especially believe that
determining the extent to which habitat connectivity can aid a coral reef’s recovery following an
economic shift is an interesting avenue for future research. Additionally, due to the large ranges of
many aquatic species, we believe that simulating economic changes in coral reef models larger than505
25 patches could produce great insights as to which areas will be most hospitable for reef species
going forward.
14
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Tables
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 Half-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
e0.6 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
21
Figures
Nutrients
Macro-
algae Coral
Detritus
Fish
Fishing boats
Tourism
viability
(vs. shing)
Figure 1: Schematic showing local interactions between model components. Red lines represent
economic interactions, blue ones represent trophic and competitive ones, and black ones repre-
sent cycling of materials. Solid lines denote positive feedback, while dashed lines denote negative
feedback.
22
(a)
0 10 20 30 40 50
Harvesting rate (%/yr)
0
20
40
60
80
100
120
Nutrient loading rate (kmol N yr-1)
0
0.1
0.2
0.3
0.4
0.5
0.6
Average coral cover
(b)
0 10 20 30 40 50
Harvesting rate (%/yr)
0
20
40
60
80
100
120
Nutrient loading rate (kmol N yr-1)
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Average sh density
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.
23
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.
24
(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.
25
(a)
0 20 40 60 80
Percentage of patches over shed
0
0.1
0.2
0.3
0.4
0.5
0.6
Average systemwide coral cover
Systemwide average
Non-over shed patches
Over shed patches
Contiguous cases
Fragmented cases
(b)
0 20 40 60 80
Percentage of patches over shed
0
0.5
1
1.5
2
2.5
3
3.5
Average systemwide sh density
Systemwide average
Non-over shed patches
Over shed patches
Contiguous cases
Fragmented cases
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.
26
(a)
1 2 3 4 5 6 7 8 9 10
% coral initially
4
8
12
16
20
24
28
32
36
40
44
48
52
56
60
64
68
72
76
80
84
88
92
96
100
% of patches transitioning
Time to 50% coral
24
26
28
30
32
34
36+
(b)
1 2 3 4 5 6 7 8 9 10
% coral initially
4
8
12
16
20
24
28
32
36
40
44
48
52
56
60
64
68
72
76
80
84
88
92
96
100
% of patches transitioning
Time to sh density of 1
14
16
18
20
22
24
26
28
30+
Figure 7: Time taken for average coral cover in a 25-patch system to return from a degraded state to
50 percent (Fig. 7a) and average fish density to return to 1 (Fig. 7b), 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.
28
Macroalgae-dominated system (no change)
Temporary sh recovery
Temporary sh and coral recovery
Long-term sh and coral recovery with tourism-based economy
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.
29
