Rotational fishery closures could enhance coral recovery in systems with alternative states

Rotational closures have potential fisheries benefits, yet their impact on coral cover is unknown. Research has shown that permanent closures can protect herbivorous fish, indirectly benefiting corals, but these observations may not apply when closed periods alternate with fishing. Here, we examine how rotational closures affect coral, focusing on systems with the potential to switch between alternative stable states, a context in which temporary closures may have persistent effects. We show that rotational closures can trigger coral recovery, and in some contexts lead to better coral recovery than fixed closures of similar size. Such benthic effects are only possible if closures last long enough for change to occur. We also note that very large fixed or rotating closures may concentrate fishing effort in areas where fishing remains permitted, leading to lower overall coral cover. Our findings offer crucial guidance to managers regarding rotational closures’ potential advantages and drawbacks.

implemented in other contexts as well (Hart et al., 2020).
There has been vastly more theoretical attention devoted to MPAs than to periodic or rotational closures (Gerber et al., 2003).Although recent work has examined the effect of periodic closures on fishery outcomes (Carvalho et al., 2019;Plagányi et al., 2015), their effects on benthic outcomes, such as coral cover, remain unexplored.This gap is surprising given widespread evidence of the benefits of MPAs for corals (Mellin et al., 2016;Selig & Bruno, 2010) and suggestions that periodic closures might have similar effects (Game et al., 2009).
Spatial closures can benefit corals by increasing populations of herbivorous fish.Overharvest of herbivores has often been suggested to cause shifts from coral-to macroalgal-dominated states (Rasher et al., 2012;Zaneveld et al., 2016).In the absence of herbivory, macroalgae can proliferate, eventually displacing corals by a range of mechanisms (Roff & Mumby, 2012;Smith et al., 2006), although the loss of herbivores does not always lead to coral loss (Bruno et al., 2019).Indeed, coral recovery or conservation is a common goal of MPAs in tropical reef systems, and coral cover is often higher in areas with reduced fishing (Steneck et al., 2018;Strain et al., 2019).However, there have been no theoretical or empirical assessments of whether periodic closures increase coral cover.
Periodic closures have unusual potential for coral reefs due to the tendency for alternative community states to persist under similar environmental conditions, with abrupt shifts between states.These abrupt shifts have been widely documented, and experimental work has demonstrated the stability of alternate coral-and macroalgaldominated states (Schmitt et al., 2019(Schmitt et al., , 2021)).When either alternate stable state can persist within the same range of environmental conditions (i.e., when hysteresis is present), the effects of temporary management actions, such as periodic closures can be amplified or nullified because coral collapse or recovery may persist beyond the triggering conditions.
In this study, we expand upon previous models to investigate how periodic closures-and specifically rotational closures-affect coral in systems with the potential for hysteresis.We analyze three published models that include a variety of feedback (Blackwood et al., 2012;Rassweiler et al., 2022;van de Leemput et al., 2016).These models were developed to explore how alternative stable states could arise in coral reef ecosystems but have not been analyzed in the context of periodic closures.We simulate rotational closures and compare their effects to outcomes from fixed MPAs of equivalent size.We seek generalities across the dynamics of the three models to identify guidelines that can be useful to managers considering rotational closures.Our scenarios focus on aspects of the ecosystem that might reasonably be known to a manager: the state of the system (i.e., existing coral cover), the risk of a shift into an alternative state, and the timescale over which the ecosystem changes.Our results give practical guidance for management, identifying the situations in which rotational closures hold promise or peril for coral communities.

Models
We explore the effect of rotational closures on coral using three published models.In each model, coral and macroal-gae compete for space, with outcomes hinging on herbivorous fish abundance.To incorporate fishing into the models, we added a herbivore mortality rate to each model (see Supporting Information S1 for a detailed explanation of all equations).The models share key dynamics: Without fishing, herbivores control macroalgae and coral is abundant; with heavy fishing, macroalgae suppress corals; and with intermediate fishing, coral can persist if initially abundant, but will not recover if its population has been reduced (Figure 1).However, the three models differ in the ecological interactions that underlie hysteresis (Figure 2).The first model (van de Leemput et al., 2016), hereafter the "three-feedback model," includes three mechanisms stabilizing the coraland algal-dominated states: a positive effect of corals on herbivores (e.g., through the provision of structure), a direct negative effect of algae on coral's ability to overgrow space, and a herbivory dilution effect in which abundant algae satiates herbivores.In the second model (Blackwood et al., 2012), here termed the "herbivory-concentration model," high coral cover can concentrate herbivory on the remaining substrate, suppressing algae.This model extends Mumby et al.'s (2007) model by adding herbivores and by including a positive effect of corals on fish.The last model (Rassweiler et al., 2022), the "vulnerable-juveniles model," introduces a juvenile macroalgal stage that is more vulnerable to herbivory, preventing algae from increasing from low density except under very low herbivory.This model builds on Briggs et al. (2018) by adding herbivores.In each model, herbivorous fish biomass follows logistic growth.We parameterized each model according to their original publications (see Supporting Information S1).
To simulate rotational closures, we implemented each model in a spatial context, modeling a set of linked management areas (e.g., sections of coastline).Within each area, interactions between coral, algae, and herbivorous fish are based on the underlying model, and fish are allowed to move between areas.Our base models assumed that 95% of fish remain in the same location annually, with 5% dispersing, but we explore alternative dispersal patterns in Supporting Information S2.
We assumed equal fishing across space, except when fishing was displaced by closures and thus concentrated in remaining open areas.If a fraction of the coastline is closed, all fishing effort is distributed evenly across the remaining open areas (Supporting Information S1.2).We also explored scenarios where regulations did not fully exclude fishing (e.g., due to poaching) in Supporting Information S3.
The impact of rotational closures depends in part on the duration of the closure relative to the ecosystem's response speed, particularly the rate at which coral could recover from low densities.We quantified this recovery time by simulating coral recovery after the cessation of intense fishing.We defined the recovery time in each model as the time required for coral cover to reach 99% of its maximum, using this recovery time to scale all simulated management actions and results.

Management scenarios
The current state of the benthic ecosystem, particularly coral cover, is an important context for considering a rotational closure.Additionally, the fishing intensity will determine whether alternative equilibria are possible or if only one outcome is stable (Figure 1).Within a given management context, a manager implementing a rotational closure must make two key decisions: the fraction of the management area to close (c) and the time period for the closure to rotate across the whole area (p).The duration of an individual closure was determined by the combination of these two decisions (duration = p*c).We compared the results of rotational closures to the results of spatially fixed MPAs covering the same fraction of the system.All simulations were conducted in Python, and all code is available at https://github.com/leemonroe/Rotational-Closures.

RESULTS
Across all three models, the effect of rotational closures on coral depends on three key factors: the period of the rotational cycle, the fraction of the management area that is closed, and the initial density of coral.Rotational cycles that are short relative to the recovery time do not have persistent effects on benthic ecosystems, whereas longer closures can help coral recover.For example, in our threefeedback model starting at low coral, closing 25% of the system has little effect if the entire rotation cycle lasts twice the coral recovery time but can lead to coral recovery in all patches if one rotation cycle lasts 2.6 times the coral recovery time (Figure 3).Strikingly, this means recovery can occur even when an individual closure is not long enough for coral to fully recover.Indeed, in this example, individual closures last only two-thirds of the recovery time.
Closures must not only be of sufficient duration but also appropriate in size, in order to benefit corals.Counterintuitively, closing too large a fraction of the coastline can prevent system-scale coral recovery because closures displace fishing, concentrating harvest in the remaining open areas.For example, in the three-feedback model, closing 25% of the landscape on a rotation lasting 2.6 times the recovery time leads to coral recovery everywhere (Figure 3b), but closing 50% of the landscape for the same rotational cycle leads to alternating periods of coral dominance and coral collapse in each patch (Figure 4).
These insights hold true across a wide range of scenarios in all three models analyzed, with outcomes depending on initial coral cover.We evaluated the performance of rotational closures and permanent MPAs in each model under conditions where the reef is initially coral-dominated (Figure 5, top row) or macroalgal-dominated (bottom row).For each model, we set the fishing intensity at the center of the range, which leads to hysteresis.
If coral is initially abundant (Figure 5, top row) and closures are small, coral persists regardless of the rotational cycle.However, larger closures can concentrate fishing effort in the remaining open areas, which enables macroalgae to outcompete corals in fished zones, leading to lower average coral cover overall.Only very short rotation cycles escape this outcome, as they equalize fishing across the landscape over relevant timescales.Longer duration rotational closures yield results similar to fixed MPAs; if a large fraction of the coastline is in an MPA or long-cycle rotational closure, coral will be at its high equilibrium in the closure and its low equilibrium outside, resulting in intermediate average coral cover across the system.These qualitative results hold across all three models.The models differ somewhat in the shape of the relationships, responding at different closure sizes depending on the width of the hysteresis range.
By contrast, if coral is initially rare, rotational closures can significantly outperform MPAs in promoting coral recovery (Figure 5, bottom row).A moderately sized rotational closure (e.g., 25% of the area) can lead to widespread coral recovery, with recovery persisting after each location is reopened to fishing (e.g., Figure 3b).The result is higher average coral cover across the system, compared to implementing an MPA of equivalent size.The potential for recovery is influenced by the duration of the rotation cycle, with shorter cycles having less effect on coral.The shape of these responses differs across models, although the qualitative results hold.In some models, large long-period closures converge on the performance of MPAs, as displaced fishing causes coral loss in fished zones.
Critical thresholds become apparent when examining outcomes across a full range of closure sizes and periods (Figure 6).In a system initially dominated by coral (top row), there is a critical size above which fishing displacement risks reducing coral by triggering a collapse in the fished areas.In a system initially dominated by algae (bottom row), a similar critical size is observed, but also a  1) and low (bottom row, red star in Figure 1) coral cover, for the three models analyzed.critical closure duration, as an individual closure must last long enough to permit coral to increase.In the bottom left region of these lower graphs, coral does not recover (as illustrated in Figure 3a); in the middle region, recovery happens everywhere (Figure 3b); and in the upper right, coral cover cycles (Figure 4b).Crucially, the critical dura-tion for coral to recover is shorter than the recovery time as evidenced by the transition from low to high coral at durations below 1 (below and to the left of the white line).Results are qualitatively similar across the models but differ in the closure size at which displaced fishing reduces coral cover.The qualitative results described in Figure 5 are retained across all models under a range of alternative assumptions.If coral cover starts low, modestly sized rotational closures can outperform fixed MPAs regardless of fish mobility, with longer closure periods having greater effects (Supporting Information S2).These results hold if poaching occurs and 25% of fishing is not displaced by closures (Supporting Information S3), under alternative parameterizations in which only one feedback is present (Supporting Information S4), and over a range of fish growth rates (Supporting Information S5) including rates consistent with empirical examples (Bozec et al., 2016).
Our results apply to fishing intensities that enable alternative stable states.With lower fishing intensity, coral cover stays high under rotational closure strategies, although large fixed closures can lead to some coral decline (Supporting Information S6).For higher fishing intensity, long-period closures benefit corals but do not outperform fixed closures of similar size.

DISCUSSION
When considering implementing a rotational closure, we show the outcome depends on the current state of the ben-thic community, the closure duration, the closure size, and the potential for alternate states in the system.Each of these factors could be known, or at least estimated, by a manager considering such an action.We show that closures are more likely to be beneficial for reefs that have already lost coral, a status that will be known to any local manager.We show that closures must last a significant fraction of the time necessary for coral to recover, although not necessarily long enough for full recovery to occur.Observed recovery times for coral cover are often 10-15 years (Holbrook et al., 2018;Tomascik et al., 1996).While recovery times are likely to vary across regions and management contexts, such studies suggest closures must be multi-year (but not multi-decade) to enable coral recovery.Finally, our results are relevant when alternate stable states are possible in the system.The potential for alternate states is a function of the system's biology and the current level of fishing.While recent experimental results have demonstrated alternate stable states (Schmitt et al., 2019(Schmitt et al., , 2021) ) in coral reef systems, there is considerable controversy over how common they are in coral reef systems (Crisp et al., 2022;Mumby et al., 2013).Our results are most useful for a manager who has experienced loss of coral; while abrupt shifts in state are not definitive evidence of alternate states (Bestelmeyer et al., 2011), an ecosystem that has experienced rapid coral loss may represent a good candidate for rotational closures.Across models, we found rotational closures have substantial potential to aid coral recovery.Our most striking result is the possible conservation advantage of rotational closures over fixed closures.While the benefits of periodic closures for fishery outcomes have been increasingly appreciated (Carvalho et al., 2019;Cohen & Foale, 2013), the consensus has been that fixed MPAs are better for conservation.Here, we show that in systems with alternate states, a temporary intervention such as a rotational closure can have persistent effects on the ecosystem, potentially outperforming MPAs.This is particularly useful in contexts where fixed MPAs face heavy social opposition or where traditional management practices favor rotational closures.
However, there are important benefits of fixed longterm closures that have not been incorporated into the models we analyze.Our models focus on a fast-growing parrotfish-like herbivore.Longer-lived browsing herbivores are important for ecosystem resilience (Cheal et al., 2010) but are slower to recover from intensive fishing (McClanahan et al., 2007).Predatory fish also take longer to recover, potentially leading to complex dynamics.Fixed protected areas will allow individual fish to reach larger sizes than rotational closures, a factor not included in these models.Larger fish may have different trophic effects on the system, and often exhibit hyper-allometric scaling in reproductive output (Barneche et al., 2018).Including these factors would reduce or potentially even reverse the advantage we showed for rotational closures (Marshall et al., 2019(Marshall et al., , 2021)).
The various simplifications noted particularly limit our ability to explore fisheries outcomes.While this study focuses on outcomes for corals, existing rotational closures mostly aim to improve fisheries yields or maintain fishery sustainability.Size structure recovers more slowly than biomass, and reef fisheries often target only larger fish (Rassweiler et al., 2020).Because our models focus on the biomass of fish, neglecting size structure, they would likely overstate yields under a dynamic management strategy such as rotational closures.Fishery and recovery dynamics may also be complicated by disturbances such as cyclones, bleaching or outbreaks of coral predators.A key goal of future models should be to simultaneously predict benthic outcomes and fishery yields under realistic disturbance regimes.
An additional striking result is the ambiguous role of closure size on coral recovery.There is a large body of published work demonstrating the benefits of larger fisheries closures for conservation (Edgar et al., 2014;Maestro et al., 2019).Here, we show that in systems with tipping points, a large closure may concentrate fishing in unprotected areas, triggering degradation.The importance of accounting for fishing displacement has been widely considered in the fisheries literature (Walters et al., 2007), but the potential for ecological thresholds to amplify this has not been fully appreciated.However, coverage of protected areas is low in most coastal ecosystems, and thus risks from oversized closures are currently low.Finally, larger protected areas have other advantages not accounted for in these models; they can protect species with larger home ranges, can be easier to enforce, and can protect a wider array of connected habitats (Wilhelm et al., 2014).
Our results show that periodic and rotational closures may improve the resilience of coral reef systems with alternative stable states.We suggest these results may also have important implications for other systems with hysteresis (e.g., kelp forests and grasslands).Although much more work is needed, our results have immediate practical relevance.Periodic closures are being widely used in coral reef (and other) systems, often with relatively little theoretical guidance.This work encourages managers to monitor benthic outcomes and to consider extending closure/rotation durations in contexts where persistent recovery from degraded states might be possible.

F
Stable equilibrium coral cover as a function of fishing in the (a) three-feedback, (b) herbivory-concentration, and (c) vulnerable-juvenile models.Blue lines are equilibria starting from low coral, while green lines start at high coral.Stars mark points of high and low coral cover under the midpoint of the hysteresis range and serve as starting points for our scenarios.F I G U R E 2 Key interactions in the three models.Boxes indicate state variables, while arrows indicate interactions, labeled in italics.Direct effects point from box to box, while arrows pointing at other arrows denote cases where the abundance of one taxon modifies another process.

F
I G U R E 3 Coral outcomes under two closure durations.Plots show time series of coral cover in the three-feedback model with 25% of the area closed on a rotational cycle of (a) two times the coral recovery time or (b) 2.6 times the coral recovery time.Both scenarios start with fishing intensity in the middle of the hysteresis range and at the low equilibrium coral cover (red star in Figure1a).Insets below each graph indicate the schedule for fishing each patch, with closed periods indicated as dotted and fished periods as solid lines.

F
I G U R E 4 Coral outcomes under two closure sizes.Plots show time series of coral cover in the three-feedback model on a rotational cycle lasting 2.6 times the coral recovery time, with (a) 25% of the area closed or (b) 50% of the area closed.Both scenarios start with fishing intensity in the middle of the hysteresis range and at the low equilibrium coral cover (red star in Figure 1a).Insets below each graph indicate the schedule for fishing each patch, with closed periods indicated as dotted and fished periods as solid lines.F I G U R E 5 Average coral cover under rotational closures of the varying area closed (x-axis) and rotation period (colored lines).The black line represents the outcome of fixed closures (marine protected areas) of a given size.Results are shown for the initially high (top row, blue star in Figure

F
Average coral cover under rotational closures of varying area (x-axis) and rotation cycle period (y-axis).Results are shown for initially high (top row) and low (bottom row) coral cover, for the three models analyzed.In the lower panels, white dotted lines trace combinations of area closed and rotation cycle that result in individual closure durations equal to recovery time.Results are scaled to the coral cover at the high coral equilibrium in each model (C* in the color bar).