Culling corallivores improves short-term coral recovery under bleaching scenarios

Our model focused on the trophic interactions among CoTS and two groups of coral within a feedback loop with natural and anthropogenic forcing. Our model draws on accepted features of the published dynamics described by Morello et al.³⁷, Condie et al.²⁸ and Condie et al.¹⁷, but is a substantial advance in terms of adding spatial structure and coupling with climate variables. Here we have resolved a fine spatiotemporal model structure, developed a novel recruitment formulation for CoTS, integrated tactical management control dynamics and incorporated the impact of broad-scale drivers upon the population dynamics of corals and CoTS at the local scale. Our model is formally fitted to a subset of the CoTS control program data described by Westcott et al.¹². We operationalised our model as a tactical and strategic tool to inform how CoTS management strategies interact with alternative disturbance and ecological realisations at the sub-reef scale, the scale at which management operates.

Data

We fitted our model to a subset of four reefs from the dataset described by Westcott et al.¹², which were consistently and intensively managed (for a map with reef locations see Fig. 2). We restricted our focus to a subset to avoid parametrisation of reef and management site dynamics. Thus, ~39% of site visits were concentrated over the 13 management sites we considered, with a mean of 20.73 ± 5.5 (mean ± standard deviation) visits across the time series relative to a mean visitation rate of 12.23 ± 4.7 (mean ± standard deviation) for the rest of the sites. Each reef in the subset contained two or more management sites where each site was visited at least 18 times. The subset was used because it contained sufficient data for estimating the 11 model parameters for each management site. Across included sites were a range of CoTS densities, coral abundances and disturbance histories^{12,72,<a data-track="click" data-track-action="reference anchor" data-track-label="link" data-test="citation-ref" aria-label="Reference 73" title="Australian Institute of Marine Science. AIMS – Manta Tow Reefs with latest survey results, 73}. Given the intensity with which these sites were managed, they therefore provided us with a valuable opportunity to formally fit the interactions between management intervention, coral abundance and CoTS dynamics in the presence of regional sequential bleaching events.

Model spatial structure and ecological components

Spatially, we considered a circular 300 km region of the Great Barrier Reef centred between Cairns and Cape Tribulation, and resolved at a daily timescale and a sub-reef spatial scale, matching the scale at which observed data were resolved^12,19. Reefs were randomly generated as points to capture possible spatial correlation in disturbance impacts between nearby reefs, as well as to allow variability in reef locations. Coral, CoTS and disturbance dynamics within the management sites of each reef were resolved relative to a 1 ha focal region. That is, each management site was captured as a 1 ha area representative of the whole site. In the Pacific, Acanthaster spp. disproportionally target faster-growing corals, predominantly Acropora, Pocillopora and Montipora²². Coral taxa characterised by slow growth rates and massive morphologies, such as Porites, are generally consumed less than expected based on their abundance²² and are thus non-preferred prey. The two modelled coral groups were the fast-growing favoured prey items of CoTS, and the slower-growing non-preferred prey. Processes resolved in the model included reproduction, density dependence, the effect of bleaching and cyclonic disturbances on corals and the impact of manual control (culling) upon CoTS and coral dynamics.

CoTS population structure

We used an age-structured approach to model CoTS population dynamics. We defined our age classes to encapsulate plausible size-at-age variation due to plastic growth. This was achieved through linking catch size classes of the management control program¹⁹ to age classes through size-age relationships developed from observations spanning multiple environmental realisations, manipulated scenarios and methodologies^55,70,74,75. Delayed growth in juvenile CoTS due to deferral of their switch to coral prey or composition of their pre-coral diet, may induce variability in the size-at-age of juveniles^52,53. However, the population-level consequences of prolonged juvenile phases are not easily observed nor understood. For example, juveniles are subject to high mortality rates in situ, delayed growth may reduce lifetime fitness and there have been no observations of juveniles during spawning periods that would indicate protracted juvenile phases^55,56,57. Consequently, suggests size-at-age is—due to an early life history mortality bottleneck or otherwise—predominantly concordant with growth curves of the literature^55,70,74,75 and the size classes we have used here. Age classes comprised annual 0, 1, 2 and 3+ groups, with 3+ being an absorbing class – once there, they stay there. Age-0 (<1 year of age) individuals were assumed to escape control program efforts due to their cryptic behaviour and small size^76,77,78, age-1 (1–2 years of age) corresponded to individuals <150 mm diameter, age-2 (2–3 years of age) individuals were 150–250 mm diameter and age-3 + (≥3 years of age) individuals were >250 mm diameter. We used empirically derived estimates of size-age detectability to model the number of CoTS within a population that would be available to control on a particular day. This accounted for the fact that some CoTS would still be undetected and remain on the reef. To this extent, we note that CoTS are voracious predators and it is unlikely that large numbers of undetected individuals would not alter coral trajectories^63,79. Individuals in the three age classes were detected by management control activities at rates of 19%, 82% and 82% respectively^63,76.

Detection rates (as perceived on SCUBA) are predominantly a function of CoTS size and population abundance^63,76. Recent studies have found little evidence for coral cover⁷⁶ or reef structural complexity⁸⁰ influencing detection rates (using SCUBA). This is likely due to divers being able to search the reef matrix for hidden CoTS unlike manta tow based approaches⁸¹. Feeding scars (which are generally a sign of proximate CoTS^24,79) are also used by culling program divers to help locate individuals hidden in the reef matrix⁸². Additionally, repeated site visits (as is the case for the sites we consider here) limit the number of CoTS that go undetected at a location¹². The detection rates described above (i.e. 19%, 82% and 82%), were therefore applied to the CoTS population within a management site independent of coral cover or structural complexity. This was such that if an individual was observable (given size-dependent detection and population abundance biases; described below under “CoTS management intervention”) then it was potentially controllable.

CoTS reproduction formulation

CoTS are a free-spawning invertebrate (i.e. releases their gametes directly into the environment), relying upon prevailing conditions to achieve fertilisation and transport larvae^49,50,83. Recruitment of CoTS was distilled into two key components—self-recruitment (same sub-reef site) from reproductively mature adults and immigrants from external sources such as neighbouring sites on the same reef and/or other hydrodynamically connected reefs^28,37,49. Due to a limited understanding of CoTS early life history and ecological processes⁵⁴, we focused only on successfully recruited and settled juveniles (age-0). Self-recruitment was represented by a novel variant of a stock-recruitment curve and immigration via a fitted constant.

Large individual CoTS contribute to the reproductive potential of a population disproportionately to their size^50,84. Moreover, the zygote production arising from a given population decreases as the female proportion of the population decreases⁵⁰. In our model, we therefore formulated recruitment in terms of female gonad mass, which in turn was a function of their size. To calculate the expected contributions of individuals within an age class, we used the biometric relationships of size-at-age^75,85,86 and gonad weight-at-size⁸⁴. Given the spatially broader and contemporary relevance of MacNeil et al.⁷⁵ to our dataset (central Great Barrier Reef; years 2013–2018) relative to the earlier works of Lucas⁸⁵ and Stump⁸⁶, we used the MacNeil et al.⁷⁵ parametrisation of the von Bertalanffy growth curve. We implemented their model fitted to all 17 reefs rather than any particular reef or subset, to capture mean dynamics across multiple environmental and CoTS density realisations. This was used in conjunction with the gonad weight-at-size model of Babcock et al.⁸⁴ to model gamete production arising from reproductively mature CoTS. Size-at-age suggested by MacNeil et al.⁷⁵. is consistent with the size-age classes implemented here in our model^70,74.

CoTS reach maturity at ~2 years of age^56,87. Consequently, to obtain the expected reproductive potential of a population, we modelled the contributions of age-2 and age-3+ female ((F)) CoTS. The expected gonad weight ({{{{{rm{GW}}}}}}) (g), of an age-2 female CoTS of size (D) on day (d) was modelled by:

Defining ({M}^{{CoTS}}left(aright)) to be the mortality rate of an age-a CoTS, we calculate the expected gonad weight of an age-3+ individual as:

This series is convergent by the ratio test, since the limiting ratio must be the proportion of individuals that survive each day. Therefore, for mathematical tractability, we estimated the average contribution of individuals aged up to 14 years (summing from (i=0) to (i=14-3), where age is (3+i)). Considering individuals up to an age of 14 years is consistent with hypothesised upper bounds of longevity in the field³¹.

Our novel formulation of the Beverton-Holt stock-recruitment relationship linked reproductively mature adult females (sex ratio ({{{{{rm{Sr}}}}}}) and proportion that spawn ({{{{{{rm{P}}}}}}}_{{{{{{rm{s}}}}}}})) to the number of successfully settled juveniles through the spawned proportion of their gonad weight (({{{{{rm{Fdy}}}}}})). As a scaffold, we employed a mathematically tractable Beverton-Holt formulation that described the steepness of the stock-recruitment relationship in terms of a parameter, ({h}_{{{{{{rm{sp}}}}}}})⁸⁸,. For shape parameters (alpha) and (beta), our novel modified Beverton-Holt stock-recruitment relationship describing this relationship was calculated as a function of reproductively mature CoTS of age-a, ({N}_{d-{delta }_{{{{{{rm{sp}}}}}}},a}^{y}) (age-2 and age-3+), on day (d-{delta }_{{{{{{rm{sp}}}}}}}). The relationship was given by:

Where parameter (alpha) was the asymptotic spawn per unit biomass and (beta) controlled the rate at which (alpha) was approached as the spawning biomass increased. Here our units of biomass were the gonad weights of spawning individuals. Defining the virgin spawning biomass of age-(a) CoTS on day (d) to be ({K}_{d}^{{{{{{rm{sp}}}}}}}left(aright)) and the virgin recruitment to be ({R}_{0}), we obtained the spawned gonad-weight per recruit, ({{{{{{rm{SPR}}}}}}}_{0}), to be

And therefore, shape parameters were given by:

and

The spawners per recruits, ({{{{{{rm{SPR}}}}}}}_{0}), was found through equilibrium calculations. Equilibrium calculation amounted to finding the number of spawners required to produce a constant population indefinitely (an equilibrium) under only CoTS natural mortality (sensu⁶³). The natural mortality rate was modelled to decrease with increasing CoTS size and age such that younger CoTS had a much higher natural mortality rate than older individuals³⁷. For a basal mortality rate of (omega) and an age-dependent decay rate of (lambda) the mortality rate of an age-(a) CoTS³⁷ was given by:

For ({K}_{d}^{{{{{{rm{sp}}}}}}}left(aright)) individuals in the virgin population of age-(a) on day (d) and for the corresponding daily instantaneous mortality of an age-(a) individuals, ({M}^{{{{{{rm{CoTS}}}}}}}(a)), we calculated the number of CoTS in each age class recursively. For a virgin population recruitment level of ({R}_{0}), the number of CoTS in their first year in said population on day (d) was described by:

For age classes (ain left{{{{{mathrm{1,2}}}}}right}):

And the absorbing age class:

Hence, we obtained an expression for the equilibrium spawned gonad weight per recruit as a function of each age classes’ natural mortality:

CoTS management intervention

A range of factors influences CoTS management efficacy and the number of CoTS that can be removed however a key driver of heterogenous impacts are CoTS size and age as well as population density^12,31,63. We incorporated a formally fitted hyperstability relationship to represent management intervention⁶³. This was based on an empirically derived relationship using data collected by Fisk and Power⁸⁹ which comprised simultaneous CPUE (CoTS.h⁻¹) and CoTS density estimates (CoTS.ha⁻¹) over a period of 20 weeks during 1995–1996. A recent study by MacNeil, et al.⁷⁶ inter-calibrated multiple data sources (including mark-recapture data) and found that Australian Marine Park Tourism Operator (AMPTO) CPUE observations (to which we fit our model) to be informative of reef-scale CoTS densities. Both MacNeil et al.⁷⁶ and Plagányi et al.⁶³ found the relationship between CPUE and known CoTS density to be hyperstable; we used the empirically validated relationship of Plagányi et al.⁶³ as it also comprised smaller CoTS compared to MacNeil et al.⁷⁶. Here, during year (y) and on day (d), CoTS were extracted through the term ({phi }_{a}^{{{{{{rm{CoTS}}}}}}}left({{{{{{rm{Fp}}}}}}}_{d}^{y}cdot {N}_{d,a}^{y}right)) where ({{{{{{rm{Fp}}}}}}}_{d}^{y}) was the fished proportion of individuals captured with ({phi }_{a}^{{{{{{rm{CoTS}}}}}}}) selectivity for age-(a) individuals given ({N}_{d,a}^{y}) CoTS of age-(a), ({t}_{d}^{y}) minutes of diver effort and a catch-per-unit-effort rate of ({{{{{{rm{CPUE}}}}}}}_{d}^{y}). The fished proportion of the sub-reef CoTS population was the number of individuals caught relative to the available or accessible population:

For a given catchability, (q), and hyperstability parameter, (h), catch-per-unit-effort was computed by:

Here the catchability accounted for the probability of removing a CoTS given its detected and the hyperstability parameter characterised the rate at which the removal rate saturated. The removal rate decoupled (saturated) when controlling high densities of CoTS populations due to handling time constraints⁶³. Hence the number of CoTS removed on a given voyage to a reef zone, ({N}_{d,a}^{y,{{{{{rm{culled}}}}}}}), was described by:

Explicitly capturing management efficacy allowed us to resolve and evaluate management’s impacts on CoTS population and coral abundance dynamics given different environmental perturbations.

CoTS population dynamics

The cumulative population dynamics equation for CoTS was obtained by amalgamating reproduction and mortality sources. We denoted the annual immigration of successful settling CoTS into a sub-reef zone on day (d) by ({I}_{{{{{{rm{d}}}}}}}^{{{{{{rm{CoTS}}}}}}}), with recruitment variability (of both immigration and self-recruitment) modelled by the parameter ({r}_{y,{{{{{rm{reef}}}}}}}^{{{{{{rm{rec}}}}}}}) with an associated standard deviation of ({sigma }_{R}). Whether recruits settled into a sub-reef zone on day (d) was captured through an impulse function ({delta }_{1}left[d+1-{delta }_{{{{{{rm{sp}}}}}}}right]). The impulse function took a value of one if its argument was true (an argument of zero i.e. (d+1-{delta }_{{{{{{rm{sp}}}}}}}=0)) and zero if the argument was false (a non-zero argument i.e. (d+1-{delta }_{{{{{{rm{sp}}}}}}};ne; 0)) which was a function of CoTS pelagic duration, ({delta }_{{{{{{rm{sp}}}}}}}). That is, all settlement was assumed to occur each year one day after the pelagic duration had elapsed. The population dynamic equations during year (y) of age-0 CoTS, ({N}_{d,a}^{y}), was therefore expressed by:

For CoTS aged 1+ years, we omitted the recruitment term and incorporated CoTS lost due to interactions with the management control program, ({N}_{d,a}^{y,{{{{{rm{culled}}}}}}}). We also captured negative feedback of low prey availability upon survival (fleft({C}_{y,d}^{{{{{{rm{f}}}}}}}right)) where ({C}_{y,d}^{{{{{{rm{f}}}}}}}) was the availability of preferred coral prey (sensu³⁷). This was such that the mortality rate increased as preferred prey decreased. The population dynamics of CoTS aged over 1 year (where (a) references CoTS age) was:

Boundary conditions ensured that the respective age classes incremented to the next age class at the end of each year. The exceptions were that there were initially no age-0 individuals at the start of the year and that age-3+ CoTS incremented back into the age-3+ class due to it being an absorbing state. Whilst Eq. (15) and Eq. (16) describe the basic population dynamics of CoTS, these dynamics were subject to perturbation through interspecific interactions with corals (see below) as well as management interventions and therefore, indirectly by thermal bleaching and cyclone events.

Coral population dynamics

Acanthaster spp. exhibit strong prey preferences and frequently consume preferred coral taxa disproportionately to their abundance^22,24,31. Reciprocally, low preferred coral abundance can induce deterioration in the condition of CoTS and increase their mortality^31,37. Resolving the differential impact of CoTS consumption upon coral taxa and the reciprocal impact of low preferred prey availability are incorporated to quantify and characterise the efficacy of management intervention in terms of coral cover dynamics. To ease subsequent notation, we have omitted superscripts that reference fast-growing corals, ({{{{{rm{f}}}}}}), and slow-growing corals, ({{{{{rm{s}}}}}}) in our following parameter descriptions.

Cyclones and bleaching are two principle threats to the Great Barrier Reef in addition to CoTS predation³⁰. In our model, both coral groups are negatively impacted by cyclones, ({M}_{y,d}^{{{{{{rm{Cyc}}}}}}}), and bleaching, ({M}_{y,d}^{{{{{{rm{Ble}}}}}}}), through the removal of coral biomass. Cyclones, as treated as an impulse source of mortality²⁸ for reefs within an explicit spatial subregion of influence and bleaching, is computed regionally over a period of 4 months between January and April^43,90,91 based on accumulated thermal stress. Bleaching and cyclone-induced mortalities are expressed as proportions. This is such that the proportion of corals that survive a given perturbation on day (d) is ({1-M}_{y,d}^{{{{{{rm{Cyc}}}}}}}) for a cyclone event or (1-{M}_{y,d}^{{{{{{rm{Ble}}}}}}}) in the case of bleaching-induced mortality. Implementation of coral dynamics involves computing coral growth minus loss due to CoTS predation, ({Q}_{y,d}), followed by abiotic factors—cyclones, ({M}_{y,d}^{{{{{{rm{Cyc}}}}}}}), and bleaching, ({M}_{y,d}^{{{{{{rm{Ble}}}}}}}). We modelled joint coral cover dynamics of the fast-growing coral group, ({C}_{y,d}^{{{{{{rm{f}}}}}}}), through:

Similarly, the dynamics of the slow-growing coral group, ({C}_{y,d}^{s}), were given by:

The distinguishing features between these two groups are their growth rates, (r), their susceptibility to CoTS predation, ({Q}_{y,d}), and their susceptibility to thermal stress, ({M}_{y,d}^{{{{{{rm{Ble}}}}}}}), and cyclones, ({M}_{y,d}^{{{{{{rm{Cyc}}}}}}}). We implemented the formally fitted coral growth rates of Morello et al³⁷.

CoTS-coral consumption

As preferred taxa are depleted, consumption increasingly switches to non-preferred taxa and individuals increase searching behaviour^22,24. We captured this dynamic such that as preferred prey items, ({C}_{y,d}^{{{{{{rm{f}}}}}}}), are depleted relative to the joint carrying capacity, individuals switched to consumption of non-preferred prey items, ({C}_{y,d}^{{{{{{rm{s}}}}}}}). We hereafter refer to this as a prey switching function which we defined on day (d) of year (y) to be ({rho }_{y,d}) through which we represented predation pressure on ({C}_{y,d}^{{{{{{rm{f}}}}}}}). Predation pressure on ({C}_{y,d}^{s}) was modelled through its reciprocal, (1-{rho }_{y,d}). Moreover, the consumption rate and feeding efficiencies of CoTS were modelled to be subject to density dependence at low abundance levels (sensu³⁷). This was such that density dependence was incorporated through a Holling type II interaction form where the CoTS per capita consumption rate was ({0.5p}_{1}^{{{{{{rm{f}}}}}}}) at low population abundance and was asymptotic to ({p}_{1}^{{{{{{rm{f}}}}}}}). The rate at which the per capita consumption rate increased as a function of CoTS abundance depending on the parameter ({p}_{2}^{{{{{{rm{f}}}}}}}) with ({{{{{rm{f}}}}}}) denoting reference to ({C}_{y,d}^{{{{{{rm{f}}}}}}}) (trading superscripts as above for ({C}_{y,d}^{{{{{{rm{s}}}}}}})). The foraging efficiency of CoTS was incorporated through a multiplicative prey switching term. We developed our prey switching as a logistics function of preferred prey depletion relative to the joint coral carrying capacity of fast and slow-growing corals, ({K}^{{{{{{rm{coral}}}}}}}), on a reef. The term was given by

Thus, the density-dependent total consumption of ({C}_{y,d}^{{{{{{rm{f}}}}}}}) within a reef site for a population of CoTS and ({C}^{{{{{{rm{f}}}}}}}) depletion level was modelled as:

And as feeding efficiency upon preferred prey items reduced, feeding rates upon non-preferred prey items, ({C}_{y,d}^{{{{{{rm{s}}}}}}}), increased as described by:

The effects of food limitation were modelled through scaling CoTS mortality rates as a function of food availability. The relationship between preferred prey abundance and CoTS mortality incorporated the prey switching term³⁷ as per:

The coral-induced mortality was tuned to the management control data available for CoTS and comparable to results obtained via estimates based on the Long Term Monitoring Program data for Lizard Island 1994–2011³⁷.

Thermal stress and coral mortality

Bleaching-induced coral mortality is a principal threat to coral reefs^3,30,92,93. Bleaching-induced mortality was formulated as a sigmoidal function relating accumulated thermal stress (Degree Heating Weeks⁹⁴) to coral mortality based on the relationship described by Condie et al.¹⁷. The sigmoidal relation described by Condie, et al¹⁷. is parametrised to the 2016 mass coral bleaching event on the Great Barrier Reef⁹². Here we extended their bleaching-induced mortality formulation to a daily sub-reef scale and considered interactions with co-occurring cyclones. The increased complexity of our formulation provided scope for capturing differential susceptibilities of corals under management intervention between and within reefs based on different disturbance regimes and their footprint/s.

The approach we implemented was parametrised to family taxonomic resolution¹⁷ which we aggregated into a bleaching-induced mortality response for CoTS’ preferred fast-growing corals and non-preferred slower-growing corals. For a given level of thermal stress in terms of Degree Heating Weeks, ({{{{{rm{DHW}}}}}}), the bleaching-induced mortality was calculated over a defined bleaching period, ({T}^{{{{{{rm{Blea}}}}}}}). The bleaching period was assumed here to last from the 1 January to the 30 of April each year (119 days) consistent with the austral summer and both the 2016 and 2017 mass bleaching events on the Great Barrier Reef^72,90,91. To account for differences in the coral groups’ susceptibility to bleaching, we defined parameter ({T}_{y}^{{{{{{rm{g}}}}}}}) as the susceptibility of group (g) to bleaching-induced mortality in a particular year. Where bleaching cooccurred with tropical cyclone/s, the ({{{{{rm{DHW}}}}}}) value was reduced to reflect the cooling induced by tropical cyclone/s at relevant locations leading up to and during the bleaching period (cyclone interactions discussed below). For purposes of induced cooling, the days since the last tropical cyclone are reset each season. The proportion of initial coral cover lost over the bleaching period given ({{{{{rm{DHW}}}}}}) accumulated thermal stress and ({d}_{{{{{{rm{postTC}}}}}}}) days post-cyclone event was described by:

With superscript ({{{{{rm{g}}}}}}) referencing either fast- or slow-growing coral groups via ({{{{{rm{f}}}}}}) or ({{{{{rm{s}}}}}}) respectively. The annual rate was calculated each day to accommodate daily changes in ({{{{{{rm{DHW}}}}}}}_{{{{{{rm{cool}}}}}}}) as the cooling signal decayed. The daily rate was then computed from the dynamic annual rate. To obtain the daily rate of loss required factoring in that ({M}_{y}^{{{{{{rm{g}}}}}},{{{{{rm{Blea}}}}}}}) was the culmination of the compounding daily proportional losses. This necessitated the use of the geometric mean to approximate the daily bleaching mortality to avoid underestimating mortality. Hence average daily loss due to bleaching was computed by:

Coral susceptibility to bleaching-induced mortality was modelled through a group-specific ‘tolerance’ based on the coral group’s intrinsic growth rate parameter¹⁷. This was such that faster-growing branching and tabular corals were more susceptible to thermal stress than their massive slower-growing counterparts^48,95,96. The thermal tolerance of coral group ({{{{{rm{g}}}}}}) described in terms of its intrinsic growth rate, ({r}^{{{{{{rm{g}}}}}}}), was modelled through¹⁷:

Where ({{{{{rm{g}}}}}}) referenced either fast- or slow-growing coral groups as previously. In addition to group-specific thermal tolerances, we also captured tolerance dynamics in response to prior bleaching events.

Recent back-to-back bleaching events on the Great Barrier Reef have highlighted that coral communities were less severely impacted if they had experienced significant bleaching in the previous year⁴³. Moreover, their adaptation and/or acclimation capacity is related to the magnitude of their prior exposure⁴³. Thus, to plausibly capture the cumulative impact of repeated bleaching events it was necessary to model the adaptation and/or acclimation of corals contingent on their recent thermal history. This was recursively achieved through incorporating a sub-reef zone’s bleaching history into the thermal tolerance of its constituents¹⁷. With superscript ({{{{{rm{g}}}}}}) referencing fast- or slow-growing corals as before, we represented the adaptation and/or acclimation of each group as per Condie et al.¹⁷ through a parameter (A). This was such that a higher value of (A) corresponded to greater reductions in the sensitivity of corals to thermal stress. Three values were considered representative of a moderate response ((A=5)), low response ((A=2.5)) and no response ((A=0)). We defined the overall bleaching-induced mortality from the previous year as ({M}_{y}^{{{{{{rm{Blea}}}}}}}) (inclusive of accumulated thermal stress and cyclone interactions). The tolerance of group (g) was therefore described by:

This formulation allowed thermal tolerance to develop proportional to bleaching mortality and adaptation and/or acclimation capacity of corals¹⁷. Combing the thermal tolerance of corals into Eq. (24) resulted in the computation of the average daily loss due to bleaching over a reef site as:

To incorporate potential cyclonic cooling signals into the adaptive capacity of coral for the following year, we recalculated ({M}_{y}^{{{{{{rm{Blea}}}}}}}) for use in the following years adaptive capacity (Eq. 26) as:

We compared projection scenarios both with and without coral adaptive capacity to quantify the cumulative impact of increased bleaching severity upon coral communities under management intervention. For projections, a single thermal stress event was specified in the year 2022 to evaluate the consequence of corallivore management in its aftermath—the focus of the present study. Thermal stress events were not stochastic as per cyclone events to establish the efficacy of CoTS management (the output) in response to a bleaching event (the input) given the expected influence of typical cyclone regimes. The year 2022 was selected to simulate the thermal stress event as this was approximately halfway through our projection period (2018–2029) and allowed sufficient time to evaluate the interaction between corallivore management and the immediate and lasting impacts of thermal stress events.

The lasting potential impacts of coral bleaching encompass reduced growth rates as well as reductions in the reproductive output of corals and lower recruitment success^97,98. Bleaching may physiologically compromise coral energy reserves and reduce growth^6,97,99. Reduced growth following bleaching is typically reported to be between one and four years, though may be longer⁴⁵. Additionally bleaching may result in the collapse of coral stock-recruitment dynamics (larval production and recruitment success) due to reductions in local and regional adult broodstock and large areas of poor settlement substrates for larvae (unstable dead corals)^43,98. For example, the loss of adult broodstock can reduce larval production to as little as 10% of historical averages^97,98. Cumulatively, reduced growth and a breakdown of stock-recruitment dynamics are likely to delay the recovery of coral assemblages⁴³. Here we captured the outcome of these processes through tuning a reduction in the net coral growth rate (previously described parameters ({r}^{{{{{{rm{f}}}}}}}) and ({r}^{{{{{{rm{s}}}}}}})) for a period of three years following a thermal stress event. This was such that net growth was reduced by half over the three years. This captured the net outcome of lower growth rates and reproductive output of surviving corals, lower settlement success and/or management sites receiving fewer recruits from other locations.

Tropical cyclone events

The approach we implemented here builds on that of Condie et al.²⁸ in that cyclone intensity was assumed to be empirically based¹⁰⁰ with rendered coral mortality random within intensity-dependent bounds²⁸. We extend this basic model by resolving cyclone intensity contours as a function of cyclone centre displacement and by scaling up impact footprints to reflect empirical cyclone sizes since 1985 on the Great Barrier Reef¹⁰¹. Our augmented approach employed cyclone intensity (implicitly through maximum wind speed) as a proxy for wave energy and explicitly resolved cyclone size and how likely coral mortality varied as a function of cyclone size, intensity and reef displacement. We assumed a cyclone impacts a reef if there existed any spatial overlap between the reef and the cyclone with coral damage rendered precautionarily based on the bounds prescribed by the highest cyclone intensity experienced by the reef. Wind speed and duration are determinant factors of wave energy¹⁰², but alternative work suggests that maximum wind speed is the best predictor of coral damage with duration or cumulative wind energy offering only marginal improvement in the prediction of coral damage¹⁰⁰. Additionally, coral community structure may lead to different susceptibilities to cyclone-induced damage which may affect damage patterns¹⁰³. Given that MICE restrict their focus to key system dynamics only, we therefore used cyclone intensity and size and different intensity-damage relationships for fast and slow-growing coral groups. This was such that increased tropical cyclone intensity increased damage ranges for corals²⁸ with wind speeds (intensity) decaying spatially away from the radius of maximum wind speed¹⁰⁴. This regionally contextualised our local-scale model under cyclone perturbation/s to characterise potential destructiveness owing to their size and the distribution of reefs¹⁰⁵.

Cyclones were modelled to inflict damage to corals on a reef as an impulse^28,100 with their frequency modelled stochastically via a Poisson process¹⁰⁶. Here, cyclone events occurred with a mean daily arrival rate of (lambda)¹⁰⁶ between the 1 November and the 1 April. For simplicity, the damaged region of a cyclone was modelled as a circular footprint with wind speed intensity contours. The centres of such footprints were calculated by uniformly generating an angular and radial displacement of the cyclone centre from the centre of a circular model focal region (diameter 300 km). This was such that a cyclone could be centred external to the focal area if the peripheral damage region overlapped the focal area. A circular model focal region capturing overlapped footprints of externally centred cyclones is consistent with the empirical work upon which the arrival rate was computed (hexagonal;¹⁰⁶).

For an event rate of ({lambda }^{{{{{{rm{cyc}}}}}}}) and an observation period of (t), the probability of observing a cyclone impacting the model region was given by:

where the observation period was fixed at the model temporal resolution, (t=1) (days), and the cyclone event rate was calculated from the annual event rate for the region¹⁰⁶ and restricted to the period over 1 November to 1 April (152 days). This yielded ({lambda }^{{{{{{rm{cyc}}}}}}} sim 0.0026). To obtain events we sampled ({{Pr }}left(Nge 1right) sim {U}left({0,1}right)) and found the time of the next event via:

If the arrival time of the next cyclone event was within a day then a cyclone impulse was simulated to occur, otherwise no cyclone impulse occurred. This approach was repeated for each day within the cyclone season and implicitly—and realistically—assumed a maximum of 1 cyclone impulse per day with a single impulse sufficient to capture cumulative mortality.

Wind speed was assumed to be constant at a given reef such that when a reef was struck by a tropical cyclone the cyclone category was constant across all sites at said reef. However, damage to reef sites varied stochastically in conjunction with its coral community composition and its associated susceptibility (Supplementary Table 4).

The cyclone category experienced by a reef was calculated as a function of the maximum wind velocity, cyclone radius and the distance of the cyclone from the reef¹⁰⁴. A reef strike was defined here as a reef’s exposure to wind speeds ≥17 m.s⁻¹ (category 1 or higher, see Supplementary Table 4) associated with a tropical cyclone. The radius of maximum wind speed, ({d}_{m}) (km), was calculated via a regression model¹⁰⁴ through:

Where (delta left({V}_{{{{{{rm{m}}}}}}}le 32.5right)) is an impulse function taking the value of one if its argument is true (i.e. ({V}_{{{{{{rm{m}}}}}}}le 32.5)) and zero otherwise (i.e. ({V}_{{{{{{rm{m}}}}}}} ; > ; 32.5)). This induced a slope change in the relationship between maximum wind velocity and its radius at a wind velocity of 32.5 m.s⁻¹ (≥ category 3 intensities). However, whilst maximum wind velocity was modelled to determine ({d}_{{{{{{rm{m}}}}}}}), the overall size of the cyclone was uncorrelated with its intensity. The overall size was uniformly sampled from 130 to 460 km diameter which allowed for the potential of complete focal area coverage and for a range of intensity-size relationships to be captured. Given a cyclone footprint of radius ({d}_{0}) (km), wind velocity, (V) (m.s⁻¹), at a distance, (d) (km), was interpolated¹⁰⁴ through:

The distance from the cyclone centre to the reef perimeter, (D) (km), is calculated through:

Thus, given a reef strike occurs ((sqrt{{d}_{0}}-sqrt{d}ge 0) required from non-integer (alpha)), the wind velocity experienced at said reef due to the tropical cyclone was calculated as (Vleft(Dright)). Wind velocity was subsequently categorised and damage to reef zone corals calculated as per Supplementary Table 4.

We resolved stochasticity in cyclone dynamics in projection scenarios. In projected scenarios cyclone arrivals, locations and intensities were probabilistically sampled and their inflicted damage upon coral communities sampled from damage ranges. Cyclone locations, their footprints, intensity ranges and corresponding damage ranges were sampled from uniform distributions. Cyclone arrivals were sampled from a Poisson distribution and considered in scenarios from 2018 to 2029. Projections were averaged over 80 simulations to capture mean dynamics and bound trajectory uncertainty due to said stochasticity.

Our cyclone model was calibrated to parameters sourced from the literature (Supplementary Tables 4-5). This was necessary since our data time series did not encompass a cyclone event and/or impacts upon a reef and cyclone-induced mortality is typically a key coral mortality source³⁰. Consequently, we were unable to validate the impacts of cyclones through formal estimation in our model. However, our endeavours to source parameters from empirical and modelling studies in conjunction with our formulation allowed us to plausibly capture the cumulative outcomes of a cyclone event at discrete locations. Our cyclone model offers a limited complexity approach that is empirically grounded to simply resolve cyclone impacts in local-scale models without the need to be coupled to a regional-scale model.

Cyclones, induced thermal stress and tactical management

The occurrence of cyclone events was modelled to directly interact with both management interventions and thermal stress events. Cyclones were assumed to realistically preclude co-occurring co-located management interventions. This was such that a management site control visit was abandoned if a cyclone preceded or was forecast within five days of a control voyage. The later interaction of cyclones with thermal stress events operated through an induced thermal cooling of sea surface temperatures (SST) at impacted locations.

In the case of the overlapping cyclone and thermally induced bleaching events, we first accounted for cyclone impacts. This was because, in addition to physical damage to corals, cyclones have the potential for regional-scale cooling of SST which can reduce coral bleaching^43,107. To capture this interaction, we resolved the duration^108,109 and amplitude¹⁰⁷ of tropical cyclone-induced cooling. We captured this interaction through Degree Heating Weeks (DHW) which is a useful metric for the accumulated thermal stress experienced by corals⁹⁴.

The duration of tropical cyclone-induced cooling was modelled through a temporal-SST response curve consistent with the work of Lloyd and Vecchi¹⁰⁸ and Vincent et al.¹⁰⁹. Cooling rapidly occurs once a tropical cyclone arrives at a location and decays in an asymptotic manner over a period of ~40–60 days^108,109. Temperatures however do not return to pre-cyclone levels and plateau at ~1/4 of the cooling signal amplitude below pre-cyclone levels^108,109. We expressed this cooling response curve as it related to bleaching-induced coral mortality through DHWs.

We based the average expected DHW cooling signal on the work of Carrigan and Puotinen¹⁰⁷. This was achieved through scaling the difference in amplitude of overlapping thermal stress-tropical cyclone events and thermal stress only events—a cooling signal amplitude of ({{{{{{rm{DHW}}}}}}}_{{{{{{rm{Amp}}}}}}} sim 1.5) DHW. Consistent with the model of Carrigan and Puotinen¹⁰⁷, we then resolved cooling within the radius of gale-force winds (category 1, 17 m.s⁻¹) to model tropical cyclone-induced cooling. Depending on the size of the tropical cyclone, this meant that an individual cyclone would not necessarily cool all reefs within the model region. However, the culmination of multiple cyclones may have limited bleaching exposure for corals across the region¹⁰⁷.

We did not treat the cooling consequences of multiple cyclones additively nor the complex interplay of oceanic feedbacks upon cyclone intensity and cooling. Such processes were beyond the scope of our study and model. If multiple cyclones occurred within our model, then the cooling signal timeline was re-initialised at impacted reefs for the last tropical cyclone at said location. Non-impacted reefs maintained the timeline for the decay of the cooling signal originating from their previous tropical cyclone interaction.

Once a tropical cyclone impacted a reef, the duration of the induced cooling signal was modelled. Price et al.¹¹⁰ found that cooling decays exponentially which is reflective of the recovery of SST following tropical cyclones as demonstrated by Lloyd and Vecchi¹⁰⁸ and Vincent et al.¹⁰⁹. We operationalised the exponential functional form in conjunction with the decay timelines of Lloyd and Vecchi¹⁰⁸ and Vincent et al.¹⁰⁹ and the DHW amplitude of Carrigan and Puotinen¹⁰⁷. We modelled the level of cooling ({{{{{{rm{DHW}}}}}}}_{{{{{{rm{cool}}}}}}}) after ({d}_{{{{{{rm{postTC}}}}}}}) days post-cyclone event by:

This ensured that once a reef experienced a tropical cyclone event, the cooling signal initialised at ({{{{{{rm{DHW}}}}}}}_{{{{{{rm{Amp}}}}}}}) and decayed to (sim frac{1}{4}{{{{{{rm{DHW}}}}}}}_{{{{{{rm{Amp}}}}}}}) after 40–60 days^108,109. The rate of decay was given by the e-folding time (days required for the cooling signal to be reduced by a factor of (e)) which we took to be 10. This is consistent with the results of Price et al.¹¹⁰, Lloyd and Vecchi¹⁰⁸ and Vincent et al.¹⁰⁹ who found e-folding times ranging from 5 through to 20 days. Thermally induced bleaching mortality of corals was computed after cyclone physical damage and cooling had been accounted for.

Formal model fitting

We formally fitted our coral-CoTS model simultaneously to coral cover data, catch-per-unit-effort data and catch numbers obtained from the management control program with dive effort (minutes) treated as an input (visits summarised in Supplementary Table 7)¹². Simultaneously fitting CoTS and coral dynamics at concurrent locations was useful here as it allowed for coral cover trajectories to help inform local CoTS abundance (sensu CoTS feeding vs. coral trajectories^63,79 and local site fidelity²⁴). Our model also used Long Term Monitoring Program (LTMP) data (based on manta tows and provided by the Australian Institute of Marine Science) which provides an independent index of relative abundance of CoTS. This was such that our model here was developed and parametrised based on an earlier version^37,111 which did not use CPUE information but was fitted to the LTMP data on CoTS relative abundance, as well as the corresponding coral cover, to estimate a number of CoTS-coral interaction parameters used in the present model (Supplementary Table 3).

Fitting and estimation of our model were achieved through Maximum Likelihood Estimation (MLE). Our objective function was the outcome of combining the negative log-likelihood contributions arising from fitting the model to multiple sets of location-specific data, across a range of environmental and ecological realisations, in conjunction with penalty terms. Specifically, we fitted coral cover (data series ({x}^{{{{{{rm{Coral}}}}}}})) and CoTS CPUEs (data series ({x}^{{{{{{rm{CoTS}}}}}}})) at each management site which contained ({n}_{{{{{{rm{Coral}}}}}}}) and ({n}_{{{{{{rm{CoTS}}}}}}}) data points respectively. This involved fitting parameters that were specific to management sites (e.g. thermal stress – DHW), reefs (e.g. recruitment variability) as well as those that were common amongst reefs (e.g. CoTS consumption rates). A parametrisation that optimised one contribution was unlikely to optimise all contributions and hence we obtained a parametrisation across all reefs and sub-regions. For a modelled catch of (N) (sum of catches across age classes), a catchability coefficient (a constant of proportionality) of ({q}_{{{{{{rm{LL}}}}}}}^{{{{{{rm{prop}}}}}}}), and data standard deviation of ({sigma }_{{{{{{rm{LL}}}}}}}) our likelihood contribution arising from a management site CPUEs was given by:

From which the data series variance and catchability coefficient were computed for the maximum likelihood estimate. The derived variance and the catchability were respectively computed as per:

and

Similarly, the likelihood contribution arising from fitting to a management site coral cover with standard deviation ({sigma }_{{Coral}}) was described by:

Where the standard deviation was given by:

We computed the negative log-likelihood objective function by summing the contributions from all management sites across considered reefs.

Fitting was conducted through the modelling language Automatic Differentiation Model Builder (ADMB) which implements a Quasi-Newton optimisation algorithm for estimation of parameters and provides Hessian based estimation of standard errors¹¹². Penalty terms were added to our likelihood function to integrate a prior understanding of system dynamics and to reduce model variability. Penalty terms encompassed recruitment variability and the magnitude of catches observed in the data.

Recruitment was expressed through recruitment deviations, ({r}_{y}), given a standard deviation of ({sigma }_{{{{{{rm{R}}}}}}}) about underlying modelled recruitment (sum of self-recruitment and immigration sources described previously). The recruitment variability negative log-likelihood penalty contribution was given by:

An additional penalty term for model deviations from the magnitude of observed catches was encompassed. This was such that a constant of proportionality relating modelled catches to observed catches tended to one. For an allowed standard deviation of ({sigma }_{{{{{{rm{CM}}}}}}}), the likelihood function was penalised for deviations from unity proportionality, ({r}^{{{{{{rm{CM}}}}}}}), through:

Model simulations were conducted in ADMB with output analysis and visualisation conducted in MATLAB.

Sensitivity to CoTS control

To test whether our projected scenarios were consistent with the period over which data were collected, we conducted a model-based before and after comparison to the impact of control. Specifically, we used the fitted trajectory for sites, including both the coral data and CoTS control data (voyages and time spent), and compared this to the model-suggested coral trajectories if CoTS control had not taken place. These were modelled over the fitted period (2013–2018) and, unlike the projected scenarios (2019–2029), were variable in terms of the timing of control (amount of time between visits was variable), the amount of time spent at sites (not a consistent number of dive minutes per visit), CoTS dynamics (recruitment was fitted and hence different annually and between reefs), and in the level of thermal stress they experienced (different sites experienced different effective levels and some sites experience back-to-back events).

Reporting summary

Further information on research design is available in the Nature Research Reporting Summary linked to this article.

Source: Ecology - nature.com