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Wolbachia, a bacterium that infects insect populations, has been examined extensively in Drosophila populations and, in recent years, has garnered significant attention for its potential to reduce the spread of dengue in the Aedes mosquito population. Similar applications to Anopheles mosquitoes for the reduction of malaria have not been as thoroughly studied, as Anopheles were previously thought to be devoid of Wolbachia infection. The recent discovery, however, of Wolbachia in two separate wild Anopheles populations suggests further study is needed. We develop and analyze an ordinary differential equation model of Wolbachia infection in Anopheles mosquitoes, which demonstrate different reproductive phenotypes than Aedes mosquitoes when infected with Wolbachia. In particular, they do not show the hallmark cytoplasmic incompatibility phenotype—absence of viable offspring when infected males mate with uninfected females—or other standard sex-biasing phenotypes. Instead, evidence of increased speed of gonotrophic cycles by Wolbachia-infected females has been reported. We show that the ability for Wolbachia to invade for a basic reproductive number less than 1 (Rpop

Although the COVID-19 disease burden is heterogeneous across space, the U.S. National Academies of Sciences, Engineering, and Medicine recommends an equitable spatial allocation of pharmaceutical interventions based, for example, on population size, in the interest of speed and workability. Utilizing economic–epidemiological modeling, we benchmark the performance of ad hoc allocation rules of scarce vaccines and drugs by comparing them to the rules for a vaccine and for a drug treatment that minimize the economic damages and expenditures over time, including a penalty cost representing the social costs of deviating from an ad hoc allocation. Under different levels of vaccine and drug scarcity, we consider scenarios where length of immunity and compliance to travel restrictions vary, and consider the robustness of the rules when assumptions regarding these factors are incorrect. Because drugs and vaccines attack different points in the disease pathology, the benefits from deviating from the ad hoc rule differ. For drug treatment, optimal policies often allocate all available treatments to one jurisdiction for a period of time, while ad hoc rules act to spread out treatments across jurisdictions. For vaccines, the benefits from deviating are especially high when immunity is permanent, when there is compliance to travel restrictions, and when the supply of vaccine is low. Interestingly, a lack of compliance to travel restrictions pushes the optimal allocations of vaccine towards the ad hoc and improves the relative robustness of the ad hoc rules, as the mixing of the populations reduces the spatial heterogeneity in disease burden. JEL Classification C61, H12, H84, I18, Q54 Significance and Key Takeaways Contribution Much of the discussion around pharmaceutical interventions for COVID-19 has focused on what segments of the population to prioritize for vaccines. Two important questions have received much less attention but could be just as significant in reducing the economic and public health costs of COVID-19. First, there is the question of how much of a limited vaccine to allocate across jurisdictions within a country and within each jurisdiction. Should we allocate based on relative population size, some normalized measure of disease burden (e.g., cases per 100,000), or should we base the allocation on numbers of essential workers? Second, other pharmaceutical interventions, such as antiviral drugs are coming online and will be in limited supply at least initially. How should these drugs be allocated across and within States? We investigate these questions by benchmarking the economic and public health performance of ad hoc allocation rules against optimally-derived rules. We also investigate how robust allocation rules are to compliance to nonpharmaceutical interventions, such as travel restrictions, and to uncertainty on the degree of immunity conveyed by the pharmaceutical interventions and prior infection. Knowledge on compliance to travel restrictions is critically important to the allocation question, as research has shown that varying levels of compliance across jurisdictions impacts the spatial distribution of disease burden. Whether the economic and public health implications from spatial allocation rules are as significant as allocation within jurisdictions to different classes of people is an open question and likely depends on the objectives of the policymakers. We find economic and public health gains from spatially targeted rules even after considering additional costs associated with deviations from the ad hoc rules. Antiviral Drugs Spatial Prioritization: Drugs should be directed towards the region that has fewer infections; optimal allocation gives rise to extreme allocations where it is preferable to give all of the allotment to one jurisdiction for a period of time rather than an allocation based on relative levels of infected individuals. Epidemiological Consequences of Spatial Prioritization: Compared to the ad hoc allocation rule, where more treatments go to locations with more infected individuals, the optimal allocation results in a higher number of cumulative cases in the jurisdictions that have a higher initial level of infected individuals and fewer cumulative cases in the jurisdictions that have a lower initial level of infected individuals. Over the period of four months, however, how well the optimal more extreme allocation does in aggregate (across jurisdictions) relative to an aggregate ad hoc allocation is dependent on epidemiological, behavioral, and logistical factors. Robustness of Spatial Allocation: The optimal allocations are not robust to incomplete information on compliance to travel restrictions and immunity, and perform worse than the ad hoc allocations in cases where they are designed under one set of assumptions but yet the true state of the world is different. Policy Recommendation: Until we have more information about compliance and immunity, our analysis leads us to conclude that ad hoc allocations may be the least risky option for the allocation of antiviral drugs. Vaccines Spatial Prioritization: Compared to an ad hoc allocation rule based on relative population size as recommended by the US National Academies of Science, Engineering, and Medicine, the optimal allocation of vaccine favors the least-burdened jurisdiction, resulting in an unequal distribution from a resource allocation perspective. Epidemiological Consequences of Spatial Prioritization: The optimal allocation results in a more equal level of infection across jurisdictions in each period while the ad hoc allocation results in a more equal distribution of aggregate cumulative infections. Robustness of Spatial Allocation: In terms of economic expenditures and cumulative cases, the optimal allocation is less impacted when assumptions on immunity are incorrect than when wrong about compliance to travel restrictions. Policy Recommendation: Imposing strict travel restrictions, or e.g. forcing quarantine when traveling to another jurisdiction, and prioritizing vaccination in jurisdictions that have lower initial disease burden could prevent a significant number of cases.

The authority to manage natural capital often follows political boundaries rather than ecological. This mismatch can lead to unsustainable outcomes, as spillovers from one management area to the next may create adverse incentives for local decision making, even within a single country. At the same time, one-size-fits-all approaches of federal (centralized) authority can fail to respond to state (decentralized) heterogeneity and can result in inefficient economic or detrimental ecological outcomes. Here we utilize a spatially explicit coupled natural-human system model of a fishery to illuminate trade-offs posed by the choice between federal vs. state control of renewable resources. We solve for the dynamics of fishing effort and fish stocks that result from different approaches to federal management that vary in terms of flexibility. Adapting numerical methods from engineering, we also solve for the open-loop Nash equilibrium characterizing state management outcomes, where each state anticipates and responds to the choices of the others. We consider traditional federalism questions (state vs. federal management) as well as more contemporary questions about the economic and ecological impacts of shifting regulatory authority from one level to another. The key mechanisms behind the trade-offs include whether differences in local conditions are driven by biological or economic mechanisms; degree of flexibility embedded in the federal management; the spatial and temporal distribution of economic returns across states; and the status-quo management type. While simple rules-of-thumb are elusive, our analysis reveals the complex political economy dimensions of renewable resource federalism.

Cumulative cultural evolution, the accumulation of sequential changes within a single socially learned behaviour that results in improved function, is prominent in humans and has been documented in experimental studies of captive animals and managed wild populations. Here, we provide evidence that cumulative cultural evolution has occurred in the learned songs of Savannah sparrows. In a first step, "click trains" replaced "high note clusters" over a period of three decades. We use mathematical modelling to show that this replacement is consistent with the action of selection, rather than drift or frequency-dependent bias. Generations later, young birds elaborated the "click train" song form by adding more clicks. We show that the new songs with more clicks elicit stronger behavioural responses from both males and females. Therefore, we suggest that a combination of social learning, innovation, and sexual selection favoring a specific discrete trait was followed by directional sexual selection that resulted in naturally occurring cumulative cultural evolution in the songs of this wild animal population.

Dengue virus causes worldwide concern with nearly 100 million infected cases reported annually. The within-host dynamics differ between primary and secondary infections, where secondary infections with a different virus serotype typically last longer, produce higher viral loads, and induce more severe disease. We build upon the variable within-host virus dynamics during infections resulting in mild dengue fever and severe dengue hemorrhagic fever. We couple these within-host virus dynamics to a population-level model through a system of partial differential equations creating an immuno-epidemiological model. The resulting multiscale model examines the dynamics of between-host infections in the presence of two circulating virus strains that involves feedback from the within-host and between-hosts interactions, encompassing multiple scales. We analytically determine the relationship between the model parameters and the characteristics of the model’s solutions, and find an analytical threshold under which infections persist in the population. Furthermore, we develop and implement a full numerical scheme for our immuno-epidemiological model, allowing the simulation of population dynamics under variable parameter conditions.

SummaryThe management of insect pests has long been dominated by the use of chemical insecticides, with the aim of instantaneously killing enough individuals to limit their damage. To minimize unwanted consequences, environmentally-friendly approaches have been proposed that utilize biological control and take advantage of intrinsic demographic processes to reduce pest populations.We address the feasibility of a novel pest management strategy based on the release of insects infected withWolbachia, which causes cytoplasmic incompatibilities in its host population, into a population with a pre-existing Allee effect. We hypothesize that the transient decline in population size caused by a successful invasion ofWolbachiacan bring the population below its Allee threshold and, consequently, trigger extinction.We develop a stochastic population model that accounts forWolbachia-induced cytoplasmic incompatibilities in addition to an Allee effect arising from mating failures at low population densities. Using our model, we identify conditions under which cytoplasmic incompatibilities and Allee effects successfully interact to drive insect pest populations toward extinction. Based on our results, we delineate control strategies based on introductions ofWolbachia-infected insects.We extend this analysis to evaluate control strategies that implement successive introductions of two incompatibleWolbachiastrains. Additionally, we consider methods that combineWolbachiainvasion with mating disruption tactics to enhance the pre-existing Allee effect.We demonstrate that Wolbachia-induced cytoplasmic incompatibility and the Allee effect act independently from one another: the Allee effect does not modify theWolbachia-invasion threshold, and cytoplasmic incompatibilities only have a marginal effect on the Allee threshold. However, the interaction of these two processes can drive even large populations to extinction. The success of this method can be amplified by the introduction of multipleWolbachiacytotypes as well as the addition of mating disruption.Our study extends the existing literature by proposing the use ofWolbachiaintroductions to capitalize on pre-existing Allee effects and consequently eradicate insect pests. More generally, it highlights the importance of transient dynamics, and the relevance of manipulating a cascade of destabilizatons for pest management.

Periodical cicadas, Magicicada spp., are a useful model system for understanding the population processes that influence range boundaries. Unlike most insects, these species typically exist at very high densities (occasionally > 1000/ m2) and have unusually long life-spans (13 or 17 years). They spend most of their lives underground feeding on plant roots. After the underground period, adults emerge from the ground to mate and oviposit over a period of just a few days. Collections of populations that are developmentally synchronized across large areas are known as “broods”. There are usually sharp boundaries between spatially adjacent broods and regions of brood overlap are generally small. The exact mechanism behind this developmental synchronization and the sharp boundary between broods remain unknown: previous studies have focused on the impacts of predator-driven Allee-effects, competition among nymphs, and their impacts on the persistence of off-synchronized emergence events. Here, we present a nonlinear Leslie-type matrix model to additionally consider cicada movement between spatially separated broods, and examine its role in maintaining brood boundaries and within-brood developmental synchrony that is seen in nature. We successfully identify ranges of competition and dispersal that lead to stable coexistence of broods that differ between spatial patches.

Pertussis is a highly infectious respiratory disease that has been on the rise in many countries worldwide over the past several years. The drivers of this increase in pertussis incidence remain hotly debated, with a central and long-standing hypothesis that questions the ability of vaccines to eliminate pertussis transmission rather than simply modulate the severity of disease. In this paper, we present age-structured case notification data from all provinces of Thailand between 1981 and 2014, a period during which vaccine uptake rose substantially, permitting an evaluation of the transmission impacts of vaccination. Our analyses demonstrate decreases in incidence across all ages with increased vaccine uptake – an observation that is at odds with pertussis case notification data in a number of other countries. To explore whether these observations are consistent with a rise in herd immunity and a reduction in bacterial transmission, we analyze an age-structured model that incorporates contrasting hypotheses concerning the immunological and transmission consequences of vaccines. Our results lead us to conclude that the most parsimonious explanation for the combined reduction in incidence and the shift to older age groups in the Thailand data is vaccine-induced herd immunity.

The U.S. art museum sector is grappling with diversity. While previous work has investigated the demographic diversity of museum staffs and visitors, the diversity of artists in their collections has remained unreported. We conduct the first large-scale study of artist diversity in museums. By scraping the public online catalogs of 18 major U.S. museums, deploying a sample of 10,000 artist records comprising over 9,000 unique artists to crowdsourcing, and analyzing 45,000 responses, we infer artist genders, ethnicities, geographic origins, and birth decades. Our results are threefold. First, we provide estimates of gender and ethnic diversity at each museum, and overall, we find that 85% of artists are white and 87% are men. Second, we identify museums that are outliers, having significantly higher or lower representation of certain demographic groups than the rest of the pool. Third, we find that the relationship between museum collection mission and artist diversity is weak, suggesting that a museum wishing to increase diversity might do so without changing its emphases on specific time periods and regions. Our methodology can be used to broadly and efficiently assess diversity in other fields., Comment: 15 pages, 2 figures, minor revisions of and enhancements to text

Periodical cicadas are enigmatic organisms: broods spanning large spatial ranges consist of developmentally synchronized populations of 3-4 sympatric species that emerge as adults every 13 or 17 years. Only one brood typically occupies any single location, with well-defined boundaries separating distinct broods. The cause of such synchronous development remains uncertain, but it is known that synchronous emergence of large numbers of adults in a single year satiates predators, allowing a substantial fraction of emerging adults to survive long enough to reproduce. Competition among nymphs feeding on tree roots almost certainly plays a role in limiting populations. However, due to the difficulty of working with such long-lived subterranean life stages, the mechanisms governing competition in periodical cicadas have not been identified. A second process that may affect synchrony among periodical cicadas is their ability to delay or accelerate their emergence as adults by 1 year and accelerate it by 4 years (stragglers). We develop a nonlinear Leslie matrix-type model that describes cicada dynamics accounting for predation, competition, and stragglers. Using numerical simulations, we identify conditions that generate dynamics in which a single brood occupies a given geographical location. Our results show that while stragglers have the potential for introducing multiple sympatric broods, the interaction of interbrood competition with predation-driven Allee effects creates a system resistant to such invasions, and populations maintain developmental synchrony.

Mosquitoes are vectors for many diseases that cause significant mortality and morbidity. As mosquito populations expand their range, they may undergo mate-finding Allee effects such that their ability to successfully reproduce becomes difficult at low population density. With new technology, creating target specific gene modification may be a viable method for mosquito population control. We develop a mathematical model to investigate the effects of releasing transgenic mosquitoes into newly established, low-density mosquito populations. Our model consists of two life stages (aquatic and adults), which are divided into three genetically distinct groups: heterogeneous and homogeneous transgenic that cause female infertility and a homogeneous wild type. We perform analytical and numerical analyses on the equilibria to determine the level of saturation needed to eliminate mosquitoes in a given area. This model demonstrates the potential for a gene drive system to reduce the spread of invading mosquito populations.

Bats are important reservoirs for emerging infectious diseases, yet the mechanisms that allow highly virulent pathogens to persist within bat populations remain obscure. In Latin America, vampire-bat-transmitted rabies virus represents a key example of how such uncertainty can impede efforts to prevent cross-species transmission. Despite decades of agricultural and human health losses, control efforts have had limited success. To establish persistence mechanisms of vampire-bat-transmitted rabies virus in Latin America, we use data from a spatially replicated, longitudinal field study of vampire bats in Peru to parameterize a series of mechanistic transmission models. We find that single-colony persistence cannot occur. Instead, dispersal of bats between colonies, combined with a high frequency of immunizing nonlethal infections, is necessary to maintain rabies virus at levels consistent with field observations. Simulations show that the strong spatial component to transmission dynamics could explain the failure of bat culls to eliminate rabies and suggests that geographic coordination of control efforts might reduce transmission to humans and domestic animals. These findings offer spatial dynamics as a mechanism for rabies persistence in bats that might be important for the understanding and control of other bat-borne pathogens.

In addition to their unusually long life cycle, periodical cicadas, {\it Magicicada} spp., provide an exceptional example of spatially synchronized life stage phenology in nature. Within regions ("broods") spanning 50,000 to 500,000 km$^2$, adults emerge synchronously every 13 or 17 years. While satiation of avian predators is believed to be a key component of the ability of these populations to reach high densities, it is not clear why populations at a single location remain entirely synchronized. We develop nonlinear Leslie matrix-type models of periodical cicadas that include predation-driven Allee effects and competition in addition to reproduction and survival. Using both analytical and numerical techniques, we demonstrate the observed presence of a single brood critically depends on the relationship between fecundity, competition, and predation. We analyze the single-brood, two-brood and all-brood equilibria in the large life-span limit using a tractable hybrid approximation to the Leslie matrix model with continuous time competition in between discrete reproduction events. Within the hybrid model we prove that the single-brood equilibrium is the only stable equilibrium. This hybrid model allows us to quantitatively predict population sizes and the range of parameters for which the stable single-brood and unstable two-brood and all-brood equilibria exist. The hybrid model yields a good approximation to the numerical results for the Leslie matrix model for the biologically relevant case of a 17-year lifespan., 19 pages, 2 figures, v3 contains a general proof of the instability of multi-brood steady states

Several West African countries - Liberia, Sierra Leone and Guinea - experienced significant morbidity and mortality during the largest Ebola epidemic to date, from late 2013 through 2015. The extent of the epidemic was fueled by outbreaks in large urban population centers as well as movement of the pathogen between populations. During the epidemic there was no known vaccine or drug, so effective disease control required coordinated efforts that include both standard medical and community practices such as hospitalization, quarantine and safe burials. Due to the high connectivity of the region, control of the epidemic not only depended on internal strategies but also was impacted by neighboring countries. In this paper, we use a deterministic framework to examine the role of movement between two populations in the overall success of practices designed to minimize the extent of Ebola epidemics. We find that it is possible for even small amounts of intermixing between populations to positively impact the control of an epidemic on a more global scale.

SUMMARYMany of the fundamental concepts in studying infectious diseases are rooted in population ecology. We describe the importance of population ecology in exploring central issues in infectious disease research including identifying the drivers and dynamics of host-pathogen interactions and pathogen persistence, and evaluating the success of public health policies. The use of ecological concepts in infectious disease research is demonstrated with simple theoretical examples in addition to an analysis of case notification data of pertussis, a childhood respiratory disease, in Thailand as a case study. We stress that further integration of these fields will have significant impacts in infectious diseases research.

Preventing the establishment of invading pest species can be beneficial with respect to averting future environmental and economic impacts and also in preventing the accumulation of control costs. Allee effects play an important role in the dynamics of newly established, low-density populations by driving small populations into self-extinction, making Allee effects critical in influencing outcomes of eradication efforts. We consider interactions between management tactics in the presence of Allee effects to determine cost-effective and time-efficient combinations to achieve eradication by developing a model that considers pesticide application, predator augmentation and mating disruption as control tactics, using the gypsy moth as a case study. Our findings indicate that given a range of constant expenditure levels, applying moderate levels of pesticides in conjunction with mating disruption increases the Allee threshold which simultaneously substantially decreases the time to eradication relative to either tactic alone. In contrast, increasing predation in conjunction with other tactics requires larger economic expenditures to achieve similar outcomes for the use of pesticide application or mating disruption alone. These results demonstrate the beneficial synergy that may arise from nonlinearities associated with the simultaneous application of multiple eradication tactics and offer new prospects for preventing the establishment of damaging non-native species.

The analysis of ecological models often focuses on their asymptotic behavior, but there is increasing recognition that it is important to understand the role of transient behavior. By introducing a time delay into a model of coral–algal interactions in Caribbean coral reefs that exhibits alternative stable states (a favorable coral rich state and a degraded coral-depleted state), we demonstrate the criticality of understanding the basins of attraction for stable equilibria in addition to the systems' asymptotic behavior. Specifically, we show that although the introduction of a time delay into the model does not change the asymptotic stability of the stable equilibria, there are significant changes to their basins of attraction. An understanding of these effects is necessary when determining appropriate reef management options. We then demonstrate that this is a general phenomenon by considering similar behavior underlying the changes in the basins of attraction in a simple Lotka–Volterra model of competition.

Coral resilience is important for withstanding ecological disturbances as well as anthropogenic changes to the environment. However, the last several decades have demonstrated a decline in resilience that has often resulted in phase shifts to a degraded coral-depleted state with high levels of algal abundance. A major defining issue in current research is to identify when and how it is possible to reverse these phase shifts allowing for the ecosystem to escape coral depletion and maintain coral-based ecosystem services. We extend an analytic model to focus on the effects of over-harvesting of herbivorous reef fish in the Caribbean by explicitly including grazer dynamics which introduces feedbacks between habitat and grazer abundance posing constraints on management options excluded in previous studies. This allows us to develop ecosystem-based management recommendations for two distinct scenarios of coral reef recovery: The first follows significant habitat damage in response to a large disturbance and the second maintains reef structure but has suffered from events such as coral bleaching. We identify critical fishing effort levels to allow for coral recovery and demonstrate that regions exhibiting severe damage to reef structure have little resilience implying that fishing reductions should be coupled with other restoration methods. Regions that are coral-depleted but maintain reef structure allow for recovery given sufficiently small levels of fishing mortality. However, we demonstrate the difference in recovery time in response to varying levels of control efforts on fishing.

The removal of invasive species is the first step toward restoring an ecosystem following invasion. We develop spatially-explicit, dynamic optimal control strategies for a large class of invasion problems using linear-quadratic control. This approach allows us to produce new insights that help guide policy that could not have emerged from existing models. We assume adults are sedentary, and heterogeneous patches are connected via dispersal of offspring. We develop a generalized approach to optimally manage species across time and space and apply the framework to several examples, primarily based on Spartina alterniflora . General conclusions are drawn and we show that strong connectivity makes invasive control much more costly, demonstrating that reducing connectivity can be a cost-effective part of invasive species control.

White-nose syndrome (WNS) is a lethal infection of bats caused by the psychrophilic fungus Pseudogymnoascus destructans ( Pd ). Since the first cases of WNS were documented in 2006, it is estimated that as many as 5.5 million bats have succumbed in the United States—one of the fastest mammalian die-offs due to disease ever observed, and the first known sustained epizootic of bats. WNS is contagious between bats, and mounting evidence suggests that a persistent environmental reservoir of Pd plays a significant role in transmission as well. It is unclear, however, the relative contributions of bat-to-bat and environment-to-bat transmission to disease propagation within a colony. We analyze a mathematical model to investigate the consequences of both avenues of transmission on colony survival in addition to the efficacy of disease control strategies. Our model shows that selection of the most effective control strategies is highly dependent on the primary route of WNS transmission. Under all scenarios, however, generalized culling is ineffective and while targeted culling of infected bats may be effective under idealized conditions, it primarily has negative consequences. Thus, understanding the significance of environment-to-bat transmission is paramount to designing effective management plans.

Pertussis is a highly infectious respiratory disease that is currently responsible for nearly 300,000 annual deaths worldwide, primarily in infants in developing countries. Despite sustained high vaccine uptake, a resurgence in pertussis incidence has been reported in a number of countries. This resurgence has led to critical questions regarding the transmission impacts of vaccination and pertussis immunology. We analyzed pertussis incidence in Thailand—both age-stratified and longitudinal aggregate reports—over the past 30 y. To dissect the contributions of waning pertussis immunity and repeat infections to pertussis epidemiology in Thailand following a pronounced increase in vaccine uptake, we used likelihood-based statistical inference methods to evaluate the support for multiple competing transmission models. We found that, in contrast to other settings, there is no evidence for pertussis resurgence in Thailand, with each model examined pointing to a substantial rise in herd immunity over the past 30 y. Using a variety of empirical metrics, we verified our findings by documenting signatures of changing herd immunity over the study period. Importantly, this work leads to the conclusion that repeat infections have played little role in shaping pertussis epidemiology in Thailand. Our results are surprisingly emphatic in support of measurable impact of herd immunity given the uncertainty associated with pertussis epidemiology.

The interaction between multiple stressors on Caribbean coral reefs, namely, fishing effort and hurricane impacts, is a key element in the future sustainability of reefs. We develop an analytic model of coral-algal interactions and explicitly consider grazing by herbivorous reef fish. Further, we consider changes in structural complexity, or rugosity, in addition to the direct impacts of hurricanes, which are implemented as stochastic jump processes. The model simulations consider various levels of fishing effort corresponding to' several hurricane frequencies and impact levels dependent on geographic location. We focus on relatively short time scales so we do not explicitly include changes in ocean temperature, chemistry, or sea level rise. The general features of our approach would, however, apply to these other stressors and to the management of other systems in the face of multiple stressors. It is determined that the appropriate management policy, either local reef restoration or fisheries management, greatly depends on hurricane frequency and impact level. For sufficiently low hurricane impact and macroalgal growth rate, our results indicate that regions with lower-frequency hurricanes require stricter fishing regulations, whereas management in regions with higher-frequency hurricanes might be less concerned with enhancing grazing and instead consider whether local-scale restorative activities to increase vertical structure are cost-effective.