A MODEL OF TROPICAL MARINE RESERVE‐FISHERY LINKAGES

ABSTRACT. The excessive and unsustainable exploitation of our marine resources has led to the promotion of marine reserves as a fisheries management tool. Marine reserves, areas in which fishing is restricted or prohibited, can offer opportunities for the recovery of exploited stock and fishery enhancement. In this paper we examine the contribution of fully protected tropical marine reserves to fishery enhancement by modeling marine reserve‐fishery linkages. The consequences of reserve establishment on the long‐run equilibrium fish biomass and fishery catch levels are evaluated. In contrast to earlier models this study highlights the roles of both adult (and juvenile) fish migration and larval dispersal between the reserve and fishing grounds by employing a spawner‐recruit model. Uniform larval dispersal, uniform larval retention and complete larval retention combined with zero, moderate and high fish migration scenarios are analyzed in turn. The numerical simulations are based on Mombasa Marine National Park, Kenya, a fully protected coral reef marine reserve comprising approximately 30% of former fishing grounds. Simulation results suggest that the establishment of a fully protected marine reserve will always lead to an increase in total fish biomass. If the fishery is moderately to heavily exploited, total fishery catch will be greater with the reserve in all scenarios of fish and larval movement. If the fishery faces low levels of exploitation, catches can be optimized without a reserve but with controlled fishing effort. With high fish migration from the reserve, catches are optimized with the reserve. The optimal area of the marine reserve depends on the exploitation rate in the neighboring fishing grounds. For example, if exploitation is maintained at 40%, the ‘optimal’ reserve size would be 10%. If the rate increases to 50%, then the reserve needs to be 30% of the management area in order to maximize catches. However, even in lower exploitation fisheries (below 40%), a small reserve (up to 20%) provides significantly higher gains in fish biomass than losses in catch. Marine reserves are a valuable fisheries management tool. To achieve maximum fishery benefits they should be complemented by fishing effort controls.     

BIOECONOMIC INTERACTIONS IN AN ESTABLISHED FISHING EXCLUSION ZONE: THE GULF OF CASTELLAMMARE,NW SICILY

ABSTRACT. Fishing exclusion zones have become a key management tool for habitat protection and species conservation within fisheries. In many instances, where overfishing or habitat destruction is taking place, they are being promoted strongly. For fisheries management, their use is widespread and their popularity growing. It is clear that in some cases marine protected areas may be crucial to sustaining resources. Most research to date has considered the biological or ecological effects of such reserves. However, little real analysis has been published that takes into account the links between the biology and the economics of the fisheries involved, making the economic benefits to fisheries less clear. This paper considers an exclusion zone which was implemented in 1990 in the Gulf of Castellammare, Sicily in the form of a trawl ban, modeling the potential effects of future policy in this area. The success of the trawl ban has far exceeded expectations, and it is simulated that it may be advantageous, under strict conditions, to relax the ban in part for some of the year.     

MODELING THE EFFECT OF RARITY VALUE ON THE EXPLOITATION OF A WILDLIFE SPECIES SUBJECTED TO THE ALLEE EFFECT

The overexploitation of wildlife species is a serious problem in the field of biodiversity conservation. The species subjected to natural Allee effects are even more threatened by exploitation. Moreover, for many wildlife species, their rarity can fuel their exploitation by making them disproportionately desirable and consequently increasing their market price. In this paper, a mathematical model is proposed and analyzed to study how the value that consumers place on rarity can threaten the survival of a species subjected to natural Allee effects. It is assumed that the value of a species increases as its density declines. The analysis of model shows that the increase in the consumers' response to rarity can drive the system to admit Hopf‐bifurcation and heteroclinic bifurcation. The occurrence of the heteroclinic cycle indicates that the increase in consumers' response to rarity can cause the extinction of the species. It is found that an increase in the Allee threshold causes a decrease in the threshold value of consumers' response below which extinction is inevitable.     

FISHERY BENEFITS OF FULLY PROTECTED MARINE RESERVES: WHY HABITAT AND BEHAVIOR ARE IMPORTANT

ABSTRACT. Fully protected marine reserves, areas that are closed to all fishing, have attracted great interest for their potential to benefit fisheries. A wide range of models suggest reserves will be most effective for species that are relatively sedentary as adults but produce offspring that disperse widely. Adult spawning stocks will be secure from capture in reserves, while their offspring disperse freely into fishing grounds. Such species include animals like reef fish, mollusks and echino‐derms, and models typically indicate that when they are over‐fished, catches will be higher with reserves than without. By contrast, the same models suggest that reserves will be ineffective for animals that are mobile as adults species like cod, tuna or sharks. They remain vulnerable to fishing whenever they move outside reserves. Unfortunately, most models lack sufficient realism to effectively gauge reserve effects on migratory species. They usually assume that individuals are homogeneously distributed in a uniform sea and move randomly. They also assume that fishers hunt at random. Neither is true. For centuries, fishers have targeted places and times when their quarry are most vulnerable to capture. Protecting these sites could have disproportionately large effects on stocks. Furthermore, models rarely take into account possible benefits from improvements in habitat within reserves. Such changes, like increased biomass and complexity of bottom‐living organisms, could alter fish movement patterns and reduce natural mortality rates in ways that enhance reserve benefits. We present a simple model of reserve effects on a migratory fish species. The model incorporates spatial variation in vulnerability to capture and shows that strategically placed reserves can offer benefits in the form of increased spawning stock and catch, especially when fishing intensities are high. We need to develop a new generation of models that incorporate habitat and behaviour to better explore the utility of reserves for mobile species. Migratory behavior does not preclude reserves from benefiting a species, but it demands that we apply different principles in designing them. We must identify critical sites to species and develop reserve networks that focus protection on those places.     

WILDLIFE RESERVES,POPULATIONS, AND HUNTING OUTCOME WITH SMART WILDLIFE

We consider a hunting area and a wildlife reserve and answer the question: How does clever migration decision affect the social optimal and the private optimal hunting levels and population stocks? We analyze this in a model allowing for two‐way migration between hunting and reserve areas, where the populations’ migration decisions depend on both hunting pressure and relative population densities. In the social optimum a pure stress effect on the behavior of smart wildlife exists. This implies that the population level in the wildlife reserve tends to increase and the population level in the hunting area and hunting levels tend to decrease. On the other hand, the effect on stock tends to reduce the population in the wildlife reserve and increase the population in the hunting area and thereby also increase hunting. In the case of the private optimum, open‐access is assumed and we find that the same qualitative results arise when comparing a situation with and without stress effects, but of course at a higher level of hunting. We also show that when net social benefits of hunting dominate the net social benefits of populations, wildlife reserves are optimally placed in areas of low carrying capacity and vice versa.     

ANALYSIS OF SENSITIVITY AND UNCERTAINTY IN AN INDIVIDUAL‐BASED MODEL OF A THREATENED WILDLIFE SPECIES

Sensitivity analysis—determination of how prediction variables affect response variables—of individual‐based models (IBMs) are few but important to the interpretation of model output. We present sensitivity analysis of a spatially explicit IBM (HexSim) of a threatened species, the Northern Spotted Owl (NSO; Strix occidentalis caurina) in Washington, USA. We explored sensitivity to HexSim variables representing habitat quality, movement, dispersal, and model architecture; previous NSO studies have well established sensitivity of model output to vital rate variation. We developed “normative” (expected) model settings from field studies, and then varied the values of ≥ 1 input parameter at a time by ±10% and ±50% of their normative values to determine influence on response variables of population size and trend. We determined time to population equilibration and dynamics of populations above and below carrying capacity. Recovery time from small population size to carrying capacity greatly exceeded decay time from an overpopulated condition, suggesting lag time required to repopulate newly available habitat. Response variables were most sensitive to input parameters of habitat quality which are well‐studied for this species and controllable by management. HexSim thus seems useful for evaluating potential NSO population responses to landscape patterns for which good empirical information is available.     

THE IMPACTS OF MARINE RESERVES ON LIMITED‐ENTRY FISHERIES

ABSTRACT. We utilize a spatial bioeconomic model to investigate the impacts of creating reserves on limited‐entry fisheries. We find that reserve creation can produce win‐win situations where aggregate biomass and the common license (lease) price increase. These situations arise in biological systems where dispersal processes are prevalent and the fishery prior to reserve creation is operating at effort levels in a neighborhood of open‐access levels. We also illustrate that using strictly biological criteria for siting reserves (e.g., setting aside the most biological productive areas) will likely induce the most vociferous objections from the fishing industry. In general, we find that the dispersal rate and the degree the patches are connected play a significant role on the net impacts on the fishing sector.     

USING RESERVES TO PROTECT FISH AND WILDLIFE SIMPLIFIED MODELING APPROACHES

ABSTRACT. This paper investigates theoretically to what extent a nature reserve may protect a uniformly distributed population of fish or wildlife against negative effects of harvesting. Two objectives of this protection are considered: avoidance of population extinction and maintenance of population, at or above a given precautionary population level. The pre‐reserve population is assumed to follow the logistic growth law and two models for post‐reserve population dynamics are formulated and discussed. For Model A by assumption the logistic growth law with a common carrying capacity is valid also for the post‐reserve population growth. In Model B, it is assumed that each sub‐population has its own carrying capacity proportionate to its distribution area. For both models, migration from the high‐density area to the low‐density area is proportional to the density difference. For both models there are two possible outcomes, either a unique globally stable equilibrium, or extinction. The latter may occur when the exploitation effort is above a threshold that is derived explicitly for both models. However, when the migration rate is less than the growth rate both models imply that the reserve can be chosen so that extinction cannot occur. For the opposite case, when migration is large compared to natural growth, a reserve as the only management tool cannot assure survival of the population, but the specific way it increases critical effort is discussed.     

A prey-predator model with harvesting for fishery resource with reserve area

Considering that over exploitation would result in the extinction of the population, we propose and investigate a Holling II functional response prey-predator model with harvesting for fishery resource in a two-patch environment: a free fishing zone (patch 1) and a reserve zone (patch 2) where fishing is strictly prohibited. First, the presence of harvesting can impact the existence of equilibria. Further, stability criteria of the model is analyzed both from local and global point of view. Our results indicate that so long as the prey population in the reserved zone does not extinct, the both prey always exist, that is marine reserves should ensure the sustainability of system. Thus, marine reserves not only protect species inside the reserve area but they can also increase fish abundance in adjacent areas. Next, the existence of bionomic equilibrium and the optimal harvesting policy are discussed. The present value of revenues is maximized by using Pontryagin’s maximum principle. It is established that an infinite discount rate leads to complete dissipation of economic rent. Finally, some numerical simulations are given to illustrate our results.     

THE ECONOMICS OF MARINE RESERVES

ABSTRACT. Marine reserves can be a useful supplement to other methods of fisheries management, but marine reserves alone are not likely to achieve a great deal in economic terms andperhaps not even in terms of conservation. The effects of marine reserves with open access elsewhere are analyzed, using a logistic model for a population with a patchy distribution. It is assumedthat a marine reserve is establishedfor the territory of one of two sub‐populations which interact through migrations. The total population increases while the total catch declines for the most part. A high rate of migration would, however, dilute the conservation effect. Examining a stochastic variant of the model shows that the variability (sum of squareddeviations) of catches may decrease as a result of protecting one of the sub‐populations. Even if all rents disappear by assumption, it is possible to identify this as an economic benefit, particularly when the average catch increases. The variability of the catch falls for a range of values of the population migration parameter and variability of growth, both when the stochastic disturbances are independent and when they are perfectly correlated for the two sub‐populations, andalso when the growth variability parameter differs between the sub‐populations.     

MODELING A RIGHTS‐BASED APPROACH FOR MANAGING HABITAT IMPACTS OF FISHERIES

ABSTRACT. Limiting adverse consequences of fishing on essential fish habitat has emerged as a key fishery management objective. The conventional approach to providing habitat protection is to create MPAs or marine reserves that prohibit all or certain types of fishing in specific areas. However, there may be more cost‐effective and flexible ways to provide habitat protection. We propose an individual habitat quota (IHQ) system for habitat conservation that would utilize economic incentives to achieve habitat conservation goals cost‐effectively. Individual quotas of habitat impact units (HIU) would be distributed to fishers with an aggregate quota set to maintain a target habitat “stock.” HIU use would be based on a proxy for marginal habitat damage. We use a dynamic, explicitly spatial fishery and habitat simulation model to explore how such a system might work. We examine how outcomes are affected by spatial heterogeneity in the fishery and the scale of habitat regulation. We find that the IHQ system is a highly cost‐effective means of ensuring a given level of habitat protection, but that spatial heterogeneity and the scale of regulation can have significant effects on the distribution of habitat protection.     

ECONOMICALLY OPTIMAL MARINE RESERVES WITHOUT SPATIAL HETEROGENEITY IN A SIMPLE TWO‐PATCH MODEL

Bioeconomic analyses of spatial fishery models have established that marine reserves can be economically optimal (i.e., maximize sustainable profit) when there is some type of spatial heterogeneity in the system. Analyses of spatially continuous models and models with more than two discrete patches have also demonstrated that marine reserves can be economically optimal even when the system is spatially homogeneous. In this note we analyze a spatially homogeneous two‐patch model and show that marine reserves can be economically optimal in this case as well. The model we study includes the possibility that fishing can damage habitat. In this model, marine reserves are necessary to maximize sustainable profit when dispersal between the patches is sufficiently high and habitat is especially vulnerable to damage.     

FISHING YIELD,CURVATURE AND SPATIAL BEHAVIOR: IMPLICATIONS FOR MODELING MARINE RESERVES

ABSTRACT. Given a paucity of empirical data, policymakers are forced to rely on modeling to assess potential impacts of creating marine reserves to manage fisheries. Many modeling studies of reserves conclude that fishing yield will increase (or decrease only modestly) after creating a reserve in a heavily exploited fishery. However, much of the marine reserves modeling ignores the spatial heterogeneity of fishing behavior. Contrary to empirical findings in fisheries science and economics, most models assume explicitly or implicitly that fishing effort is distributed uniformly over space. This paper demonstrates that by ignoring this heterogeneity, yield‐per‐recruit models systematically overstate the yield gains (or understate the losses) from creating a reserve in a heavily exploited fishery. Conversely, at very low levels of exploitation, models that ignore heterogeneous fishing effort overstate the fishing yield losses from creating a reserve. Starting with a standard yield‐per‐recruit model, the paper derives a yield surface that maps spatially differentiated fishing effort into total long‐run fishing yield. It is the curvature of this surface that accounts for why the spatial distribution of fishing effort so greatly affects predicted changes from forming a reserve. The results apply generally to any model in which the long‐run fishing yield has similar curvature to a two‐patch Beverton‐Holt model. A simulation of marine reserve formation in the California red sea urchin fishery with Beverton‐Holt recruitment, eleven patches, and common larval pool dispersal dynamics reinforces these results.     

MODELING: A TOOL FOR ENHANCING THE SURVIVAL PROSPECTS OF AFRICAN WILDLIFE

ABSTRACT. In this article we consider the role of modeling in some aspects of the conservation of African wildlife. The first study is concerned with the endangered black rhino. Animals are being translocated from high density areas to new sites in an attempt to build up the South African population as rapidly as possible. We investigate the efficacy of different translocation strategies. Next we discuss a spatial stochastic metapopulation model used to test management strategies to enhance the survival likelihood of the rare samango monkey. The value of the model is to encourage the use of corridor policies even though there may be little apparent observable benefit in a manager's lifetime. Finally, we look at some commercial aspects of exploiting wildlife on a sustainable basis. By increasing the profitability of wildlife enterprises the incentive to conserve is increased. We look at improving the financial returns from game ranches.     

CREATION OF MARINE RESERVES AND INCENTIVES FOR BIODIVERSITY CONSERVATION

Abstract Despite a number of benefits, marine reserves provide neither incentives for fishermen to protect biodiversity nor compensation for financial loss due to the designation of the reserves. To obtain fishermen's support for marine reserves, some politicians have suggested that managers of new marine reserves should consider subsidizing or compensating those fishermen affected by the new operations. The objective of this paper is to apply principal–agent theory, which is still infrequently applied to fisheries, to define the optimal reserve area, fishing effort, and transfer payments in the context of symmetric and asymmetric information between managers and fishermen. The expected optimal reserve size under asymmetric information is smaller than that under symmetric information. Fishing efforts encouraged with a transfer payment are always less compared to those without payment. This reflects the fact that as the manager induces the fishermen to participate in the conservation program, the fishermen will take into account their effects on fish stock by decreasing their effort. Examples are also supplied to demonstrate these concepts.     

Shooting at the poachers while the rhinos drown: Managing short‐ and long‐term threats to endangered wildlife in conservation reserves

This paper addresses management challenges associated with conserving endangered wildlife facing multiple threats from illegal poaching, habitat encroachment, and climate and land‐use change‐induced flooding. While poaching and encroachment challenges in conservation parks are of immediate nature, climate‐related risks exist in the long term. The park manager faces a utility function that includes as its arguments local community’s incomes, benefits to the larger society from preserving threatened species and the financial costs of monitoring and land‐use change efforts. Using the case of single‐horned rhinos in the Kaziranga National Park, India, an optimal mix of monitoring and land‐use changes is designed in presence of tradeoffs between short‐ and long‐term management efforts. As monitoring only addresses immediate challenges associated with poaching and encroachment, long‐term climatic risks remain ignored. Land‐use management offers risk‐protection as well as risk‐insurance benefits with respect to climate change‐induced flooding of the park. Recommendations for Resource Managers

• It is important to incorporate both short‐ and long‐term risks posed to endangered wildlife while investing in conservation efforts. There may exist a tradeoff between mitigating short‐ and long‐run risks due to financial and physical resource constraints. However, ignoring long‐term risks to wildlife habitats can jeopardize past conservation efforts.
• Land‐use management, both within and outside of conservation reserves, enhances resilience to climatic shocks through reducing flooding risks and must be an essential part of wildlife conservation efforts.
• Conservation efforts ignoring local community welfare considerations can become suboptimal as they lead to reduced cooperation and potential conflicts. When wildlife conservation efforts account for local community welfare implications, optimal management plans could result in lower species abundance in the short term. However, increasing the park size through additional land enrollment can mitigate some of this tradeoff.

     

CONSIDERATION OF STOCHASTIC DEMOGRAPHY IN THE DESIGN AND MANAGEMENT OF BIOLOGICAL RESERVES

A generalized birth–and–death process serves as a simple, flexible model for computing the expected persistence time of a small population in a random world. We may reparametrize the model in ways that allow explicit incorporation of density dependence, random differences in events experienced by different individuals, and random environmental variation experienced by all individuals in concert. This model seems to capture the important features of real population dynamics for purposes of computing the mean persistence time, even though the underlying mechanisms presumed in the mathematics of the model are decidedly unrealistic. The lack of isomorphism between birth and death rates, as they feature in the model, and vital rates of real biological populations can lead to extremely misleading results, if the classic formulation, rather than the reparametrization is applied without due circumspection. Using the reparametrized model, we find that environmental variation poses a greater problem for population persistence than does individual variation. In particular, with purely individual variation, the expected persistence time increases approximately with the power of the ceiling on population size; but with purely environmental variation, the expected persistence time increases somewhat less than linearly with the size of the population ceiling. The birth–and–death process model can also be applied to calculating the persistence time of a population on an ensemble of reserves which are linked by natural migration or by deliberate reintroduction programs. Results of this model, for an idealized ensemble, show that multiple independent reserves with a sufficient recolonization rate (natural or otherwise) will confer a longer persistence time than a single reserve with the same total carrying capacity, but in the absence of recolonization, the system of smaller separate reserves confers a shorter persistence time than the single large reserve.     

THE IMPACT OF AGE-, SPACE-AND STOCHASTIC-STRUCTURE ON THE EXTINCTION PROBABILITY OF A CHINOOK SALMON METAPOPULATION

ABSTRACT. Using a mechanistic model, based on chinook life history, incorporating environmental and demographic stochasticity, we investigate how the probability of extinction is controlled by age, space and stochastic structure. Environmental perturbations of age dependent survivorships, combined with mixing of year classes in the spawning population, can lower the probability of extinction dramatically. This is an analog of the more familiar metapopulation result where dispersal between asynchronously fluctuating populations enhances persistence. For a two-river chinook metapopulation, dispersal between rivers with asynchronous environmental perturbations also dramatically enhances persistence, and anti-synchronous population fluctuations provide an even greater persistence probability. Anti-synchronous fluctuations would most likely occur in pristine habitat with naturally high levels of heterogeneity. Fifty percent dispersal between two populations provides the greatest insurance against extinction, a rate unrealistically high for salmon. In contrast, dispersal between exactly correlated populations with large amplitude environmental perturbations does not help persistence, no matter how high the dispersal rate. This is in spite of weak asynchrony provided by demographic stochasticity. Dispersal between rivers, one degraded and the other pristine, can substantially increase the probability of metapopulation extinction. Population structure, combined with asynchronous environmental perturbations and dispersal (or age class mixing) lowers the probability of chinook extinction dramatically but is almost useless when survivorships are impaired.     

SUSTAINABLE FOREST MANAGEMENT FOR OPTIMIZING MULTISPECIES WILDLIFE HABITAT: A COASTAL DOUGLAS-FIR EXAMPLE

Wildlife species viability optimization models are developed to convert a given set of initial forest conditions, through a combination of natural growth and management treatments, to a forest system which addresses the joint habitat needs of multispecies populations over time. A linear model of forest cover and wildlife populations is used to form a system of forest management control variables for wildlife habitat modification. The paper examines two objective functions coupled to this system for optimizing sustainable joint species viability. The first maximizes the product of periodic joint viabilities over all time periods, focusing management resources on long-term equilibria, with less emphasis on conversion strategy. The second iteratively maximizes the minimum periodic joint viability over all time periods. This focuses management resources on the most limiting time periods, typically the conversion phase periods. Both objective functions resulted in either point or cyclic equilibria, with cycle lengths equal to minimum forest treatment ages. A third objective, based on maximizing the minimum individual species periodic viability is used to examine single species emphasis. Examples are developed through a case study of 92 vertebrate species found in coastal Douglas-fir stands of northwestern California.     

Multiobjective programming methods in the reserve selection problem

Many ecological criteria have been proposed to assign conservation values to nature reserves in the reserve selection problem. Multiobjective programming is used to identify the best compromise solution among a set of alternative solutions that have been obtained from single objective linear programming methods based upon different criteria. Endemic plant species from the island of Crete in Greece are used as a model and a number of cells, as they have been implemented by ARC/INFO, are selected based on four criteria: (1) species richness, (2) species rarity, (3) cell richness, (4) cell rarity. Best compromise solution is identified by (i) a simple multiattribute rating technique, (ii) geometrical methods based on four distance metrics. The two methods are compared and the degree to which they fulfil the four criteria is examined.