Effects of market price on the dynamics of a spatial fishery model: Over-exploited fishery/traditional fishery

We present a dynamical model of a spatial fishery describing the time evolution of the fish stock, the fishing effort and the market price of the resource. The market price is fixed by the gap between the supply and the demand. Assuming two time scales, we use “aggregation of variables methods” in order to derive a reduced model governing fish density and fishing effort at a slow time scale. The bifurcation analysis of the reduced model is performed. According to parameters values, three main cases can occur: (i) a stable fishery free equilibrium, (ii) a stable persistent fishery equilibrium and (iii) coexistence of three strictly positive equilibria, two of them being stable separated by a saddle. In this last case, a stable equilibrium corresponds to a traditional fishery with large fish stock, small fishing effort and small market price. The second stable one corresponds to over-exploitation of the resource with small fish stock, large fishing effort and large market price.     

A Bioeconomic Model of a Multi-site Fishery with Nonlinear Demand Function: Number of Sites Optimizing the Total Catch

We present a mathematical model of a fishery on several sites with a variable price. The model takes into account the evolution during the time of the resource, fish and boat movement between the different sites, fishing effort and price that varies with respect to supply and demand. We suppose that the movements of the boats and resource as well as the variation of the price go on at a fast time scale. We use methods of aggregation of variables in order to reduce the number of variables and we derive a reduced model governing two global variables, respectively the biomass of the resource and the fishing effort of the whole fishery. We look for the existence of equilibria of the aggregated model and perform local stability analysis. Two main cases can occur. The first one corresponds to over-exploitation leading to fish extinction. At extinction, the fishing effort tends to a positive value. The second case corresponds to a durable fishery equilibrium which is globally asymptotically stable. In the later case, we show that there exists a number of fishing sites that optimizes the total catch of the fishery.     

Basic reproduction ratio for a fishery model in a patchy environment

We present a dynamical model of a multi-site fishery. The fish stock is located on a discrete set of fish habitats where it is catched by the fishing fleet. We assume that fishes remain on fishing habitats while the fishing vessels can move at a fast time scale to visit the different fishing sites. We use the existence of two time scales to reduce the dimension of the model : we build an aggregated model considering the habitat fish densities and the total fishing effort. We explore a regulation procedure, which imposes an average residence time in patches. Several equilibria exist, a Fishery Free Equilibria (FFEs) as well as a Sustainable Fishery Equilibria (SFEs). We show that the dynamics depends on a threshold which is similar to a basic reproduction ratio for the fishery. When the basic reproduction ratio is less or equal to 1, one of the FFEs is globally asymptotically stable (GAS), otherwise one of the SFEs is GAS.     

The intrinsic vulnerability to fishing of coral reef fishes and their differential recovery in fishery closures

Coral reef fishes differ in their intrinsic vulnerability to fishing and rates of population recovery after cessation of fishing. We reviewed life history-based predictions about the vulnerability of different groups of coral reef fish and examined the empirical evidence for different rates of population recovery inside no-take marine reserves to (1) determine if the empirical data agree with predictions about vulnerability and (2) show plausible scenarios of recovery within fully protected reserves and periodically-harvested fishery closures. In general, larger-bodied carnivorous reef fishes are predicted to be more vulnerable to fishing while smaller-bodied species lower in the food web (e.g., some herbivores) are predicted to be less vulnerable. However, this prediction does not always hold true because of the considerable diversity of life history strategies in reef fishes. Long-term trends in reef fish population recovery inside no-take reserves are consistent with broad predictions about vulnerability, suggesting that moderately to highly vulnerable species will require a significantly longer time (decades) to attain local carrying capacity than less vulnerable species. We recommend: (1) expanding age-based demographic studies of economically and ecologically important reef fishes to improve estimates of vulnerability; (2) long term (20–40 years), if not permanent, protection of no-take reserves to allow full population recovery and maximum biomass export; (3) strict compliance to no-take reserves to avoid considerable delays in recovery; (4) carefully controlling the timing and intensity of harvesting periodic closures to ensure long-term fishery benefits; (5) the use of periodically-harvested closures together with, rather than instead of, permanent no-take reserves.     

Ten years of dynamic co-management of a multi-species reef fishery

Co-management, a governance process whereby management responsibility is shared between resource users and other collaborators, is a mainstream approach for governing social and ecological aspects of small-scale fisheries. While many assessments of co-management are available for single time periods, assessments across longer time-scales are rare–meaning the dynamic nature, and long-term outcomes, of co-management are insufficiently understood. In this study we analyse ten-years of catch and effort data from a co-managed, multi-species reef fishery in Solomon Islands. To further understand social, ecological and management dynamics we also draw on interviews with fishers and managers that had been conducted throughout the same decade. We aimed to answer (1) what are the temporal trends in fishing effort, harvesting efficiency, and catch composition within and beyond a periodically-harvested closure (i.e. a principal and preferred management tool in Pacific island reef fisheries), and, (2) what are the internal and external drivers that acted upon the fishery, and its management. Despite high fishing effort within the periodically-harvested closure, catch per unit effort remained stable throughout the ten years. Yet the taxonomic composition of catch changed substantially as species targeted early in the decade became locally depleted. These observations indicate that both the frequency of harvesting and the volumes harvested may have outpaced the turnover rates of target species. We argue that this reflects a form of hyperstability whereby declining abundance is not apparent through catch per unit effort since it is masked by a shift to alternate species. While the community sustained and adapted their management arrangements over the decade as a response to internal pressures and some signs of resource changes, some external social and ecological drivers were beyond their capabilities to govern. We argue the collaborative, knowledge exchange, and learning aspects of adaptive co-management may need even more attention to deal with this complexity, particularly as local and distal pressures on multi-species fisheries and community governance intensify.

Graphical abstract

     

Marine reserve effects on fishery profit

Some studies suggest that fishery yields can be higher with reserves than under conventional management. However, the economic performance of fisheries depends on economic profit, not fish yield. The predictions of higher yields with reserves rely on intensive fishing pressures between reserves; the exorbitant costs of harvesting low-density populations erode profits. We incorporated this effect into a bioeconomic model to evaluate the economic performance of reserve-based management. Our results indicate that reserves can still benefit fisheries, even those targeting species that are expensive to harvest. However, in contrast to studies focused on yield, only a moderate proportion of the coast in reserves (with moderate harvest pressures outside reserves) is required to maximize profit. Furthermore, reserve area and harvest intensity can be traded off with little impact on profits, allowing for management flexibility while still providing higher profit than attainable under conventional management.     

Adaptive behaviour of fishers to external perturbations: simulation of the Tasmanian rock lobster fishery

The rock lobster, Jasus edwardsii, lies on a global “hotspot” for climate change in the southeastern Australian state of Tasmania. The short-term effects of climate change are predicted to lead to an increasing exploitable biomass in the south and declining biomass in the north of the state. The future of the fishery is highly uncertain due to climate change, but also due to insecurities linked to the market conditions. The market for Tasmanian rock lobster is driven by the demand of a single market, China, which absorbs 75 % of the catch. This study examines how fishers can adapt to external perturbations that affect the social and economic viability of the fleet and the ecological dynamics of the stock. Three fleet dynamic models of increasing complexity are used to investigate the effects of climate change and lobster price changes on the fishery. There could be local depletion leading to negative short-term profit for the fleet if it is static and the proportion of the total catch taken in each region of the fishery does not respond to climate-induced-changes. Better outcomes would occur if the fleet adapts dynamically to environmental conditions, and fishing effort follows stock abundance, which would counter-act the short-term effects of climate change. Only a model with explicit representation of economic drivers can fully capture the local economic and social impacts of large scale global perturbations.     

An adaptive management approach to an octocoral fishery based on the Beverton-Holt model

Coral reef species are frequently the focus of bio-prospecting, and when promising bioactive compounds are identified there is often a need for the development of responsible harvesting based on relatively limited data. The Caribbean gorgonian Pseudopterogorgia elisabethae has been harvested in the Bahamas for over a decade. Data on population age structure and growth rates in conjunction with harvest data provide an opportunity to compare fishery practices and outcomes to those suggested by a Beverton-Holt fishery model. The model suggests a minimum colony size limit of 7–9 years of age (21–28 cm height), which would allow each colony 2–4 years of reproduction prior to harvesting. The Beverton-Holt model assumes that colonies at or above the minimum size limit are completely removed. In the P. elisabethae fishery, colonies are partially clipped and can be repeatedly harvested. Linear growth of surviving colonies was up to 3 times that predicted for colonies that were not harvested and biomass increase was up to 9 times greater than that predicted for undisturbed colonies. The survival of harvested colonies and compensatory growth increases yield, and yields at sites that had previously been harvested were generally greater than predicted by the Beverton-Holt model. The model also assumes recruitment is independent of fishing intensity, but lower numbers of young colonies in the fished populations, compared to unfished populations, suggest possible negative effects of the harvest on reproduction. This suggests the need for longer intervals between harvests. Because it can be developed from data that can be collected at a single time, the Beverton-Holt model provides a rational starting point for regulating new fisheries where long-term characterizations of population dynamics are rarely available. However, an adaptive approach to the fishery requires the incorporation of reproductive data.     

A technique for estimating maximum harvesting effort in a stochastic fishery model

Exploitation of biological resources and the harvest of population species are commonly practiced in fisheries, forestry and wild life management. Estimation of maximum harvesting effort has a great impact on the economics of fisheries and other bio-resources. The present paper deals with the problem of a bioeconomic fishery model under environmental variability. A technique for finding the maximum harvesting effort in fluctuating environment has been developed in a two-species competitive system, which shows that under realistic environmental variability the maximum harvesting effort is less than what is estimated in the deterministic model. This method also enables us to find out the safe regions in the parametric space for which the chance of extinction of the species is minimized. A real life fishery problem has been considered to obtain the inaccessible parameters of the system in a systematic way. Such studies may help resource managers to get an idea for controlling the system.     

On the Optimal Size of Marine Reserves

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. This study examines the impact of the creation of marine protected areas, from both economic and biological perspectives. The consequences of reserve establishment on the long-run equilibrium fish biomass and fishery catch levels are evaluated. We include reserve size as control variable to maximize catch at equilibrium. A continuous time model is used to simulate the effects of reserve size on fishing catch. Fish movements between the sites is assumed to take place at a faster time scale than the variation of the stock and the change of the fleet size. We take advantage of these two time scales to derive a reduced model governing the dynamics of the total fish stock and the fishing effort. Simulation results suggest that the establishment of a protected marine reserve will always lead to an increase in total fish biomass, an optimal size of a marine reserve can achieve to maximize the catch at equilibrium.     

Assessing the risk of alternative management strategies in a Mediterranean fishery: protecting the younger vs reducing fishing effort

A stochastic age-structured population model was developed to explore biologically favourable levels of effort and closing periods within the sardine pelagic fishery in the eastern Mediterranean Sea. Results suggested that the developed age-structured model captured the observed biomass fluctuations and catches reasonably well and represents the first comprehensive investigation of alternative management strategies for eastern Mediterranean sardine fishery that include stochasticity. The present study provided direct evidence for the importance of the correct timing of the temporal fishing ban. Significant benefits were found both in terms of biomass and catch from a corrective shift in the fishing closed period. The current findings suggested that protecting the younger age groups from fishing in the period October–December, by shifting the ban period earlier than December may profit, biologically, the stock and economically the fishing sector. Progressive reductions in fishing mortality/effort also yield significant positive biological and fishery benefits in the short term.     

A Mathematical Model of a Fishery with Variable Market Price: Sustainable Fishery/Over-exploitation

We present a mathematical bioeconomic model of a fishery with a variable price. The model describes the time evolution of the resource, the fishing effort and the price which is assumed to vary with respect to supply and demand. The supply is the instantaneous catch while the demand function is assumed to be a monotone decreasing function of price. We show that a generic market price equation (MPE) can be derived and has to be solved to calculate non trivial equilibria of the model. This MPE can have 1, 2 or 3 equilibria. We perform the analysis of local and global stability of equilibria. The MPE is extended to two cases: an age-structured fish population and a fishery with storage of the resource.     

Modelling harvesting strategies for the lobster fishery in northern Europe: the importance of protecting egg-bearing females

European lobster populations in Norway and Sweden are severely reduced as a result of intense harvesting over a long time. Various alternative management options have been proposed or endorsed to both facilitate recovery and increase yield. Accordingly, Minimum Landing Size (MLS) regulations are widely used for the European lobster. We developed an individual-based population model which integrates biological knowledge about lobsters’ population dynamics to explore how available harvesting strategies and management options influence abundance and yield. The model reproduced basic features of a real lobster population in Sweden. Even for a relatively large MLS high fishing effort may still be detrimental to the long term production of the stock, while increasing the MLS further prevents this recruitment overfishing. A moratorium on berried females, in combination with the MLS appears to stabilize population fluctuations and yield, leading to higher yield for all MLS's considered. The female moratorium harvesting strategy also performed better than a maximum size limit. Yield per recruit calculations gave similar quantitative results, and also shows that a larger MLS reduce the risk of growth overfishing. A smaller MLS enables the harvest of many individuals but is very sensitive to increase in effort which easily promotes overfishing.     

The Dynamics of a Fish Stock Exploited in Two Fishing Zones

This work presents a specific stock-effort dynamical model. The stocks correspond to two populations of fish moving and growing between two fishery zones. They are harvested by two different fleets. The effort represents the number of fishing boats of the two fleets that operate in the two fishing zones. The bioeconomical model is a set of four ODE's governing the fishing efforts and the stocks in the two fishing areas. Furthermore, the migration of the fish between the two patches is assumed to be faster than the growth of the harvested stock. The displacement of the fleets is also faster than the variation in the number of fishing boats resulting from the investment of the fishing income. So, there are two time scales: a fast one corresponding to the migration between the two patches, and a slow time scale corresponding to growth. We use aggregation methods that allow us to reduce the dimension of the model and to obtain an aggregated model for the total fishing effort and fish stock of the two fishing zones. The mathematical analysis of the model is shown. Under some conditions, we obtain a stable equilibrium, which is a desired situation, as it leads to a sustainable harvesting equilibrium, keeping the stock at exploitable densities.     

The state of exploitation of the commercial demersal fishery of Cameroon

The state of exploitation of the demersal fisheries resources of Cameroon has been assessed using the classic Schaefer's (1954) model and the Gulland'ss (1961) moving average. The euilibrium yield found with the Schaefer method is statistically different (95 % probability) and higher than the Gulland approach. Because equilibrium models consistently over-estimate MSY and its related optimum effort, management option should target the 95 % value of the estimated parameters. The resources are being over-fished; as an immediate alternative to the urgent concern, catch and/or effort quotas could be allocated to the various fishing companies, with the total allocated catch and/or effort (for all fishing companies) 5% less than the estimated parameters. Enforcement control of that policy would be simplified as fishing activities are localised in the two main estuaries of the “Cameroon River” and Riodel-Rey;results should be complemented by economic studies of the fishery, as these economic factors would explain or better predict the behaviour of the fishing industry.     

A pulse fishery model with closures as function of the catch: conditions for sustainability

We present a model of single species fishery which alternates closed seasons with pulse captures. The novelty is that the length of a closed season is determined by the remaining stock size after the last capture. The process is described by a new type of impulsive differential equations recently introduced. The main result is a fishing effort threshold which determines either the sustainability of the fishery or the extinction of the resource.     

Landscape variables affecting fishery yield in lake systems of the Central Amazon region, Brazil

According to fisheries data, lakes are important systems for fish production in the Amazon basin. However, there is no information about the relationship between landscape variables and fishing yield that allows foresight into potential resource exploitation in this environment. The present study aims to evaluate this relationship with the hypothesis: lakes of different shapes give the same fishery yield in the Amazon, after considering the effects of lake size, distance to the river, fishing effort, fuel and ice used. Fishery data from 1994 to 1996 were analyzed with regard to 3228 trips on 50 lakes of the main white water tributaries of the Amazon basin. Analysis of covariance was applied to test this hypothesis. With variables such as fishing grounds access, fishing effort and lake shape the model explained a significant 72% of variabilities in the fisheries yield. Fishing yields among lake systems were different, thus the null hypothesis was rejected (P < 0.05). Results indicate that dendritic lakes far distant from the main river have greater productivity than floodplain lakes because there are more habitats of fish refuge for reproduction and feed available to the fish; there are also more limitations to access by predators.     

Lack of Cross-Scale Linkages Reduces Robustness of Community-Based Fisheries Management

Community-based management and the establishment of marine reserves have been advocated worldwide as means to overcome overexploitation of fisheries. Yet, researchers and managers are divided regarding the effectiveness of these measures. The “tragedy of the commons” model is often accepted as a universal paradigm, which assumes that unless managed by the State or privatized, common-pool resources are inevitably overexploited due to conflicts between the self-interest of individuals and the goals of a group as a whole. Under this paradigm, the emergence and maintenance of effective community-based efforts that include cooperative risky decisions as the establishment of marine reserves could not occur. In this paper, we question these assumptions and show that outcomes of commons dilemmas can be complex and scale-dependent. We studied the evolution and effectiveness of a community-based management effort to establish, monitor, and enforce a marine reserve network in the Gulf of California, Mexico. Our findings build on social and ecological research before (1997–2001), during (2002) and after (2003–2004) the establishment of marine reserves, which included participant observation in >100 fishing trips and meetings, interviews, as well as fishery dependent and independent monitoring. We found that locally crafted and enforced harvesting rules led to a rapid increase in resource abundance. Nevertheless, news about this increase spread quickly at a regional scale, resulting in poaching from outsiders and a subsequent rapid cascading effect on fishing resources and locally-designed rule compliance. We show that cooperation for management of common-pool fisheries, in which marine reserves form a core component of the system, can emerge, evolve rapidly, and be effective at a local scale even in recently organized fisheries. Stakeholder participation in monitoring, where there is a rapid feedback of the systems response, can play a key role in reinforcing cooperation. However, without cross-scale linkages with higher levels of governance, increase of local fishery stocks may attract outsiders who, if not restricted, will overharvest and threaten local governance. Fishers and fishing communities require incentives to maintain their management efforts. Rewarding local effective management with formal cross-scale governance recognition and support can generate these incentives.     

南极半岛北部南极磷虾渔业空间点格局特征

南极磷虾作为南极生态系统中的关键物种,在空间分布上常表现出集群特征.这也反映到磷虾渔业生产的空间格局特征上.为了探讨捕捞能力有明显差异的船队在高/低单位捕捞努力量渔获量(CPUE)的情况下空间点分布格局特征及其生态学效应,基于南极半岛北部海域的两艘中国南极磷虾渔船(船A为专业南极磷虾渔船,船B为在智利竹筴鱼渔场与南极磷虾渔场转换的兼作渔船)的磷虾渔业数据,从空间点格局的角度出发,分别从两船的高、低CPUE的空间点格局在不同尺度上聚集特征,高、低CPUE在不同尺度上的二元点格局相关关系,以及CPUE点标记格局下的相关性关系等3个方面进行了分析.Ripley的L函数和标记相关函数分析结果表明: 研究对象在空间窗口所有尺度上的空间格局均表现为聚集性,高、低CPUE下均有聚集发生;在15 km尺度上,聚集强度近最大,在15~50 km尺度下,聚集程度稳定;总体上点格局分布的聚集强度依次为:船A高CPUE>船B低CPUE>船B高CPUE>船A低CPUE.船A高、低CPUE在0~75 km尺度上为正相关关系,在大于75 km尺度上为随机关系;船B在所有尺度上的高、低CPUE均为正相关,说明了低CPUE点事件伴随高CPUE的点事件同步发生,两者在大部分尺度下均显著相关.这是磷虾集群模式的动态性和复杂性造成.船A各点的CPUE值在0~44 km尺度上呈正相关,在44~80 km尺度上呈负相关;船B各点的CPUE值在50~70 km尺度上呈负相关,在其他尺度上无显著相关性;正相关反映了磷虾密集集群的种群分布特性,而负相关表明了磷虾群间由于食物和空间原因存在一定的竞争关系.捕捞能力强的船A和捕捞能力较弱的船B在点格局分布上存在较大差异.专业南极磷虾渔船更适于开展磷虾作业空间点格局分析及相关科学调查工作.     

Mobility, expansion and management of a multi-species scuba diving fishery in East Africa

Background

Scuba diving fishing, predominantly targeting sea cucumbers, has been documented to occur in an uncontrolled manner in the Western Indian Ocean and in other tropical regions. Although this type of fishing generally indicates a destructive activity, little attention has been directed towards this category of fishery, a major knowledge gap and barrier to management.

Methodology and Principal Findings

With the aim to capture geographic scales, fishing processes and social aspects the scuba diving fishery that operate out of Zanzibar was studied using interviews, discussions, participant observations and catch monitoring. The diving fishery was resilient to resource declines and had expanded to new species, new depths and new fishing grounds, sometimes operating approximately 250 km away from Zanzibar at depths down to 50 meters, as a result of depleted easy-access stock. The diving operations were embedded in a regional and global trade network, and its actors operated in a roving manner on multiple spatial levels, taking advantage of unfair patron-client relationships and of the insufficient management in Zanzibar.

Conclusions and Significance

This study illustrates that roving dynamics in fisheries, which have been predominantly addressed on a global scale, also take place at a considerably smaller spatial scale. Importantly, while proposed management of the sea cucumber fishery is often generic to a simplified fishery situation, this study illustrates a multifaceted fishery with diverse management requirements. The documented spatial scales and processes in the scuba diving fishery emphasize the need for increased regional governance partnerships to implement management that fit the spatial scales and processes of the operation.