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 fishery with saturated catch and variable price: Stabilizing effect of marine reserves on fishery dynamics

In this paper, we study a mathematical bio-economic model of a fishery with varying price. The three dimensional model describes the time evolution of the resource, the fishing effort and the price. The model is original because it considers a nonlinear harvesting function assumed to depend upon stock size and fishing effort with a saturation effect with respect to the resource as well as a price equation depending on demand and supply which is in addition proportional to price. Assuming that the price varies at a fast time scale, we are able to use ”aggregation of variables methods” in order to reduce the model in a two dimensional model at a slow time scale. This aggregated (reduced) model is analyzed. Several numerical simulations of the model are performed to substantiate our analytical findings. The existence of nonlinear harvesting makes the dynamics of the model more complicated, including multiple equilibria, bi-stability and limit cycle. Such large amplitude cycle variations are not desirable because they generate periods of overfishing at periods of very low activity. We then study the effects of marine reserves on the dynamics of the fishery, showing that for an adequate number of small reserves, limit cycle oscillations are switched off.     

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.     

Effect of Small Versus Large Clusters of Fish School on the Yield of a Purse-Seine Small Pelagic Fishery Including a Marine Protected Area

We consider a fishery model with two sites: (1) a marine protected area (MPA) where fishing is prohibited and (2) an area where the fish population is harvested. We assume that fish can migrate from MPA to fishing area at a very fast time scale and fish spatial organisation can change from small to large clusters of school at a fast time scale. The growth of the fish population and the catch are assumed to occur at a slow time scale. The complete model is a system of five ordinary differential equations with three time scales. We take advantage of the time scales using aggregation of variables methods to derive a reduced model governing the total fish density and fishing effort at the slow time scale. We analyze this aggregated model and show that under some conditions, there exists an equilibrium corresponding to a sustainable fishery. Our results suggest that in small pelagic fisheries the yield is maximum for a fish population distributed among both small and large clusters of school.     

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 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.     

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.     

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.     

The potential trade‐off between artisanal fisheries production and hydroelectricity generation on the Kafue River,Zambia

1. Freshwater resource managers are increasingly obligated to consider the impacts of large river engineering projects on ecosystem services. We evaluated the effect of altered water regime from the operation of a large dam on the production of the downstream tropical floodplain fishery of the Kafue River, Zambia. We compared the benefits of increased hydropower relative to potentially lost fishery production. 2. We compiled a long‐term data set consisting of experimental gillnet catches, artisanal harvesting effort and monthly river flows for 25 years prior to and 29 years after the 1977 completion of the upstream Itezhi‐Tezhi Dam. As a metric of the flood regime, we calculated a canonical correlation score for each hydrological year before and after dam closure. For the period following dam construction, we used the Muskingum method of flood routing to estimate ‘no‐dam’ flows through the fishery area and downstream hydroelectric turbines at the Kafue Gorge Dam. 3. We compared 16 alternative models of catch per unit effort (CPUE) with and without an effect of water regime on fish population growth rate. Using the two best fitting models, we estimated the total observed fishery harvest and simulated ‘no‐dam’ fisheries harvest and found no significant effect of altered water regime on fishery production. 4. We estimate that the large upstream dam increases downstream hydropower production by about $18 million USD per annum. The reduction in fishery production caused by the altered water regime is not significantly different than zero, although the average reduction amounts to about $2.3 million annually. The total estimated value of harvest ranges from $1.3 million to $56 million annually. 5. Large observed declines in fish abundance over the 54‐year study period are attributed primarily with similarly large increases in total fishing effort in this mostly open‐access artisanal fishery. 6. These results contrast with other examples of the effects of flow alteration on fish, probably because levels of fisheries exploitation on the Kafue River are very high relative to better studied regions on other continents; our focus on the whole fish community; and the unprecedented length of the time series we considered. If the goal is to sustain fishery production, investments in altering flow regime are likely to be less effective than investments to decrease fishing effort.     

Living on predictability: modelling the density distribution of efficient foraging seabirds

In areas with regular fishing coastal fleets seabirds may benefit from the predictability of discards from fishing vessels, but it is not clear to what extent birds rely on this predictable resource and whether foraging is synchronized with the diel availability of discards. In this paper we investigate if a typical scavenger species, the yellow‐legged gull Larus michahellis, takes advantage of the temporal and spatial predictability of fish discards in the western Mediterranean Sea. The activity and distribution of the trawling fleet in this area is regulated and very predictable in time and space. We gathered aerial survey data across a relatively large area close to the coast to study the spatial distribution and density of L. michahellis, and modelled the density distribution of the species in relation to several oceanographic, ecological and temporal variables, using two different modelling approaches: MARS (multivariate adaptative regression splines) and GLM (generalized linear models). Our models suggest that the spatial density of trawlers at sea and the time of the day are the best explanatory variables of gull distribution, and that gulls concentrate in areas with vessels mainly during fish discarding time, supporting the hypothesis that gulls optimize time foraging to take advantage of fishery waste predictability. Additional surveys from the main gull roosting sites inshore support this hypothesis, as gulls start leaving to the sea just before fishing is completed and vessels begin discarding fish scraps when back to the harbour. This study represents one of the few examples of applying MARS to density distribution modelling, although its application to marine ecosystems should be conducted with caution because of large areas with real absence data. GLMs have shown to be more adaptable to such kind of data. Our data confirm the importance of fishery waste for L. michahellis, not only as a food resource but also as a major driver of their activity and distribution patterns. The ability of seabirds to predict accurately when a food resource will be available implies that modelling their distribution at sea needs to include such variables, both in spatial and temporal dimensions.     

A Viability Analysis of Fishery Controlled by Investment Rate

This work presents a stock/effort model describing both harvested fish population and fishing effort dynamics. The fishing effort dynamic is controlled by investment which corresponds to the revenue proportion generated by the activity. The dynamics are subject to a set of economic and biological state constraints. The analytical study focuses on the compatibility between state constraints and controlled dynamics. By using the mathematical concept of viability kernel, we reveal situations and management options that guarantee a sustainable system.     

Interspecific Resource Competition Effects on Fisheries Revenue

In many fisheries multiple species are simultaneously caught while stock assessments and fishing quota are defined at species level. Yet species caught together often share habitat and resources, resulting in interspecific resource competition. The consequences of resource competition on population dynamics and revenue of simultaneously harvested species has received little attention due to the historical single stock approach in fisheries management. Here we present the results of a modelling study on the interaction between resource competition of sole (Solea solea) and slaice (Pleuronectus platessa) and simultaneous harvesting of these species, using a stage-structured population model. Three resources were included of which one is shared with a varied competition intensity. We find that plaice is the better competitor of the two species and adult plaice are more abundant than adult sole. When competition is high sole population biomass increases with increasing fishing effort prior to plaice extinction. As a result of this increase in the sole population, the revenue of the stocks combined as function of effort becomes bimodal with increasing resource competition. When considering a single stock quota for sole, its recovery with increasing effort may result in even more fishing effort that would drive the plaice population to extinction. When sole and plaice compete for resources the highest revenue is obtained at effort levels at which plaice is extinct. Ignoring resource competition promotes overfishing due to increasing stock of one species prior to extinction of the other species. Consequently, efforts to mitigate the decline in one species will not be effective if increased stock in the other species leads to increased quota. If a species is to be protected against extinction, management should not only be directed at this one species, but all species that compete with it for resource as well.     

Navigating Over Space and Time: Fishing Effort Allocation and the Development of Customary Norms in an Open-Access Mangrove Estuary in Ecuador

Fisheries are increasingly understood as complex adaptive systems; but the cultural, behavioral, and cognitive factors that explain spatial and temporal dynamics of fishing effort allocation remain poorly understood. Using Geographic Information Systems (GIS) as a visualization tool, this paper combines catch-per-unit-effort (CPUE) and ethnographic data on the Ecuadorian mangrove cockle fishery to explore patterns in fishing effort and the social production of fishing space. I argue that individual decisions about where, when, and how to fish result in spatial and temporal patterns in effort allocation, ultimately regulating open-access fisheries that typically operate on a first-come, first-served basis. These emergent patterns in the fishing effort are explained by individual-level preferences and adaptations; the development of knowledge and customary norms through the habitual use of resource space by individuals and groups; ecological conditions; and access. New adaptive challenges threaten to undermine such self-organization of open-access systems on larger spatial and temporal scales prompting a likely re-allocation of the fishing effort in the future.     

Fish, Fact and Fantasy: a Long View

This paper suggests ways forward from the widely perceived present failures of fishery assessment and management. A history of fishery yield modelling is presented from the carefree days of the 1950s to the depressing series of stock collapses and depletions of the 1980s. Underlying this gruesome story has been the failure of management by quotas to arrest overcapacity in fishing power, the lack of robust and informative reference points and the inadequacy of methods dealing with some multispecies fisheries. The paper refines the use of the concept of Fext, defined as the minimum value of F in a self-regenerating yield model that leads to eventual extinction in a family of yield curves generated with a range of stock recruitment curves. Model reconstructions for North Sea cod and Icelandic herring make evident calamitous losses in catches forgone as result of the failure of rational management. An optimistic agenda that may achieve more effective fishery management in the future is presented. In some ways, we may have been trying to be too clever. A simple management system based on careful monitoring of fishing effort, biological targets such as F95, and exploitation of a diversity of fish resources may suffice to avert further disaster and hedge against uncertainty.     

基于持续高产的近海渔业双寡头捕捞策略

海洋鱼类是人类一种重要的生活物质资料,当代人在进行渔业捕捞满足自身生活需求时,应合理确定捕捞努力量以实现渔业资源的可持续利用,不危及后代人的需求,假定存在两个捕捞主体,分别就Cournot模型和Stackelbeerg模型分析了两个主体为了自身获得最大持续产量而投入的捕捞努力量,研究表明,与只有一个捕捞主体相比,当存在两个捕捞主体时,每个捕捞主体都将投入更多的捕捞努力量,但最大持续产量不随之增加,甚至还会减少,产生这种后果的原因在于每个主体只考虑自己投入的捕捞 努力量对自己产出量的影响,而不考虑对对方或社会产生的负面影响,对渔业捕捞进行全面规划,综合管理是消除这种后果所必要的。     

The stabilizability of a controlled system describing the dynamics of a fishery

This work presents two stock-effort dynamical models describing the evolution of a fish population growing and moving between two fishing zones, on which it is harvested by a fishing fleet, distributed on the two zones. The first model corresponds to the case of constant displacement rates of the fishing effort, and the second one to fish stock-dependent displacement rates. In equations of the fishing efforts, a control function is introduced as the proportion of the revenue to be invested, for each fleet. The stabilizability analysis of the aggregated model, in the neighborhood of the equilibrium point, enables the determination of a Lyapunov function, which ensures the existence of a stabilizing discontinuous feedback for this model. This enables us to control the system and to lead, in an uniform way, any solution of this system towards this desired equilibrium point.     

A bioeconomic model of the pacific whiting

The Pacific whiting (Merluccius productus) is a highly migratory fish occupying the continental shelf and slope off the west coast of North America. The species spawns in January off southern California and northern Mexico. During spring and summer the older and larger fish will migrate as far north as central Vancouver Island. Recruitment is highlys variable, with strong year classes often supporting the commercial fishery during several years of low recruitment. The level of recruitment appears to be independent of the size of the spawning population. A simple bioeconomic model of the Pacific whiting is constructed with independent recruitment. Fishery production functions are estimated from data on U.S. catch, average annual biomass and the number of vessels in the U.S. fleet. A stochastic optimization problem, seeking to maximize the expected value of industry profit, is formulated. Its solution would require a joint distribution on future recruiment and other bioeconomic parameters. Such a distribution is problematic. As an alternative, the certainty-equivalent problem is solved yielding solution values for the stochastic equilibrium and an approximately-optimal rule that sets allowable catch based on an estimate of current-year biomass. Adaptive management can result in large changes in fleet size and allowable catch from year to year. The whiting fishery might be characterized as an opportunistic fishery, requiring a generalist fleet to expand or contract as bioeconomic conditions warrant. It is possible that longrun conditions would not support a profitable fishery, but that short-run fishing is profitable based on previous years of strong recruitment. The situation is not dissimilar to that facing the owner of a marginal gold mine that opens or closes depending on the price of gold. In the case of the whiting fishery, the optimal level of short-run fishing will depend not only on price, but on current biomass, the annual cost of fishing, the discount rate and vessel productivity. A simple interactive program is provided for would-be managers. This paper was written in July 1990 while the author was a Summer Faculty Fellow at the Southwest Fisheries Center, La Jolla, California. The author gratefully acknowledges the support of the U.S. National Marine Fisheries Service.     

A Mixed-Method Approach for Quantifying Illegal Fishing and Its Impact on an Endangered Fish Species

Illegal harvest is recognized as a widespread problem in natural resource management. The use of multiple methods for quantifying illegal harvest has been widely recommended yet infrequently applied. We used a mixed-method approach to evaluate the extent, character, and motivations of illegal gillnet fishing in Lake Hovsgol National Park, Mongolia and its impact on the lake’s fish populations, especially that of the endangered endemic Hovsgol grayling (Thymallus nigrescens). Surveys for derelict fishing gear indicate that gillnet fishing is widespread and increasing and that fishers generally use 3–4 cm mesh gillnet. Interviews with resident herders and park rangers suggest that many residents fish for subsistence during the spring grayling spawning migration and that some residents fish commercially year-round. Interviewed herders and rangers generally agree that fish population sizes are decreasing but are divided on the causes and solutions. Biological monitoring indicates that the gillnet mesh sizes used by fishers efficiently target Hovsgol grayling. Of the five species sampled in the monitoring program, only burbot (Lota lota) showed a significant decrease in population abundance from 2009–2013. However, grayling, burbot, and roach (Rutilus rutilus) all showed significant declines in average body size, suggesting a negative fishing impact. Data-poor stock assessment methods suggest that the fishing effort equivalent to each resident family fishing 50-m of gillnet 11–15 nights per year would be sufficient to overexploit the grayling population. Results from the derelict fishing gear survey and interviews suggest that this level of effort is not implausible. Overall, we demonstrate the ability for a mixed-method approach to effectively describe an illegal fishery and suggest that these methods be used to assess illegal fishing and its impacts in other protected areas.     

Overfishing and the Replacement of Demersal Finfish by Shellfish: An Example from the English Channel

The worldwide depletion of major fish stocks through intensive industrial fishing is thought to have profoundly altered the trophic structure of marine ecosystems. Here we assess changes in the trophic structure of the English Channel marine ecosystem using a 90-year time-series (1920–2010) of commercial fishery landings. Our analysis was based on estimates of the mean trophic level (mTL) of annual landings and the Fishing-in-Balance index (FiB). Food webs of the Channel ecosystem have been altered, as shown by a significant decline in the mTL of fishery landings whilst increases in the FiB index suggest increased fishing effort and fishery expansion. Large, high trophic level species (e.g. spurdog, cod, ling) have been increasingly replaced by smaller, low trophic level fish (e.g. small spotted catsharks) and invertebrates (e.g. scallops, crabs and lobster). Declining trophic levels in fisheries catches have occurred worldwide, with fish catches progressively being replaced by invertebrates. We argue that a network of fisheries closures would help rebalance the trophic status of the Channel and allow regeneration of marine ecosystems.