Fishery Model Research Articles

Dynamic Analysis and Optimal Control of a Fractional Order Fishery Model with Refuge and Protected Area

In this paper, a mathematical analysis of fractional order fishery model with stage structure for predator is carried out under the background of prey refuge and protected area. First, it is demonstrated that the solution exists and is unique. The paper aims to analyze predator-prey dynamics in a fishery model through the application of fractional derivatives. It is worth emphasizing that we explicitly examine how fractional derivatives affect the dynamics of the model. The existence of each equilibrium point and the stability of the system at the equilibrium point are proved. The theoretical results are proved by numerical simulation. Alternatively, allocate harvesting efforts within an improved model aimed at maximizing economic benefits and ecologically sustainable development. The ideal solution is obtained by applying Pontryagin’s optimal control principle. A large number of numerical simulations show that the optimal control scheme can realize the sustainable development of the ecosystem.

Optimal fisheries management and the response to price changes

The literature on how price changes affect optimally managed fisheries is mostly concerned with how fish stocks and harvest rates are affected in steady state. There is little published on how prices affect optimal harvest rates at stock levels outside of steady state. Here we show the effect of an unanticipated and permanent price increase. It is shown that in a model of a pure schooling fishery, if the stock is below the steady state, it is optimal to harvest less if the price goes up and vice versa. It is also shown that in a model with stock dependent harvest costs, the optimal response to a price increase is to reduce the harvest rate for low stock levels even if the optimal harvest rate increases close to the steady state. Empirical relevance is demonstrated by illustrating the theoretical results in an estimated model.

Problems with combining modelling and social science approaches to understand artisanal fisheries bycatch

AbstractAimArtisanal fisheries account for 40% of the world's fisheries catch, yet its environmental impacts remain poorly understood. This is especially the case in developing countries. In this study, we sought to integrate Local Fisher's Knowledge with distribution modelling to estimate the annual bycatch of Titicaca Grebe (Rollandia microptera), an endangered endemic bird from Lake Titicaca whose main anthropogenic threat is bycatch.LocationLake Titicaca, Peru and Bolivia.MethodsWe conducted transect and point counts of fishing nets in March–September 2022 and conducted interviews with fishers across the Lake Titicaca region. Using bathymetry, distance from shore, distance from a settlement, distance from the protected area, presence/absence of aquaculture, distance from aquaculture, and wetland cover, we constructed a distribution model of fisheries using maximum entropy modelling. We conducted interviews with fishers asking about the frequency of grebe bycatch and conducted short‐term monitoring at various sites while conducting transect points for dead grebes.ResultsWe estimate 3270 km2 of the surface area of Lake Titicaca is used for fishing, which amounts to 39.40% of the lake's surface area. The area under the curve (AUC) of the distribution model was 0.89 and the True Skill Statistic was 0.67, which suggests maximum entropy modelling can model fisheries occurrence. The results of our interviews suggested a biologically implausible large number of grebes caught as bycatch annually. The cultural context of the interviews, including potential influences of non‐response and social‐desirability bias, being with fishers who often view the Titicaca Grebe as a nuisance species, might have caused over‐reporting of bycatch and hence led to these implausible figures.Main ConclusionsIt is possible to map fisheries using distribution models as one might with species. However, obtaining accurate measures of fisheries bycatch through interviews is more difficult, due to cultural factors which affect the accuracy in fisher's responses. While we hope that this method provides a low‐cost alternative to monitoring, it is not a suitable replacement for it.

A nonlinear fractional fishery resource system model with Crowley–Martin functional response under Mittag-Leffler kernel

This article studies the action of predators and the predator-dependent functional response in the fishery resource model. We employ the Atangana–Baleanu–Caputo fractional derivative to study the proposed fractional fishery resource model in the presence of predators with Crowley–Martin functional response. We present a theoretical and numerical analysis of the governing nonlinear differential equations of the model consisting of the biomass density of the fish population inside the unrestricted fishing zone, the biomass density of the fish population inside the reserve or restricted fishing zone, and the predator population. Using the fixed point theory and nonlinear analysis, we establish the existence and uniqueness results of the proposed ABC fractional fishery resource model. We establish stability analysis of the fishery model using the Ulam–Hyers stability approach. The numerical scheme of the fractional Adams–Bashforth method is provided and the approximate solutions for the model under consideration are given and discussed. We observe that an increase in the fish capturing rates increases the size of the predator population and reduces the fish subpopulations. To maintain a high number of fish species, we recommend a control measure to reduce the fish capturing rate by the predators.

Time series modeling of coastal fishery landings on the Southwestern Atlantic shelf: Influence of environmental drivers

AbstractTime‐series modeling of fisheries provides insights into stock tendencies and enables short‐term forecasting of landings, aiding decision makers in establishing management priorities. The Rio de la Plata Estuary and its maritime front sustain valuable fisheries for Argentina and Uruguay, with striped weakfish (Cynoscion guatucupa), whitemouth croaker (Micropogonias furnieri), and Argentine hake (Merluccius hubbsi) historically representing highest catches. However, their landings have declined in recent decades. To support resource management, we investigated the effectiveness of Autoregressive Integrated Moving Average (ARIMA) models in capturing fishery landing dynamics and providing reliable short‐term predictions. The best models exhibited a good fit and accurately captured the overall trends of landings. Residual variability unaccounted for by the model was analyzed in relation to time‐lagged environmental conditions. A wavelet coherence analysis was employed to examine the effect of the most significant variables on landings. Results revealed that environmental conditions affect differentially landings of each species as a result of their particular ecological traits. Turbidity and salinity affected mainly M. furnieri, which inhabits the innermost part of the estuary. Additionally, C. guatucupa, inhabiting the outer estuary and coastal region, exhibited a stronger association with river runoff compared to M. hubbsi, which inhabits the continental shelf. This study provides the first evidence of ARIMA models' reliability in representing the temporal evolution of catch in these fisheries, offering valuable tools for short‐term landings forecasting and facilitating sustainable management. Wavelet analysis findings will also contribute to enhancing our comprehension of trends in the correlation between environmental conditions and commercial landings.

Spatial-temporal neural networks for catch rate standardization and fish distribution modeling

Catch-per-unit-effort (CPUE) standardization is crucial for fishery stock assessment but often presents challenges due to spatial-temporal variations in species distribution and fishing effort. In this simulation study, we propose the use of customized artificial neural networks (ANNs) for modeling the spatial-temporal variations in CPUE standardization. This is achieved by encoding prior knowledge of the dependency structure between the variables into the architecture of the ANNs. We conducted numerical experiments on simulated data to compare our customized ANNs with Generalized Linear Models (GLMs), Generalized Additive Models (GAMs), and fully connected ANNs used in previous studies. Our simulated data cover three spatial-temporal dynamics scenarios with different degrees of species distribution shift over time: (1) steady fish distribution; (2) gradual directional shift over time; (3) sudden directional shift. In predicting the standardized CPUE in this simulation study, the customized ANNs demonstrated greater accuracy compared to the commonly used fully connected ANNs with an error reduction of over 70 %, more than 80 % compared to GLMs, and more than 40 % compared to GAMs, in terms of an error metric called the scaled mean absolute relative error. Our findings suggest that customized ANNs can serve as an alternative modeling tool alongside GLMs and GAMs in fisheries modeling.

Dynamics and Optimal Harvesting for Fishery Models with Reserved Areas

Dynamics and Optimal Harvesting for Fishery Models with Reserved Areas

The switch point algorithm applied to a harvesting problem.

In this paper, we investigate an optimal harvesting problem of a spatially explicit fishery model that was previously analyzed. On the surface, this problem looks innocent, but if parameters are set to where a singular arc occurs, two complex questions arise. The first question pertains to Fuller's phenomenon (or chattering), a phenomenon in which the optimal control possesses a singular arc that cannot be concatenated with the bang-bang arcs without prompting infinite oscillations over a finite region. 1) How do we numerically assess whether or not a problem chatters in cases when we cannot analytically prove such a phenomenon? The second question focuses on implementation of an optimal control. 2) When an optimal control has regions that are difficult to implement, how can we find alternative strategies that are both suboptimal and realistic to use? Although the former question does not apply to all optimal harvesting problems, most fishery managers should be concerned about the latter. Interestingly, for this specific problem, our techniques for answering the first question results in an answer to the the second. Our methods involve using an extended version of the switch point algorithm (SPA), which handles control problems having initial and terminal conditions on the states. In our numerical experiments, we obtain strong empirical evidence that the harvesting problem chatters, and we find three alternative harvesting strategies with fewer switches that are realistic to implement and near optimal.

ТЕХНИЧЕСКОЕ ОСНАЩЕНИЕ И ДОБЫЧА РЫБЫ В ИРКУТСКОЙ ОБЛАСТИ В 1947–1960-е гг.

The fishing industry plays a vital role in the development of the national economy, so its study is one of the most pressing problems for the economy of the region as a whole. The paper analyzes and summarizes the historical experience of the fishing industry, which is necessary to assess the current situation in the fishing industry and determine the further development of the industry. The functioning of the Soviet model of fisheries was ensured by a system of state support, which made it possible to successfully develop the fishing industry and solve social problems of coastal regions. The country's leadership always paid great attention to the development of the fishing industry as the most important sector of food supply for the population. During the years of Soviet power, in a short period of time, based on the implementation of plans for the industrialization of the country, the material and technical base of the fishing industry was created. Using the example of the Republic of Buryatia, the author examines the historical experience of combating poaching and notes the role of mobilization decisions of the Soviet state in this process. The current Soviet legislation on nature protection, the history of creation, structure and main functions of fisheries protection bodies are analyzed. Based on archival data, the number of detained offenders, the number of seized fish, fishing equipment and gear are given. A special place is given to the nature conservation society and the role of public inspectors, who, along with fisheries protection authorities, fought against poaching. An assessment is made of the technical equipment of fisheries protection authorities and criminal legal measures in preventing aquatic poaching based on an analysis of the established practice of their use in the period 1917–2000 in the Republic of Buryatia.

Walking sideways? Management of the Norwegian snow crab fishery

The snow crab (Chionoecetes opilio) in the Barents Sea is an invasive species, first discovered in 1997. Since 2012, a commercial fishery has developed, and various management measures have been implemented. Despite fishing gear restrictions, limits for the catch season and the implementation of a TAC-regime in 2017 onwards, the fishery struggles with substantial sustainability challenges. Vessels allocated a licence demonstrate radical differences in catches, and the fleet suffers from an unprofitable overcapacity and lack of environmentally friendly harvesting operations. The management authorities and the fishermen's organizations seem to agree that the regulated open access and the Olympic fisheries model are the main sources of the present problems. The Directorate of Fisheries (DoF) [1] has introduced a discussion paper outlining various options for closing the fishery. The article outlines these- and other options, and discusses the alternatives in terms of improved sustainability, i.e., environmental, economic as well as social. A key point is that closing the fishery (like many other management measures), are not only technical interventions. They are also political, and they contribute to modify both the regulating system and the system to be regulated.

Dynamics of a predator–prey fishery model with birth pulse, impulsive releasing and harvesting on prey

Dynamics of a predator–prey fishery model with birth pulse, impulsive releasing and harvesting on prey

Ecosystem-based management approaches for watershed conservation and geosustainability

When contributors' goals and legislative and political structures vary, as they often do in the case of worldwide fish populations, it becomes more challenging to implement ethical fishing tactics. Canada, the United States, and Mexico all fish from Pacific regions anchovies in the California Modern. Climate-driven numbers and geographic dynamics may pollute the waters of collaborative aquaculture and lead to overloading. This research expands upon prior works using a game theoretic model of Tran's boundary sardine fisheries in different climatic conditions to account for ecological links. More significant economic advantages accrue from cooperation fishing tactics that consider the mackerel's role as feed for other species in the natural system, as opposed to plans that merely take note of the worth of mackerel harvests to a particular fishing nation. The maximum environmental benefit is obtained at a fishery rate for sardines barely less than the sardine Fishery Management Safe Yield. Ecological-based control of fisheries can increase sustainability and profits, but only if investors and policy makers consider the ecology in business-applicable models. Understanding and adapting to the fast alterations in habitat distributions due to climate change and designing ways to achieve viable and lucrative fishery amidst altering environments will necessitate an increased emphasis on ecosystem-based governance.

Optimal harvest for predator–prey fishery models with variable price and marine protected area

In this paper, we propose a predator–prey fishery model with prey harvesting, variable price and marine protected area. We assume the price changes faster than other processes such as population growth and predation, and get a slow fast Ordinary Differential Equation (ODE) system. A simplified three-dimensional model is obtained by using approximate aggregation methods. The results show that there are two main scenarios, one is the depletion of fish stocks due to overfishing by fishermen, which is called a “catastrophic” equilibrium; and the other is a stable and sustainable fishery equilibrium. In order to avoid the extinction of fish, we consider establishing marine protected area (MPA) near fishing areas where fishermen only catch the prey. The results of the study provide the conditions for the establishment of MPA, allowing us to avoid the extinction of prey populations and establish sustainable fisheries. As another possibility, we consider increasing taxes to discourage overfishing by fishermen. In addition, when the tax revenue increases, the optimal harvest strategy is obtained. The optimal policy ensures the sustainable development of fisheries and maximizes the interests of fishermen.

The allocation of carbon resources in marine capture fisheries.

Marine fishery carbon emissions play a significant role in agricultural carbon emissions, making resource allocation a crucial topic for the overall marine ecological protection. This paper evaluates the dynamic iteration method as a research approach with the factors of resource allocation consisting of value assessment, optimization objective, difference between value assessment and objective, and optimization calculation. The paper selects the shadow price from the Super-SBM model as the judgment function for the goal value, aiming for the fairness criterion. From an equity standpoint, the allocation of carbon resources in marine capture fisheries proves to be unreasonable. The fishery model exhibits an excessive supply of carbon resources, resulting in wastage, while the green fishery model faces a relatively limited supply, with a focus on energy conservation and environmental protection. To address this issue, this paper proposes a new method and discusses the corrective results. This result shows that the stabilization point achieved is a short-term equilibrium rather than a long-term one. By rectifying the social contradiction of profit-oriented approaches, this research provides a fresh perspective for economic studies and applications, particularly in industrial layout and resource utilization optimization.

Non-smooth dynamics of a fishery model with a two-threshold harvesting policy

The non-linear dynamical systems theory helps implement regulatory measures to control the growth and evolution of various populations. While invasion by alien fish species is an emerging threat to native fish species in marine ecosystems, a suitable fishery management protocol needs to be incorporated in marine protected areas (MPAs) to mitigate the problem. We propose a policy of selective harvesting whenever the density of a species crosses a predefined threshold. An ecosystem with such a harvesting policy is modelled by a piece-wise smooth prey-predator type fishery model, where a control function defined by two thresholds evokes signals to cease or commence harvesting. This work reports the dynamics and bifurcations of a Filippov system, including the possibility of sliding mode dynamics. We show that the variations in the growth rate and the harvesting rate of the invasive fish species can lead to hysteresis through saddle–node and transcritical bifurcations and the appearance of a stable homoclinic orbit. We obtain the conditions for sliding domains, regular or virtual equilibria, boundary equilibria, pseudo-equilibria, and tangent points. Depending on the parameter choice, the system can stabilize at a regular equilibrium, a pseudo-equilibrium, or a pseudo-attractor, exhibiting multistability. We report the occurrence of regular or virtual equilibrium bifurcation, boundary node bifurcation and pseudo-saddle–node bifurcation. Our findings indicate that proper harvesting strategies can prevent the proliferation of invasive fish species in MPAs.

Characterization of a Cournot–Nash Equilibrium for a Fishery Model with Fuzzy Utilities

The article deals with the extensions of discrete-time games with infinite time horizon and their application in a fuzzy context to fishery models. The criteria for these games are the total discounted utility and the average utility in a fishing problem. However, in the fuzzy case, game theory is not the best way to represent a real fishing problem because players do not always have enough information to accurately estimate their utility in the context of fishing. For this reason, in this paper, trapezoidal-type fuzzy utility values are considered for a fishing model, and the terms of the Nash equilibrium are given in the fuzzy context, i.e., this equilibrium is represented using the partial order of the α-cuts of the fuzzy numbers; to the best of the authors’ knowledge, there is no work with this type of treatment. To obtain each equilibrium, a suitable fully determined fuzzy game is used in combination with the dynamic programming technique applied to this game in the context of fishing. The main results are (i) the Nash equilibria of the fuzzy games coincide with the Nash equilibria of the nonfuzzy games and are explicitly determined in a fishery model and (ii) the values of the fuzzy games are of trapezoidal type and are also explicitly given in the fishery model.

Simulation of fishery energy consumption and carbon emissions in Zhoushan City based on the long-range energy alternatives planning system model

To understand the current situation and development trend of energy consumption and carbon emissions in the fishery industry, a Long-Range Energy Alternatives Planning System (LEAP)-fishery model for Zhoushan City was constructed, and the trends of energy consumption and carbon emissions in the Zhoushan City fishery industry were analyzed under the business-as-usual scenario, the low-carbon scenario, and the strengthened low-carbon scenario. The results show that under the business-as-usual scenario, the future energy consumption of Zhoushan City’s fisheries in general shows an increasing trend, and the composition of energy consumption in all scenarios is primarily dominated by fossil energy, with diesel and coal predominating. In terms of the structure of end-use energy consumption, fishing vessels and aquaculture consume the most energy, with energy consumption exceeding 30% of total energy consumption in all scenarios. In terms of the emission reduction contribution rate, which the promotion of clean energy generation, the improvement of energy efficiency, and the reduction of aquaculture production play key roles in the low-carbon development of the fishery industry. From an economic perspective, carbon reduction measures such as reduction of aquaculture production and increased efficiency of energy delivery would have significant economic benefits, but these measures have limitations. Finally, suggestions are made to optimize the energy structure, improve the implementation of energy intensity and total energy control, and strengthen public awareness of energy conservation to reduce carbon emissions from the fishery industry, thus making the research in this paper relevant to real-world situations.

Intraguild predation in a tri-trophic age-structured fishery model

Intraguild predation in a tri-trophic age-structured fishery model

Optimal control problem of a discrete spatiotemporal prey–predator three-species fishery model

In this work, we discuss a spatiotemporal discrete prey–predator model. It consists of three compartments: prey, predator, and super-predator. The proposed model describes the interaction between prey, predator, and super-predator in a region with a discrete displacement. We also provide research on appropriate regional control strategies. The controls are applied to the predator and the super-predator, respectively; they represent catching these in measured quantities in a space and a time chosen. The aim is to increase the number of prey and reduce the number of predators, restore the food chain system, and ensure its sustainability. Finally, we provide graphical visuals and numerical simulations to support our analytical findings.

Stability and Hopf bifurcation of an intraguild prey-predator fishery model with two delays and Michaelis-Menten type predator harvest.

In this paper, we have proposed and investigated an intraguild predator-prey system incorporating two delays and a harvesting mechanism based on the Michaelis-Menten principle, and it was assumed that the two species compete for a shared resource. Firstly, we examined the properties of the relevant characteristic equations to derive sufficient conditions for the asymptotical stability of equilibria in the delayed model and the existence of Hopf bifurcation. Using the normal form method and the central manifold theorem, we analyzed the stability and direction of periodic solutions arising from Hopf bifurcations. Our theoretical findings were subsequently validated through numerical simulations. Furthermore, we explored the impact of harvesting on the quantity of biological resources and examined the critical values associated with the two delays.