Optimal Harvesting Strategy Research Articles

Optimal Harvesting Strategies for Timber and Non-Timber Forest Products with Nonlinear Harvesting Terms

Optimal Harvesting Strategies for Timber and Non-Timber Forest Products with Nonlinear Harvesting Terms

The impact of pollution reduction on the optimal harvesting strategy in a seasonally changing and polluted environment

The impact of pollution reduction on the optimal harvesting strategy in a seasonally changing and polluted environment

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 Minimum Target Diameter and the Harvest Age of Oak Natural Secondary Forests in Different Sites Conditions: Case Study in Hunan Province, China

Maintaining permanent forest canopy cover and eventually harvesting timber by predetermined target diameter are often considered as a prototype for future management of the oak natural forest. However, target diameters and harvest age based on average forest growth rates from wide geographical areas often hamper improved management of oak forests. In this study, based on the sampling of 129 target trees from 51 oak natural secondary forest plots in Hunan Province, China, an individual-tree DBH (diameter at breast height) growth model of oak target trees was developed, and the site type (41 levels) was related to the model as random effects by a nonlinear mixed-effects approach. Moreover, the 41 site types were clustered into four site type groups (STG1, STG2, STG3, and STG4) by the K-means clustering algorithm to improve the model performance and practicality. With the help of the model, the five target diameters (including 24, 30, 40, 50, and 60 cm) were simulated in each of the four STGs, and the minimum target diameter was determined for each STG based on the theory of quantitative maturity. In the four STGs, the harvest age of the 24 cm diameter target ranged from 30 to 51 years; the harvest age of the 60 cm target diameter ranged from 131 to 220 years, with the oaks failing to reach 60 cm in the lowest-quality STG4; the minimum target diameter ranged from 21 cm to 29 cm. Results showed that lower-quality sites exclude higher target diameters from optimal harvesting strategies, in contrast to the higher target diameter as a more reasonable strategy in higher quality sites, and that the minimum target diameter is significantly influenced by site conditions. Therefore, it is necessary to develop a diverse target-diameter-harvesting strategy adapted for the complex site conditions of oak forests in Hunan Province towards site-specific timber management to improve the sustainability of timber production in oak forests.

Bifurcation and optimal harvesting analysis of a discrete-time predator–prey model with fear and prey refuge effects

<p>In this contribution, the complicated dynamical behaviors and optimal harvesting policy of a discrete-time predator–prey model with fear and refuge effects are formulated. Both the fear and prey refuge effects refer to an interaction between predator and prey. In the first place, the existence and local stability of three fixed points of proposed model are investigated by virtue of our methodology, that is, the eigenvalues of the Jacobian matrix. One step further, it is worth mentioning that the model undergoes flip bifurcation (i.e., period–doubling bifurcation) and Neimark–Sacker bifurcation at the interior fixed point by the utilization of bifurcation theory and center manifold theory. Also, optimal harvesting strategy is investigated, and the expressions of optimal harvesting efforts are determined. Two examples, in the end, are put forward to prove that they are consistent with the previous theoretical results.</p>

Complex dynamics of a nonlinear discrete predator–prey system with fear factor and harvesting effect

In this paper, a class of discrete-time predator–prey system with fear factor and harvesting effect is proposed, and its complex dynamic behavior is analyzed. First, the existence and stability of equilibrium points of the discrete system are studied. Second, the critical value expressions of Neimark–Sacker bifurcation and flip bifurcation are obtained by bifurcation theory. Third, we control the bifurcation and chaos of the system by using feedback control strategies. The optimal harvesting strategy is obtained by using the Pontryagin maximum principle. Finally, we use MATLAB software to carry out some numerical simulations, which not only verify our theoretical results, but also analyze the rich dynamic behavior of the system.

Global non-sustainable harvest of renewable resources reduces their present price but increases their net present value

Over-exploitation of natural resources is a major problem, and transitions to sustainable harvest are taking place worldwide. To determine the optimal harvesting strategy, including the optimal speed and approach to transition toward sustainable harvest, policymakers need to estimate the net present values of natural resources. Previous studies have shown that discounting reduces the future value of natural resources, but the long-term increase in their price may partially compensate for discounting. However, the price and future values of natural resources may also be affected by the transition from over-harvesting to sustainable harvest. Here we present a model that endogenizes the effect of non-sustainable harvest on the price of a renewable natural resource. We show that the transition to sustainable harvest is expected to increase the resource’s price significantly, at a rate that is greater than its long-term increase. Incorporating this effect increases the estimated net present value of ecosystems providing renewable natural resources.

Improving microalgae growth modeling of outdoor cultivation with light history data using machine learning models: A comparative study

Accurate prediction of microalgae growth is crucial for understanding the impacts of light dynamics and optimizing production. Although various mathematical models have been proposed, only a few of them have been validated in outdoor cultivation. This study aims to investigate the use of machine learning algorithms in microalgae growth modeling. Outdoor cultivation data of Phaeodactylum tricornutum in flat-panel airlift photobioreactors for 50 days were used to compare the performance of Long Short-Term Memory (LSTM) and Support Vector Regression (SVR) with traditional models, namely Monod and Haldane. The results indicate that the machine learning models outperform the traditional models due to their ability to utilize light history as input. Moreover, the LSTM model shows an excellent ability to describe the light acclimation effect. Last, two potential applications of these models are demonstrated: 1) use as a biomass soft sensor and 2) development of an optimal harvest strategy for outdoor cultivation.

The effect of quota portfolio composition on optimal harvest strategy and profitability in a multi-species fishery

Abstract The benefits of individual vessel quota (IVQ) management in terms of improved harvest strategy and profitability are well recognized, but there is less focus on how different components of a quota portfolio can influence decisions underlying the effort allocation and profit-maximizing behaviour of fishers. Variations in the components of the quota portfolio may create economic incentives that alter the optimal harvest strategy and profitability. Thus, we study the potential impact of different components of quota portfolio on the intra-annual harvest strategy and profitability in two segments of the Norwegian bottom trawl fleet. By developing a vessel-based spatio-temporal bioeconomic framework, we demonstrate and compare adopted harvest strategies and accrued profits for small and large trawl vessels under three scenarios regarding restrictive quotas in codfish fishery. Our analysis confirms that alternations in the components of the quota portfolio influence the spatio-temporal dynamics of the fishing effort for small and large trawl vessels in different ways, probably due to the differences in vessel-specific characteristics. We also demonstrate that the differences in profit between small and large vessels in part depend on the overall size of the quota portfolio. The economies of scale in the trawl industry are being eroded as the shares of higher-priced species in the quota portfolio decreases. The benefits of economies of scale cannot be reaped as trawlers respond to the reduction in profit by redirecting effort from offshore areas of the Arctic to nearshore waters or staying ashore. Likewise, having small quotas of high-priced species reduces the effectiveness of the IVQ system in meeting management objectives, and could in some cases undermine sustainability outcomes. Our results also demonstrate that both the intensity with which fishers react to the fluctuations in market price levels and fishers’ perceptions of location attractiveness are influenced by the components of the quota portfolio.

Analysis of interval-valued model for interaction between plankton-fish population in marine ecosystem

The crux of present investigation is to develop an interval-valued population model for the interaction between phytoplankton, zooplankton and fish population under cyrtoid type functional response. The present study is also concerned to analyze the mathematical model under impreciseness and the parametric functional form for an interval valued model parameters. The boundedness, existence of the solution, stability analysis and all possible feasible equilibrium points have been examined. The optimal harvesting strategy has been implemented and obtained the optimal solution with the help of the Pontryagin maximum principle. The significant impact of interval valued biological parameters has been analyzed and portrayed by means of graph for given different fit values, approximate to the model system in real scenario.

Effects of harvesting and planktivorous fish on bioeconomic phytoplankton-zooplankton models with ratio-dependent response functions and time delays

This work presents a prey-predator model for plankton interactions in aquatic environments and the influence of planktivorous fish predation. Considering that some phytoplankton and zooplankton can be harvested due to their economic value, the time lag required for zooplankton gestation (representing the time delay) is included. The current study's main objective is to analyze planktivorous fish's influence on harvesting activity in both populations and the corresponding discrete delay (delay in zooplankton gestation) in the model. The stability characteristics of models with and without gestation delay are investigated, and the gestation delays threshold value is determined. The periodic solution's stability and the Hopf bifurcations' direction are determined by employing the center manifold theory. We use Lyapunov's method to investigate the global stability of the model without time delay. Bioeconomic equilibrium is obtained in three cases, each with certain conditions. In addition, the optimal harvesting strategy from the model is obtained by using the Pontryagin Maximum Principle and considering harvesting effort as a control variable. Finally, numerical simulations are performed to illustrate our analytical findings, and the ecological implications of our analytical findings are also discussed.

A study on imprecise mathematical model for optimal management and utilization of renewable resource by population

The development and survival of the biological population depend heavily on the availability of food and other materials that may be produced from renewable resources. In real life situation the information reported about the parameters of ecological model system may not be precise due to various issues like insufficient data, error in data collection, wrongly measurement etc. To address all of these challenges, an ecological model system must be developed in an ambiguous setting where the ecological parameters are handled as different kinds of fuzzy numbers. In this article, we present an imprecise mathematical model for optimal management and utilization of renewable resources by population. We introduce the model system in interval environment and apply a parametric form of interval number which makes different form of crisp ecological model. The positivity and boundedness of the proposed model system are checked. The stability criterion of feasible equilibrium points and bionomical equilibrium have been discussed. Moreover maximum sustainable strategy and optimal harvesting strategy are analyzed using interval number. Numerical discussion are provided to verify the result of the proposed system.

Optimal hydraulic energy harvesting strategy for PaT installation in Water Distribution Networks

Water Distribution Networks (WDNs) represent a noteworthy field for possible implementation of Small Hydropower (SHP), by replacing Pressure Reduction Valves (PRV) with turbomachines, in particular Pump as Turbines (PaTs), to control and regulate the pressure, while harvesting energy otherwise wasted. Different models were developed to predict the performance and select the positioning of the PaTs for the maximum energy recovery but most of them neglect practical aspect such as: power grid limitations and optimal harvesting strategy. In this framework, we intend to propose a new method to select a PaT, defining its optimal working point, by introducing an energy exploitation coefficient. The proposed methodology is based on the experimental results of a real PaT tested in the high capacity hydraulic laboratory at Polytechnic University of Bari. Firstly, the selected commercial centrifugal pump was tested in both pump and turbine modes. Then, three different approaches, for the Best Efficiency Point (BEP) selection, are described and compared in terms of energy exploitation and capacity factor for a WDN. The first consists of selecting the BEP at the average flow rate, the second one considers the probability distribution of the flow rate and the corresponding available hydraulic energy, whereas the latter is based on the highest energy harvesting. By applying energy production, economic and environmental analyses, the new proposed methodology, based on the third approach, shows a remarkable advantage in terms of exploited energy. Indeed a remarkable 60% energy recovery is achieved with 334 ton CO2/year avoided. Furthermore, the impact of the electrical motor on the maximum power generation (cut-off) is considered. Eventually, useful insights for the future PaT selection and installation are discussed.

Complex dynamics of two prey–predator harvesting models with prey refuge and interval‐valued imprecise parameters

In view of the phenomena that species in nature are affected by the complexity of the ecosystem, some key biological parameters have certain inaccuracy or uncertainty and part of the prey hides in the shelter from predation. Moreover, different species exhibit different living habits, so it is of certain interest to investigate species‐related imprecise biological parameters. Besides, from the perspective of scientific and reasonable exploitation and utilization of fishery resources, two types of harvesting strategies are introduced into the system. Firstly, the dynamic properties of the system guided by continuous harvesting strategy are analyzed, which demonstrates the impact of refuge rate, imprecision indexes and harvesting efforts on the system dynamics. Meanwhile, the bio‐economic equilibrium is discussed, and the optimal harvesting strategy is obtained. Secondly, the complex dynamics of the system induced by weighted harvesting activity are analyzed. The predator‐extinction periodic solution and coexistent order‐1 periodic solution is discussed according to different weights and thresholds. Finally, the correctness of the obtained results and the feasibility of the harvesting strategy are verified through numerical simulation in MATLAB. The results of this study provide a reference for the scientific and reasonable exploitation and utilization of prey–predator fishery resources in the imprecise parameter environment.

A predator-prey model for the optimal control of fish harvesting through the imposition of a tax

This paper is devoted to the study of ecosystem based fisheries management. The model represents the interaction between prey and predator population with Holling II functional response consisting of different carrying capacities and constant intrinsic growth rates. We have considered the continuous harvesting of predator only. It is observed that if the intrinsic growth rate of predator population crosses a certain critical value, the system enters into Hopf bifurcation. Our observations indicate that tax, the management object in fisheries system play huge impacts on this system. The optimal harvesting policy is disposed by imposing a tax per unit of predator biomass. The optimal harvest strategy is determined using Pontryagin's maximum principle, which is subject to state equations and control limitations. The implications of tax are also examined. We have derived different bifurcations and global stability of the system. Finally, numerical simulations are used to back up the analytical results.

Complex dynamics and optimal harvesting strategy of competitive harvesting models with interval-valued imprecise parameters

Considering that species in nature are affected by the complexity of the ecosystem, biological parameters present certain inaccuracy or uncertainty. Different species exhibit different living habits, so it is of certain interest to investigate species related imprecise parameters. Besides, from the perspective of scientific and reasonable exploitation and utilization of fishery resources, two types of two-species competitive models with species related interval-valued imprecise parameters and harvesting are established. Firstly, the influence of interval-valued imprecise parameters on the dynamic behavior of the system without harvest are analyzed. Then, for continuous harvesting system, the existence of bio-economic equilibrium is discussed, and the optimal harvesting strategy is obtained by using Pontryagin’s maximum principle. Next, for the system guided by weighted harvesting strategy, the existence and stability of the order-1 periodic solution are discussed. Besides, in order to find the harvesting strategy that maximizes the economic profit in the harvest process, an optimization problem is constructed according to the actual situation, and the optimal set values of the weight and threshold of the strategy are obtained. Finally, the correctness of the obtained results and the feasibility of the harvesting strategy are verified through numerical simulation in MATLAB. The results of this study provide a reference for the scientific and reasonable exploitation and utilization of competitive fishery resources in the imprecise parameter environment.

Optimal harvesting strategy for stochastic hybrid delay Lotka-Volterra systems with Lévy noise in a polluted environment.

This paper concerns the dynamics of two stochastic hybrid delay Lotka-Volterra systems with harvesting and Lévy noise in a polluted environment (i.e., predator-prey system and competitive system). For every system, sufficient and necessary conditions for persistence in mean and extinction of each species are established. Then, sufficient conditions for global attractivity of the systems are obtained. Finally, sufficient and necessary conditions for the existence of optimal harvesting strategy are provided. The accurate expressions for the optimal harvesting effort (OHE) and the maximum of expectation of sustainable yield (MESY) are given. Our results show that the dynamic behaviors and optimal harvesting strategy are closely correlated with both time delays and three types of environmental noises (namely white Gaussian noises, telephone noises and Lévy noises).

Optimal harvesting strategy of a stochastic $ n $-species marine food chain model driven by Lévy noises

<abstract><p>A stochastic $ n $-species marine food chain model with harvesting and Lévy noises is proposed. First, the criterion on the asymptotic stability in distribution is established. Second, the criterion on the existence of optimal harvesting strategy (OHS) and the maximum of expectation of sustainable yield (MESY) are derived. Furthermore, the numerical simulations are presented to verify the theoretical results. Our results show that (i) noises intensity can easily affect the dynamics of marine populations, leading to the imbalances of marine ecology, (ii) the establishment of an optimal harvesting strategy should fully consider the impact of noises intensity for better managing and protecting marine resources.</p></abstract>

Dynamics study of nonlinear discrete predator-prey system with Michaelis-Menten type harvesting.

In this paper, we study a discrete predator-prey system with Michaelis-Menten type harvesting. First, the equilibrium points number, local stability and boundedness of the system are discussed. Second, using the bifurcation theory and the center manifold theorem, the bifurcation conditions for the system to go through flip bifurcation and Neimark-Sacker bifurcation at the interior equilibrium point are obtained. A feedback control strategy is used to control chaos in the system, and an optimal harvesting strategy is introduced to obtain the optimal value of the harvesting coefficient. Finally, the numerical simulation not only shows the complex dynamic behavior, but also verifies the correctness of our theoretical analysis. In addition, the results show that the system causes nonlinear behaviors such as periodic orbits, invariant rings, chaotic attractors, and periodic windows by bifurcation.

The dynamics and harvesting strategies of a predator-prey system with Allee effect on prey

<abstract><p>The study of harvesting mechanisms in predator-prey systems with an Allee effect on prey has always garnered significant attention. In this paper, the dynamics and harvesting strategies of a predator-prey system are investigated, where the prey is subject to the Allee effect. The positivity and boundedness of solutions, the existence and stability of equilibria are further studied. The existence of a Hopf bifurcation at the interior equilibrium point of the system is investigated and verified by numerical simulations. Furthermore, we investigate the maximum sustainable yield (MSY), maximum sustainable total yield (MSTY) and the optimal economic profit of the proposed system. We find that MSY can be attained through predator harvesting, while MSTY is observed when harvesting efforts are uniform across species. In these situations, the biological system maintains stability. Using the method of control parametrization, the optimal economic profit and harvesting strategy are obtained. The results show that the harvesting efforts can affect the stability of the system, resulting in several interesting biological phenomena. This research provides a theoretical basis for biological resource management.</p></abstract>