Harvesting Effort Research Articles

Maximum principle for the optimal harvesting problem of a size-stage-structured population model

<p style='text-indent:20px;'>The optimal harvesting of biological resources, which is directly relevant to sustainable development, has attracted more attention. In this paper, we first prove the existence and uniqueness of generalized solution of a size-stage-structured population model while the optimal harvesting effort is discontinuous. Next, we demonstrate the existence of the optimal harvesting policy. Further, based on the idea of the Pontryagin's maximum principle of the optimal control problem in ordinary differential equations, we derive the maximum principle describing the optimal control. Finally, the dynamical behavior of the population is simulated by solving the corresponding optimality system numerically with an algorithm based on the method of backward Euler implicit finite-difference approximation. The numerical simulations indicate harvesting activity will reduce the quantity of the population and that increasing harvesting cost will result in less adult harvested. This provides guideline of implementing harvesting tactic to guarantee the persistence of the population.</p>

Harvesting optimization with stochastic differential equations models: is the optimal enemy of the good?

We can describe the size evolution of a harvested population in a randomly varying environment using stochastic differential equations. Previously, we have compared the profit performance of four harvesting policies: (i) optimal variable effort policy, based on variable effort; (ii) optimal penalized variable effort policies, penalized versions based on including an artificial running energy cost on the effort; (iii) stepwise policies, staircase versions where the harvesting effort is determined at the beginning of each year (or of each biennium) and kept constant throughout that year (or biennium); (iv) constant harvesting effort sustainable policy, based on constant effort. They have different properties, so it is also worth looking at combinations of such policies and studying the single and cross-effects of the amount of penalization, the absence or presence and type of steps, and the restraints on minimum and maximum allowed efforts. Using data based on a real harvested population and considering a logistic growth model, we perform such a comparison study of pure and mixed policies in terms of profit, applicability, and other relevant properties. We end up answering the question: is the optimal enemy of the good?

Gulf fisheries supported resilience in the decade following unparalleled oiling

AbstractThe 2010 Deepwater Horizon (DwH) disaster challenged the integrity of the Gulf of Mexico (GOM) large‐marine ecosystem at unprecedented scales, prompting concerns of devastating injury for GOM fisheries in the post‐spill decade. Following the catastrophe, projected economic losses for regional commercial, recreational, and mariculture sectors for the decade after oiling were US$3.7–8.7 billion overall, owing to the vulnerability of economically prized, primarily nearshore taxa that support fishing communities. State and federal fisheries data during 2000–2017 indicated that GOM fishery sectors appeared to serve as remarkable anchors of resilience following the largest accidental marine oil spill in human history. Evidence of post‐disaster impacts on fisheries economies was negligible. Rather, GOM commercial sales during 2010–2017 were US$0.8–1.5 billion above forecasts derived using pre‐spill (2000–2009) trajectories, while pre‐ and post‐spill recreational fishery trends did not differ appreciably. No post‐spill shifts in target species or effort distribution across states were apparent to explain these findings. Unraveling the mechanisms for this unforeseen stability represents an important avenue for understanding the vulnerability or resilience of human–natural systems to future disturbances. Following DwH, the causes for fishery responses are likely multifaceted and complex (including exogenous economic forces that typically affect fisheries‐dependent data), but appear partially explained by the relative ecological stability of coastal fishery assemblages despite widespread oiling, which has been corroborated by multiple fishery‐independent surveys across the northern GOM. Additionally, we hypothesize that damage payments to fishermen led to acquisition or retooling of commercial fisheries infrastructure, and subsequent rises in harvest effort. Combined, these social–ecological dynamics likely aided recovery of stressed coastal GOM communities in the years after DwH, although increased fishing pressure in the post‐spill era may have consequences for future GOM ecosystem structure, function, and resilience.

Stability analysis of two predators and one prey population model with harvesting in fisheries management

The discussion is focussed in the interaction between two predators and one prey population model in fishery management. Mathematically model is built by involving harvesting with constant efforts in the two predators and one prey populations. The positive equilibrium point of the model is analyzed via linearization and Routh-Hurwitz stability criteria. From the analysis, there exists a certain condition that makes the positive equilibrium point is asymptotically stable. The stable equilibrium point is then related to the maximum profit problem. With suitable value of harvesting efforts, the maximum profit is reached and the predator and prey populations remain stable. Finally, a numerical simulation is carried out to find out how much the maximum profit is obtained and to visualize how the trajectories of predator and prey tend to the stable equilibrium point.

Dynamics of a harvested stage‐structured predator–prey model with distributed maturation delay

A new delayed predator–prey model with stage‐structure and harvesting on prey and predator is proposed, where the stage‐structure is modeled by the introduction of distributed time delay. The positivity, boundedness and the conditions for uniform persistence have been derived. We investigate the dynamical behavior of the system in terms of local stability of each feasible equilibria, global stability, and persistence. We find that the dynamics of the model depends largely on the harvesting efforts on the two species and the specific form of the birth and death functions.

Stability and Bifurcation Analysis of a Discrete Singular Bioeconomic System

The main concern of this paper is to discuss stability and bifurcation analysis for a class of discrete predator-prey interaction with Holling type II functional response and harvesting effort. Firstly, we establish a discrete singular bioeconomic system, which is based on the discretization of a system of differential algebraic equations. It is shown that the discretized system exhibits much richer dynamical behaviors than its corresponding continuous counterpart. Our investigation reveals that, in the discretized system, two types of bifurcations (i.e., period-doubling and Neimark–Sacker bifurcations) can be studied; however, the dynamics of the continuous model includes only Hopf bifurcation. Moreover, the state delayed feedback control method is implemented for controlling the chaotic behavior of the bioeconomic model. Numerical simulations are presented to illustrate the theoretical analysis. The maximal Lyapunov exponents (MLE) are computed numerically to ensure further dynamical behaviors and complexity of the model.

Stability analysis of a delayed predator–prey model with nonlinear harvesting efforts using imprecise biological parameters

Abstract In this paper, the dynamical behaviors of a delayed predator–prey model (PPM) with nonlinear harvesting efforts by using imprecise biological parameters are studied. A method is proposed to handle these imprecise parameters by using a parametric form of interval numbers. The proposed PPM is presented with Crowley–Martin type of predation and Michaelis–Menten type prey harvesting. The existence of various equilibrium points and the stability of the system at these equilibrium points are investigated. Analytical study reveals that the delay model exhibits a stable limit cycle oscillation. Computer simulations are carried out to illustrate the main analytical findings.

Evaluating the Impact of Recreational Harvest and Management Strategies for Bay Scallops Argopecten irradians concentricus in a Florida Gulf Coast Management Zone

AbstractSince 1994, the fishery for bay scallops Argopecten irradians concentricus in Florida has been limited to a recreational fishery that operates during the summer, before the spawning season in fall. Recent growth of the fishery necessitates a study of the effect of this increased exploitation on the bay scallop population. The study focused on one management zone, centered on the community of Steinhatchee, that is known for high rates of exploitation. Within this zone, we created a model of bay scallop harvest using fishery‐independent and fishery‐dependent survey methods and evaluated the risk of extirpation of the stock. We found that the fishery in the zone functions as a derby, with most harvest effort occurring when the season opens, followed by a steady decline throughout the season. Effort estimates suggest that 21,579 vessels, or 82,398 people, from 94% of Florida’s counties and 16 other states participated in the 2018 season in the Steinhatchee zone. The influx of harvesters generated approximately US$1.8 million in revenue for this small coastal community and resulted in an estimated fishing mortality of 57–72% of the population in the zone. The exploitation rate of the fishery in 2018 exceeded 0.4, suggesting that the fishery may be unable to sustain itself under current conditions. We evaluated management strategies and found that the bay scallop population in this zone would be in danger of being extirpated if harvest effort doubled, suggesting the need for regular monitoring of effort in this fishery in this zone and probably in the fishery statewide.

Optimal control of harvesting effort in a phytoplankton–zooplankton model with infected zooplankton under the influence of toxicity

In the present investigation, a prey–predator model consisting of phytoplankton, susceptible zooplankton, and infected zooplankton, incorporating the response function of Holling type II, has been explored. Logistic growth is assumed to be followed by the phytoplankton species. A combined effort (E) is applied to harvest all of the three populations. Environmental toxicity is considered to affect the phytoplankton species directly and the predating zooplankton indirectly. The dynamical behaviour of the model is examined for each of the possible steady states. Hopf-bifurcation analysis has been carried out with the combined harvesting effort E as the bifurcation parameter. The optimal control is characterized by using Pontryagin’s maximum principle. In the end, the analytical discoveries found so far have been established employing numerical simulations.

On the Dynamics of an Eco-Epidemiological System Incorporating a Vertically Transmitted Infectious Disease

An eco-epidemiological system incorporating a vertically transmitted infectious disease is proposed and investigated. Micheal-Mentence type of harvesting is utilized to study the harvesting effort imposed on the predator. All the properties of the solution of the system are discussed. The dynamical behaviour of the system, involving local stability, global stability, and local bifurcation, is investigated. The work is finalized with the numerical simulation to observe the global behaviour of the solution.

Theoretical results of optimal harvesting in a hierarchical size-structured population system with delay

We investigate an optimal control problem for a hierarchical size-structured population model, which incorporates the inoculation delay into the globally feedbacked boundary condition. After the establishment of the continuity of the states with respect to the harvesting efforts, the existence of the optimal solutions is proved by a result in convex analysis, and the maximum principle is obtained via conjugate system and tangent-normal cones.

Integrating harvest and camera trap data in species distribution models

Wildlife managers need reliable information on species distributions (i.e. patterns of occurrence and abundance) to make effective decisions. Historically, managers have relied on harvest records (collected at broad spatial extents but coarse resolution) to monitor wildlife populations. However, emerging citizen-science datastreams can potentially supplement harvest-based monitoring by providing fine-resolution data that permit identification of species-environment relationships needed to predict occurrence and abundance. We combined harvest records and citizen-science camera-trap data in integrated species distribution models (iSDMs) to estimate species-environment relationships and distribution patterns of six wildlife species in Wisconsin, USA. We expected that iSDMs would more precisely estimate species-environment relationships and predict spatial abundance patterns intermediate between camera- and harvest-only SDMs. We also conducted simulations to explore the consequences of incomplete knowledge of harvest effort for estimates of abundance and species-environment relationships. Integrated models produced more precise species-environment relationships than camera-only models in 53% of the relationships we tested; all harvest-only models failed to converge. Moreover, integrated and camera-only models showed low agreement (mean: 19.67%) in identifying abundance “hotspots” but considerably higher agreement (mean: 45.17%) in identifying abundance “cold spots”. Our simulations showed that abundance patterns estimated by iSDMs may suffer from imprecision if harvest effort is poorly measured. We recommend that harvest records be collected at finer spatial resolutions and be paired with in-depth effort reporting. Our work demonstrates the potential for integrating an existing datastream (harvest records) with an emerging one (citizen-science camera-trap monitoring) for modeling species distributions and providing support for wildlife management decisions.

Reactivity in prey–predator models at equilibrium under selective harvesting efforts

Reactivity is an important feature of every stable state to measure the short-term instability of such stable state in prey–predator models. Asymptotic stability is not a powerful tool to study the dynamics immediately after an equilibrium has disturbed. We are interested in studying the effect of disturbance made by harvesting effort to the stable state of a set of prey–predator models. We consider different scenarios of disturbance made by prey harvesting only, predator harvesting only and selective harvesting on both. We show that disturbance made by prey harvesting causes reactivity of stable state but not in a sustainable way (non-existence of maximum sustainable yield). Further, it is shown that disturbance made by predator harvesting causes reactivity of stable state but in a sustainable way. We study how disturbance made by different harvesting strategies to the asymptotically stable state in the prey–predator system where intraspecific competition rule applied to predator species affects transient dynamics. We find that the transient dynamics properties like reactivity and non-reactivity switch through disturbance made by harvesting but in a sustainable way (maximum sustainable yield exists). Further, we find that asymptotically stable state remains reactive following multiple disturbances made by selective harvesting on both but in a sustainable way (maximum sustainable total yield exists)

Dynamical Behaviour of Infected Predator–Prey Eco-epidemics with Harvesting Effort

This investigation accounts for a predator–prey system where the predator community is affected by infectious disease and also subjected to harvest. The model considers the behavioural change in susceptible predators due to the crowding effect of infected predators. The dynamical characteristics are studied encompassing asymptotic stability of the existing equilibrium points and bifurcation analysis. A sufficient parametric condition for global stability of the interior equilibrium point is investigated using a geometric approach. The system undergoes a Hopf-bifurcation around interior equilibrium point considering disease transmission rate as a bifurcation parameter. An optimal control problem is formulated by considering a time-dependent fishing effort as a control variable. The objective of this optimal control problem is to maximize the present value of the economic revenue obtained by fishing. Finally, several numerical simulations are conducted to visualize our analytical results.

Balanced harvesting in two predators one prey system

In this research, we discuss balancing two essential ecosystem services, known as resilience and yield, in a harvested two predators one prey system. We study how these two ecosystem services respond to different types of harvesting plans applied to the system. In individual harvesting, we observe that prey harvesting is suitable for generating more yield while either predator harvesting gives more resilience. Several patterns are possible based on the intensity of harvesting efforts applied to prey or the predator in simultaneous harvesting. This study shows that a balanced harvest between prey and predators may give more than the selective harvesting of any species yielding and stabilizing the ecosystem. Even if this fair strategy is not a cooperative situation for both resilience and yield, it may be the most favorable approach to scale those services. Finally, we may state that it would help us correlate the safest position (corresponds to the maximizing resilience yield) and the good views (which corresponds to the maximum sustainable return) to safeguard our ecosystems.

Bogdanov\u2013Takens bifurcation of a Holling IV prey\u2013predator model with constant-effort harvesting

A prey–predator model with constant-effort harvesting on the prey and predators is investigated in this paper. First, we discuss the number and type of the equilibria by analyzing the equations of equilibria and the distribution of eigenvalues. Second, with the rescaled harvesting efforts as bifurcation parameters, a subcritical Hopf bifurcation is exhibited near the multiple focus and a Bogdanov–Takens bifurcation is also displayed near the BT singularity by analyzing the versal unfolding of the model. With the variation of bifurcation parameters, the system shows multi-stable structure, and the attractive domains for different attractors are constituted by the stable and unstable manifolds of saddles and the limit cycles bifurcated from Hopf and Bogdanov–Takens bifurcations. Finally, a cusp point and two generalized Hopf points are found on the saddle-node bifurcation curve and the Hopf bifurcation curves, respectively. Several phase diagrams for parameters near one of the generalized Hopf points are exhibited through the generalized Hopf bifurcation.

Optimal harvesting strategies of a stochastic competitive model with S-type distributed time delays and L\xe9vy jumps

The aim of this paper is to investigate the optimal harvesting strategies of a stochastic competitive Lotka–Volterra model with S-type distributed time delays and Lévy jumps by using ergodic method. Firstly, the sufficient conditions for extinction and stable in the time average of each species are established under some suitable assumptions. Secondly, under a technical assumption, the stability in distribution of this model is proved. Then the sufficient and necessary criteria for the existence of optimal harvesting policy are established under the condition that all species are persistent. Moreover, the explicit expression of the optimal harvesting effort and the maximum of sustainable yield are given.

Time-dependent probability density function for general stochastic logistic population model with harvesting effort

We derive and analyze the time-dependent probability density function for the number of individuals in a population at a given time in a general logistic population model with harvesting effort using the Fokker–Planck equation. The time-dependent probability density function (obtained as the unique principal solution of the Fokker–Planck equation corresponding to certain initial value and boundary conditions) is used to describe how the distribution of the population process changes with time. We assume the environment is randomly varying and the population is subject to a continuous spectrum of disturbances, with fluctuations in the intrinsic growth rate and the harvesting effort. The randomness is expressed as independent white noise processes. The effect of changes in the intrinsic growth rate, harvesting effort, and noise intensities on the distribution is investigated. In addition, conditions for the existence of optimal harvesting policy are obtained using properties of the time-dependent probability density function. The results obtained in this work are validated using population and published parameters.

Relationship between multiple ecosystem services and sustainability in three species food chain

The world fisheries are mainly focused on the yield from fishing, and hence maximum sustainable yield (MSY) policy has become the most popular management tool. But this aim of maximum productivity, particularly in the multitrophic system, impacts the resilience, considering the potential of the system to absorb the disturbances applied to the system. Due to harvesting effort used on different individual trophic levels, the trade-offs and synergies between yield and resilience of a tri-trophic food chain system have been studied. In Holling type II functional response, the enrichment of carrying capacity can destabilize the system and may adversely affect the system resilience. In the case of prey harvesting, for both Holling type I and II responses, the existence of MSY depends on some parametric restrictions, but resilience maximizing yield (RMY) always exists. For predator harvesting, only RMY may be a favorable harvesting strategy as MSY does not exist. But for the top predator harvesting with both for Holling type I and II functional responses, both the pair MSY and RMY exist. Either MSY, or RMY, or a balanced approach between them, maybe implemented depending upon the requirements of more yield, or more resilience, or balancing them.

An ecological golden rule

Most renewable biotic resources are subject to random variability in natural growth. We investigate the implications of such variability for long-term management by a risk averse social planner, who maximizes expected long-run utility. In the canonical model of a stochastic fishery, we show that the optimal level of harvesting effort need not necessarily be reduced by variability in stock growth. However, optimal effort is reduced if variability of growth increases for smaller base populations, as suggested in the ecology literature.