Harvesting Effort Research Articles

Policy effectiveness in spatial resource wars: A two-region model

We develop a spatial resource model in continuous time in which two agents strategically exploit a mobile resource in a two-region setup.To counteract the overexploitation of the resource (the tragedy of commons) that occurs when players are free to choose where to harvest, the regulator can establish a series of spatially structured policies. We compare the equilibria in the case of a common resource with those that emerge when the regulator either creates a natural reserve, or assigns Territorial User Rights to the players.We show that, when technological and preference parameters dictate a low harvesting effort, the policies are ineffective in promoting the conservation of the resource and, in addition, they lead to a lower payoff for at least one of the players. Conversely, in a context of higher harvesting effort, the intervention can help to safeguard the resource, preventing extinction while also improving the welfare of both players.

Stability and bifurcation analysis of Filippov food chain system with food chain control strategy

In the present work, we introduce a control model to describe three species food chain interaction model composed of prey, middle predator, and top predator. The middle predator preys on prey and the top predator preys on middle predator. The control techniques of the exploited natural resources are used to modulate the harvesting effort to avoid high risks of extinction of the middle predator and keep stability of the food chain, by prohibiting fishing when the population density drops below a prescribed threshold. The behavior of the system stability of the regular, virtual, pseudo-equilibrium and tangent points are discussed. The complicated non-smooth dynamic behaviors (sliding and crossing segment and their domains) are analyzed. The bifurcation set of pseudo-equilibrium and the sliding crossing bifurcation have been investigated. Our analytical findings are verified through numerical investigations.

Optimal Harvesting for Size-Dependent Control

We investigate some optimal harvesting problems concerning the age-structured population dynamics. The goal is to maximize the profit with respect to a size-dependent harvesting effort. The harvesting is made either by fishing or by hunting. For each studied problem, we state the necessary optimality conditions and use them to get the structure of the optimal control. For the problem related to hunting, we derive an iterative algorithm to improve at each step the harvesting effort, in order to increase the profit. Numerical tests are performed to show that the proposed methods are effective.

Maximum Sustainable Yield (MSY) value in predator-prey model with holling type ii functional response

Maximum Sustainable Yield (MSY) is a management exploitation that aims to maximize the catch but still maintain its sustainability. In this article, the authors try to build a model which have been modified from basic Lotka-Volterra model with addition logistic function to prey population and Holling Type II functional response to predator population as well as harvesting of both population. The equilibrium points and the stabilityvare done here through the linearization. Dynamical simulations are shown to illustrate the dynamics of the two populations. Based on the results of analysis and dynamical simulation, the MSY value can be achieved when the harvesting efforts does not exceed or equal the MSY value.

Optimal fishery with coastal catch

AbstractIn many spatial resource models, it is assumed that an agent is able to harvest the resource over the complete spatial domain. However, agents frequently only have access to a resource at particular locations at which a moving biomass, such as fish or game, may be caught or hunted. Here, we analyze an infinite time‐horizon optimal control problem with boundary harvesting and (systems of) parabolic partial differential equations as state dynamics. We formally derive the associated canonical system, consisting of a forward–backward diffusion system with boundary controls, and numerically compute the canonical steady states and the optimal time‐dependent paths, and their dependence on parameters. We start with some one‐species fishing models, and then extend the analysis to a predator–prey model of the Lotka–Volterra type. The models are rather generic, and our methods are quite general, and thus should be applicable to large classes of structurally similar bioeconomic problems with boundary controls.Recommedations for Resource Managers Just like ordinary differential equation‐constrained (optimal) control problems and distributed partial differential equation (PDE) constrained control problems, boundary control problems with PDE state dynamics may be formally treated by the Pontryagin's maximum principle or canonical system formalism (state and adjoint PDEs). These problems may have multiple (locally) optimal solutions; a first overview of suitable choices can be obtained by identifying canonical steady states. The computation of canonical paths toward some optimal steady state yields temporal information about the optimal harvesting, possibly including waiting time behavior for the stock to recover from a low‐stock initial state, and nonmonotonic (in time) harvesting efforts. Multispecies fishery models may lead to asymmetric effects; for instance, it may be optimal to capture a predator species to protect the prey, even for high costs and low market values of the predators.

Some Aspect on the Biology of Pen Shell Atrina Pectinata (Linneaus, 1767) In Coastal Waters of Maqueda Bay, Philippines

A Total of 379 pen shells Atrinapectinata were collected from February 2017 to January 2018 in the coastal waters of Maqueda Bay. Measurement and analysis of length and weight were done using FiSAT software. Population parameters were assessed to evaluate the stock status which includes the asymptotic length (L∞) and growth coefficient (K) to be 34.65 cm, 0.77 year−1 respectively. Specimens of A. pectinata reached a mean length of 20.98 cm. Length-weight relationship resulted to “negative allometric” 0.0462L2.6533 R2 = 0.7823; signifying pen shells growth was faster in length than on weight. The recruitment pattern was continuous over the year with one major peak during rainy season (July). In addition, the highest catch based on collected sampling date catch was during summer, which suggest as the peak season of the species in the area. Furthermore, the average catch annually of hookah diver was 17.69208. Higher condition index was recorded from April to May, September and January, indicating the high quality of pen shell meat and is recommended as the best period to harvest pen shell whereas June to August and October to December can be concluded as the spawning period of the pen shell and the ideal period to institute close season. Further analysis revealed that the pen shell was nearly facing overexploitation with the exploitation rate (E = 0.46) mainly due to lack of a minimum limit size and also due to an increase in the harvesting effort. The estimated total mortality (Z), natural mortality (M) and fishing mortality (F); 1.36 year−1, 1.01year−1 and 0.62 year−1, respectively. Using the mentioned (Z), (M), (F) and (E), the total population resulted to 84725.7 suggesting that half of the population has been exploited due to overfishing

Model Predictive Control of the Harvesting Effort of a Sustainable Seafood with a Nonlinear State Equation

This paper is concerned with the nonlinear model predictive control of the harvesting effort of a renewable resource system, namely, sustainable seafood (farmed fish), with a nonlinear state equation. A solution approach is proposed and discussed, and numerical illustrations are provided.

Discrete optimal capital investment and financing policies in fishery resource harvesting with reserve area

This research discusses a problem in renewable resource (fish) harvesting on single-owner fishery where the dynamics of growth are expressed by system of difference equations. The model involves three state variables (stock of equity, resource stock in reserve zone and unreserved zone) and two control variables (effort rate and dividend payout rate). Discrete Pontryagin maximum principle was applied to obtain optimality conditions which must be satisfied by the variables. Further, the forward-backward sweep method was used to determine the numerical solution of optimal control model. Three scenarios of interest rate applied to find out the response of company in managing harvesting effort and dividend payout rate were investigated.

ANALISIS KESTABILAN DAN KONTROL OPTIMAL MODEL LESLIE-GOWER FUNGSI RESPON HOLLING III DENGAN PEMANENAN PADA POPULASI PREDATOR DAN PREY

This article modified the leslie-gower model on harvesting with predator and prey population. This study aims at construct a modification of leslie-gower model with holing III response function. In addition, there is an effort harvesting in predator and prey population, analyzing an equilibrium point, finding bionomic equilibrium and the condition where the present value is maximum from net income by controlling harvesting in both populations. In the modified leslie-gower model there is an equilibrium point which is asymptotically stable and when there have harvesting, the equilibrium point is also asymptotically stable. Bionomic equilibrium from harvesting on the modified leslie-gower model is maximizing the profit function π of harvesting on a model with the maximum pontryagin principle resulting an optimal equilibrium) affected by instantaneous rate of discount δ.

Bias and consequences in attempts to estimate historical salmon abundance

Status of salmon populations thought to be at risk is frequently evaluated by comparing estimated abundances in recent decades with approximations of peak abundance in the era when fisheries began. However, spawner escapements of Pacific salmon were generally not surveyed until 1950 or later, so most estimates of salmon abundance before 1950 have been derived from harvest data alone. We investigated historical data on Oregon Coast coho (Oncorhynchus kisutch) to test the reliability of such estimates. In the “Recovery Plan for Oregon Coast Coho” (prepared by National Marine Fisheries Service (NMFS) in 2016), coho abundance was estimated back to 1892 by assuming that in-river landings before 1950 represented a constant 40% of the population. The first mark–recapture studies enabling estimation of harvest rates were completed in the early 1950s, shortly after regulatory action in 1947 sharply curtailed harvesting of coho. We used annual data on fishing licenses sold and length of fishing seasons before 1950 as indices of harvesting effort to reconstruct harvest rates before 1947 and determined in-river landings were near 80%, twice the level postulated by the Recovery Plan. Thus, spawner escapements before 1947 were roughly 20% rather than the 60% of adult recruitment assumed in the Recovery Plan. Actual spawner counts during the first decade of surveys (1945–1955) indicated that coho abundance was much lower and the population trend was opposite of that estimated in the Recovery Plan. However, when spawner abundance was estimated by assuming in-river harvest rates were 80% before 1947, predicted trends in spawner abundance and ocean harvest rates aligned with those from the earliest decade of studies, enabling direct estimates of spawner abundance and ocean harvest rates. Further, the revised simulations indicate that Oregon Coast coho abundance during 1892–1956 probably varied within a range similar to recent decades. We find that use of landings data to speculate about historical salmon abundance is unreliable and can lead to recovery goals that are unattainable, errant interpretation of population limiting factors, and high investment in well-intentioned but misaligned recovery actions. Correct diagnosis of population trends and their causes is best attained with contemporary data for which both precision and accuracy can be validated.

Impact of Harvesting on a Bioeconomic Predator-Prey Fishery Model Subject to Environmental Toxicant.

The present paper studies a predator-prey fishery model which incorporates the independent harvesting strategies and nonlinear impact of an anthropogenic toxicant. Both fish populations are harvested with different harvesting efforts, and the cases for the presence and non-presence of harvesting effort are discussed. The prey fish population is assumed to be infected by the toxicant directly which causes indirect infection to predator fish population through the feeding process. Each equilibrium of the proposed system is examined by analyzing the respective local stability properties. Dynamical behavior and bifurcations are studied with the assistance of threshold conditions influencing the persistence and extinction of both predator and prey. Bionomic equilibrium solutions for three possible cases are investigated with certain restrictions. Optimal harvesting policy is explored by utilizing the Pontryagin's Maximum Principle to optimize the profit while maintaining the sustainability of the marine ecosystem. Bifurcation analysis showed that the harvesting parameters are the key elements causing fishery extinction. Numerical simulations of bionomic and optimal equilibrium solutions showed that the presence of toxicant has a detrimental effect on the fish populations.

Harvesting in a toxicated intraguild predator–prey fishery model with variable carrying capacity

Latterly, variable carrying capacity in the predator–prey population models has been widely studied to provide more realistic understanding about population dynamics. In the present paper, we discuss the bio-economic harvesting of an intraguild fishery model where the logistic carrying capacities of both predator and prey fish populations are variable based on the shared biotic resource. Distinct from most fishery models, we incorporate the independent harvesting strategies on the fisheries with different harvesting efforts by assuming them to have different economic values. In our model, the prey fish population is assumed to be infected directly by an anthropogenic toxicant from the environment while the predator is infected indirectly when they feed on prey. We investigate the local stability of trivial equilibria with Routh–Hurwitz criterion and the global stability of non-trivial equilibrium by constructing a Lyapunov function. Bifurcation and numerical analyses are presented to show distinctive result that a Hopf bifurcation occurs with respect to harvesting parameter instead of resource enrichment parameter as in the literature. Bionomic equilibrium is explored with several possibilities and restrictions. The nontrivial bionomic equilibrium is found to depend critically on the resource density. Finally, the optimal harvesting policy of the three dimensional model is derived by utilizing Pontryagin Maximum Principle. From this study, harvesting parameter is a crucial factor for the stability of the intraguild system. The objective is to obtain the optimal sustainable yield that provides maximum monetary profit while conserving the marine ecosystem.

Analisis Kestabilan dan Usaha Pemanenan Model Predator Prey Tipe Holling III dengan Keuntungan Maksimum

In this paper discussed Stability Analysis and Harvesting Effort at second Predator Prey Populations model Holling Type III with Maximum Profit. The step this research is to determine the equilibrium point, linearize the model, stability analysis of the equilibrium point, and numerical simulation. Result shows that obtained an interior point T that asymptotic stable based on Hurwitz stability test then obtained maximum profit from exploitation harvesting effort of second predator prey populations. This second populations will always exist, even though exploited with harvesting effort done by humans. Harvesting effort of second predator-prey populations given maximum profit that occur on critical points of surface profit function

Optimal harvesting policy of logistic population model in a randomly fluctuating environment

In this paper, we investigate the optimal harvest policy of a stochastic logistic population model. The value of this study lies in two aspects: mathematically, we establish a stochastic threshold theorem to govern whether the population persists or not. In the case of population persistence, we prove the existence, uniqueness and global asymptotic stability of the invariant density of the Fokker–Planck equation associated with the SDE model, and we further show the relation between these two models. In addition, we give the unique optimal harvesting effort and the corresponding maximum of expectation of sustainable yield, which gives us the profile of the optimal harvesting policy of the SDE model. Ecologically, we find that big harvesting effort or big intensity of noise will lead the population to extinct risk almost surely. In addition, we find that under a fixed randomness strategy and proper harvesting, the maximum sustainable yield increases systematically as the harvesting effort increases, but overexploitation will reduce the level of maximize sustainable yield and eventually make the whole population extinct with probability one. Hence in order to obtain the optimal harvesting policy, we must decrease the harvesting effort and the intensity of noise. Furthermore, we find that our parameter perturbation method in this paper is more beneficial to the exploitation of renewable resources than the classical one given by Beddington and May (1977). The results show that different perturbation method can exhibit different stochastic population dynamics.

Using experimental trapping seasons to explore fisher harvest management uncertainties: is timing everything?

ABSTRACT An experimental trapping season was used to address structural and partial controllability uncertainties related to the timing and duration of a fisher (Martes pennanti) trapping season in northern New York. Uncertainties regarding capture vulnerability and harvest effort have thwarted serious consideration of altering the season structure. An experimental extension to the trapping season was implemented in a portion of northern New York to explore these uncertainties. The study found that capture vulnerability did not change between the traditional portion of the season (25 October–10 December) and the experimental season extension (11 December–10 January). Trapping effort was significantly less during the extended portion of the season, in terms of both number of active trappers and mean individual effort. Thus, changes in the cumulative harvest appear to be driven by changes in harvest effort, rather than changes in capture vulnerability. Increasing harvest opportunity in this system does not appear to increase cumulative harvest proportionally.

Dynamics Analysis and Optimality in Selective Harvesting Predator-Prey Model With Modified Leslie-Gower and Holling-Type II

Abstract In this work, we consider the optimal harvesting and stability problems of a prey-predator model with modified Leslie-Gower and Holling-type II functional response. The model is governed by a system of three differential equations which describe the interactions between prey, predator and harvesting effort. Boundedness and existence of solutions for this system are showed. The existence and local stability of the possible steady states are analyzed and the conditions of global stability of the interior equilibrium are established by using the Lyapunov function, we prove also the occurrence of Hopf bifurcation at this point. By using the Pontryagin’s maximal principle, we formulate and we solve the problem of the optimal harvest policy. In the end, some numerical simulations are given to support our theoretical results.

Dynamical Analysis and Optimal Harvesting Strategy for a Stochastic Delayed Predator-Prey Competitive System with Lévy Jumps

This paper develops a theoretical framework to investigate optimal harvesting control for stochastic delay differential systems. We first propose a novel stochastic two-predator and one-prey competitive system subject to time delays and Lévy jumps. Then we obtain sufficient conditions for persistence in mean and extinction of three species by using the stochastic qualitative analysis method. Finally, the optimal harvesting effort and the maximum of expectation of sustainable yield (ESY) are derived from Hessian matrix method and optimal harvesting theory of delay differential equations. Moreover, some numerical simulations are given to illustrate the theoretical results.

Optimal harvesting for a single-species population governed by Gompertz law: Influence of environmental fluctuation and limited harvesting capacity

This work presents an optimal harvesting problem associated with a single-species population governed by Gompertz law in a seasonally fluctuating environment. The influence of environmental fluctuation is accommodated by choosing the coefficients in the differential equation to be periodic functions with the same period and restriction on the harvesting effort is accommodated by considering binding constraints on the control variable. Hence, a linear optimal control problem has been considered where the state dynamics is governed by Gompertz equation and the control variable is subject to the binding constraints. With the help of maximum principle and the concept of blocked intervals, an optimal periodic solution has been obtained which is followed by the construction of optimal solution using the theory of most rapid approach. Important results of the study are demonstrated through numerical simulations.

On the interplay of harvesting and various diffusion strategies for spatially heterogeneous populations

The paper explores the influence of harvesting (or culling) on the outcome of the competition of two species in a spatially heterogeneous environment. The harvesting effort is assumed to be proportional to the space-dependent intrinsic growth rate. The differences between the two populations are the diffusion strategy and the harvesting intensity. In the absence of harvesting, competing populations may either coexist, or one of them may bring the other to extinction. If the latter is the case, introduction of any level of harvesting to the successful species guarantees survival to its non-harvested competitor. In the former case, there is a strip of “close enough” to each other harvesting rates leading to preservation of the original coexistence. Some estimates are obtained for the relation of the harvesting levels providing either coexistence or competitive exclusion.

Optimal harvesting for age-structured population dynamics with size-dependent control

We investigate two optimal harvesting problems related to age-dependent population dynamics; namely we consider two problems of maximizing the profit for age-structured population dynamics with respect to a size-dependent harvesting effort. We evaluate the directional derivatives for the cost functionals. The structure of the harvesting effort is uniquely determined by its intensity (magnitude) and by its area of action/distribution. We derive an iterative algorithm to increase at each iteration the profit by changing the intensity of the harvesting effort and its distribution area. Some numerical tests are given to illustrate the effectiveness of the theoretical results for the first optimal harvesting problem.