Optimal Harvesting Strategy Research Articles

Does size matter? A bioeconomic perspective on optimal harvesting when price is size-dependent

Body size is a key parameter influencing demographic characteristics of fish populations as well as market value of landed catch. Yet in bioeconomic modelling, body size is often an overlooked biological and economic parameter. Here we evaluate how size-dependent pricing influences optimal harvest strategies in a model parameterized for two pelagic fisheries, those targeting Atlantic herring ( Clupea harengus ) and Atlantic mackerel ( Scomber scombrus ), in Norway. In our model, positively size-dependent pricing clearly shifts optimal harvest strategies towards lower harvest rates and higher mean body size of caught fish. The results are relatively insensitive to biological (e.g., natural mortality) and economic details of the model (e.g., discount rate or demand function). These findings show that size-dependent pricing influences optimal harvest strategies aiming at maximum economic yield and, hence, requires more attention in resource economics and in fisheries management.

On Optimal Harvesting Problems in Random Environments

This paper investigates the optimal harvesting strategy for a single species living in random environments whose growth is given by a regime-switching diffusion. Harvesting acts as a (stochastic) control on the size of the population. The objective is to find a harvesting strategy which maximizes the expected total discounted income from harvesting {\em up to the time of extinction} of the species; the income rate is allowed to be state- and environment-dependent. This is a singular stochastic control problem with both the extinction time and the optimal harvesting policy depending on the initial condition. One aspect of receiving payments up to the random time of extinction is that small changes in the initial population size may significantly alter the extinction time when using the same harvesting policy. Consequently, one no longer obtains continuity of the value function using standard arguments for either regular or singular control problems having a fixed time horizon. This paper introduces a new sufficient condition under which the continuity of the value function for the regime-switching model is established. Further, it is shown that the value function is a viscosity solution of a coupled system of quasi-variational inequalities. The paper also establishes a verification theorem and, based on this theorem, an $\varepsilon$-optimal harvesting strategy is constructed under certain conditions on the model. Two examples are analyzed in detail.

The impact of alternative harvesting strategies in a resource–consumer metapopulation

Summary1. The majority of our knowledge of harvested populations has been drawn from studies on single‐species occupying continuous landscapes. Population dynamics in spatially structured landscapes are markedly different from those in continuous habitats. We investigate the effects of several harvesting strategies on the metapopulation dynamics of the bruchid beetle Callosobruchus maculatus and its parasitoid Anisopteromalus calandrae, when locally extinction prone populations of bruchids were harvested. By harvesting the resource in this closed resource–consumer interaction, we could examine the scenario where humans and natural predators share a common resource.2. Using population‐level models in single and coupled‐patch systems, simulations were run to estimate sustainable harvesting levels for each harvesting strategy. These harvesting levels were then implemented in experimental metapopulation microcosms. Experiments were run for multiple generations and long‐term time series of population size and harvest yield were collected.3. Controversially, harvesting resulted in larger regional population sizes in harvested metapopulations than in unharvested metapopulations. Similarly, conservative harvesting strategies such as fixed escapement harvesting and harvesting with refuges resulted in smaller population sizes than fixed quota or fixed proportion harvesting strategies. Fixed proportion harvesting gave rise to the largest population sizes, fewest local extinctions and largest yields. Assuming both species are of ecological importance, fixed proportion is therefore the optimal harvesting strategy for this model system.4. Synthesis and applications. We demonstrate that, under certain conditions, increasing local mortality can increase population sizes. This ‘hydra effect’ may be caused by the advantage of higher rates of local population turnover for dispersive species in patchy landscapes, or due to the interruption of overcompensatory density‐dependence in the host populations. These results are of particular relevance both in the development of sustainable harvesting policies in multi‐species communities or, conversely, the control of pest species inhabiting spatially structured landscapes. We have shown that predictive models can be a useful tool in the estimation of sustainable harvesting limits where no a priori knowledge of the system exists. We also demonstrate that spatial structure, the effects of interspecific interactions and knowledge of density‐dependent population dynamics must be included in the generation of sustainable harvesting theory.

Optimal site-specific fertilization and harvesting strategies with respect to crop yield and quality response to nitrogen

Incorrect fertilizer decisions can be costly if quality of the output, in addition to yield, is influenced by the application rate, which contrasts the flat payoff function estimated for fertilizer by previous studies focusing only on quantity. This study aims at modelling economic potentials of the combination of site-specific fertilization and quality specific harvesting at the example of wheat ( Triticum aestivum L.), in Germany. Crop yield and protein response data to different nitrogen fertilizer applications were used from 15 locations to simulate site-specific wheat management. Four different management strategies were compared using a step wise price function for wheat qualities: uniform management, completely separate management, site-specific fertilization with uniform harvest, uniform fertilization with quality-specific harvest. It was found that opportunity costs (>50 €/ha) may apply, if threshold values for crop qualities are missed. Separation of different qualities can reduce this risk and create incentives for producing higher qualities on heterogeneous fields. Completely separate management had an economic advantage of up to 30 €/ha for the gross revenue, while site-specific fertilization alone had only marginal economic effects. However, these advantages have to cover costs for the use of technologies used, to be economically preferable.

SUSTAINABLE YIELDS IN FISHERIES: UNCERTAINTY, RISK-AVERSION, AND MEAN-VARIANCE ANALYSIS

We consider a model of a fishery in which the dynamic of the unharvested fish population is given by the stochastic logistic growth equation dx(t) = [�x(t)(� − x(t))]dt + �x(t)dW(t). Similar as in the classical deterministic analogon, we assume that the fishery harvests the fish population following a constant effort strategy. In a first step we derive the effort level that leads to maximum expected sustainable yield, which is understood as the expectation of the equilibrium distribution of the stochastic dynamics. This replaces the non-zero fixed point in the classical deterministic setup. In a second step, we assume that the fishery is risk averse and that there is a trade off between expected sustainable yield and uncertainty measured in terms of the variance of the equilibrium distribution. We derive the optimal constant effort harvesting strategy for this problem. In a final step, we consider an approach which we call the mean-variance analysis to sustainable fisheries. Similar as in the now classical mean-variance analysis in Finance, going back to Markowitz (1957), we study the problem of maximizing expected sustainable yields under variance constraints, and dual to this, minimizing the variance, e.g. risk, under guaranteed minimum expected sustainable yields. We derive explicit formulas for the optimal fishing effort in all four problems considered and study the effects of uncertainty, risk aversion and mean reversion speed on fishing efforts.

Designing marine reserve networks for both conservation and fisheries management

Marine protected areas (MPAs) that exclude fishing have been shown repeatedly to enhance the abundance, size, and diversity of species. These benefits, however, mean little to most marine species, because individual protected areas typically are small. To meet the larger-scale conservation challenges facing ocean ecosystems, several nations are expanding the benefits of individual protected areas by building networks of protected areas. Doing so successfully requires a detailed understanding of the ecological and physical characteristics of ocean ecosystems and the responses of humans to spatial closures. There has been enormous scientific interest in these topics, and frameworks for the design of MPA networks for meeting conservation and fishery management goals are emerging. Persistent in the literature is the perception of an inherent tradeoff between achieving conservation and fishery goals. Through a synthetic analysis across these conservation and bioeconomic studies, we construct guidelines for MPA network design that reduce or eliminate this tradeoff. We present size, spacing, location, and configuration guidelines for designing networks that simultaneously can enhance biological conservation and reduce fishery costs or even increase fishery yields and profits. Indeed, in some settings, a well-designed MPA network is critical to the optimal harvest strategy. When reserves benefit fisheries, the optimal area in reserves is moderately large (mode ≈30%). Assessing network design principals is limited currently by the absence of empirical data from large-scale networks. Emerging networks will soon rectify this constraint.

An Application of Simulation Modelling and Optimization in Fisheries Management

The distribution of scallop density and size varies spatially as scallops are nearly sessile species and large scallops grow slowly and die naturally at a constant rate, even without fishing. Harvesting scallops at the right time and the right place, therefore, greatly increases the utilization of this renewable resource. This paper presents a simulation-based optimization method for deriving the optimal temporal and spatial scallop harvest strategy. The initial population distribution is estimated through high-resolution video surveys. A simulation model estimates the new population after each harvest through a Markov chain type analysis. The optimal harvest policies are then determined by calculating the amount of scallops to be harvested in each region at any given time period. This optimization process is conducted through an interaction of a genetic algorithm (GA) – based stochastic optimization method and the simulation model.

Simulation and validation of a reinforcement learning agent-based model for multi-stakeholder forest management

Spatial optimization and agent-based modeling present two distinct approaches that have been implemented in forest management research for incorporating the objectives of multiple stakeholders. However, challenges arise in their implementation as optimization procedures do not consider the interactions amongst stakeholders, and agent-based models generate results from which it is difficult to determine if objectives have been successfully achieved. The purpose of this research is to overcome these limitations by improving the ability of an agent-based model to achieve optimal forest harvesting strategies through the integration of reinforcement learning (RL). A simulation model is developed in which forest company agents harvest trees in order to maximize their profits while considering the potential to cooperate with a conservationist agent whose objectives are based on protecting species habitat. RL algorithms are implemented to allow the forest company agents and the conservationist agent to learn where harvesting should occur in order to achieve their objectives. The model is validated by determining if generated solutions can be considered optimal given system constraints, and by comparing observed agent behavior against learning functions as defined by the RL algorithms. The obtained results demonstrate a non-linear relationship between different levels of cooperation and the ability of agents to achieve their objectives. The model also provides outputs that depict the relative quality of forest areas and the tradeoffs between objectives for different optimal solutions.

The effect of site quality on economically optimal stand management

This paper proposes a discrete-time type timber harvesting model for simultaneously determining (i) the optimal quantity of seedlings to be planted, (ii) the optimal quantities of timber harvested by thinnings, and (iii) the optimal rotation age. With the help of Microsoft Excel Solver, a generalized reduced gradient algorithm, numerical examples are developed to evaluate the impact of the variations in the quality level of a forest site on the optimal harvest strategy. It is shown that the level of optimal rotation age and optimal quantity of seedlings to be planted can individually exhibit non-monotonicity to the increase in site quality.

Optimal harvesting of diffusive models in a nonhomogeneous environment

We study the optimal harvesting strategy for populations whose dynamics is described by reaction-diffusion equations. The production function can be of logistic, Gilpin–Ayala or Gompertz type. The diffusion structure is discussed; we suggest to consider Δ ( u / K ) , where K is the carrying capacity of the environment, rather than Δ u , and study optimal harvesting for models with this diffusion type. Maximum yield is investigated for both continuous and impulsive models. For continuous harvesting, the optimal policy is obtained; for the impulsive equation some limit cases are considered. The paper also outlines a variety of open problems.

Forecasting Fish Stock Recruitment and Planning Optimal Harvesting Strategies by Using Neural Network

Recruitment prediction is a key element for management decisions in many fisheries. A new approach using neural network is developed as a tool to produce a formula for forecasting fish stock recruitment. In order to deal with the local minimum problem in training neural network with back-propagation algorithm and to enhance forecasting precision, neural network’s weights are adjusted by optimization algorithm. It is demonstrated that a well trained artificial neural network reveals an extremely fast convergence and a high degree of accuracy in the prediction of fish stock recruitment.

A BIOECONOMIC APPROACH TO THE FAUSTMANN–HARTMAN MODEL: ECOLOGICAL INTERACTIONS IN MANAGED FOREST

Abstract This paper develops a bioeconomic forestry model that makes it possible to take ecosystem services that are independent of the age structure of trees into account. We derive the Faustmann–Hartman optimal harvesting strategy as a special case. The bioeconomic model is then extended to account for the fact that forest harvesting decisions impact on other ecological resources, which provide benefits for the wider community. The paper focuses on impacts associated with disturbance caused by logging operations and habitat destruction due to tree removal. This enables us to explore the interactions between forest management and the dynamics of ecological resources. The optimal rotation rule is obtained as a variation on the traditional Faustmann–Hartman equation, where an additional term captures the potential benefits derived from the growth of the ecological resource valued at its shadow price. The steady‐state solutions to the problem and sensitivity to model parameter are identified using numerical analysis.

Sustainable Yields in Fisheries: Uncertainty, Risk-Aversion and Mean-Variance Analysis

We consider a model of a fishery in which the dynamic of the unharvested fish population is given by the stochastic logistic growth equation. Similar as in the classical deterministic analogon, we assume that the fishery harvests the fish population following a constant effort strategy. In a first step we derive the effort level that leads to maximum expected sustainable yield, which is understood as the expectation of the equilibrium distribution of the stochastic dynamics. This replaces the non-zero fixed point, in the classical deterministic setup. In a second step, we assume that the fishery is risk averse and that there is a trade off between expected sustainable yield and uncertainty measured in terms of the variance of the equilibrium distribution. We derive the optimal constant effort harvesting strategy for this problem. In a final step, we consider an approach which we call the mean-variance analysis to sustainable fisheries. Similar as in the now classical mean-variance analysis in Finance, going back to Markowitz (1957), we study the problem of maximizing expected sustainable yields under variance constraints, and dual to this, minimizing the variance, e.g. risk, under guaranteed minimum expected sustainable yields. We derive explicit formulas for the optimal fishing effort in all four problem considered and study the effects of uncertainty, risk aversion and mean reversion speed on fishing efforts.

Climate change and the future for coral reef fishes

AbstractClimate change will impact coral‐reef fishes through effects on individual performance, trophic linkages, recruitment dynamics, population connectivity and other ecosystem processes. The most immediate impacts will be a loss of diversity and changes to fish community composition as a result of coral bleaching. Coral‐dependent fishes suffer the most rapid population declines as coral is lost; however, many other species will exhibit long‐term declines due to loss of settlement habitat and erosion of habitat structural complexity. Increased ocean temperature will affect the physiological performance and behaviour of coral reef fishes, especially during their early life history. Small temperature increases might favour larval development, but this could be counteracted by negative effects on adult reproduction. Already variable recruitment will become even more unpredictable. This will make optimal harvest strategies for coral reef fisheries more difficult to determine and populations more susceptible to overfishing. A substantial number of species could exhibit range shifts, with implications for extinction risk of small‐range species near the margins of reef development. There are critical gaps in our knowledge of how climate change will affect tropical marine fishes. Predictions are often based on temperate examples, which may be inappropriate for tropical species. Improved projections of how ocean currents and primary productivity will change are needed to better predict how reef fish population dynamics and connectivity patterns will change. Finally, the potential for adaptation to climate change needs more attention. Many coral reef fishes have geographical ranges spanning a wide temperature gradient and some have short generation times. These characteristics are conducive to acclimation or local adaptation to climate change and provide hope that the more resilient species will persist if immediate action is taken to stabilize Earth’s climate.

An information-based adaptive strategy for resource exploitation in competitive scenarios

Given an exploitation problem, in which a number of agents compete for a limited renewable resource, the optimal harvesting strategy depends on the ratio between resource availability and exploitation effort. For scarce resource a purely competitive, greedy strategy outperforms a more collaborative approach based on the Collective Intelligence, while for more abundant resource the opposite holds. The rationale for this behaviour lies in the amount of information each strategy is able to provide and a combined strategy is possible according to which agents choose dynamically the most informative strategy according to a minimum entropy criterion. This approach, which provides best performance for both under and over-exploited scenarios, can be used to monitor the resource status for management purposes and is effective in both centralised and decentralised decision making.

CONTROL OF A METAPOPULATION HARVESTING MODEL FOR BLACK BEARS

ABSTRACT. We develop a metapopulation harvesting model that includes density-dependent immigration and emigration and apply Pontryagin's maximum principle to derive an optimal harvesting and reserve design strategy. The model is designed to mimic the black bear population of eastern Tennessee and western North Carolina. Model results suggest that a forest region's population can be maintained despite high harvest levels due to emigration from a connected, un-harvested park region. The amount of shared border between the park and forest region is important in determining the optimal harvesting strategy. This technique offers new insight on the spatial control of protected populations.

Optimal Spatial Harvesting Strategy and Symmetry-Breaking

A reaction-diffusion model with logistic growth and constant effort harvesting is considered. By minimizing an intrinsic biological energy function, we obtain an optimal spatial harvesting strategy which will benefit the population the most. The symmetry properties of the optimal strategy are also discussed, and related symmetry preserving and symmetry breaking phenomena are shown with several typical examples of habitats.

Experimental or precautionary? Adaptive management over a range of time horizons

Summary Many studies of adaptive harvest management already exist in the literature, but most (if not all) use long, sometimes infinite, time horizons. Such long‐term objectives provide an opportunity to manage experimentally, so that poorly understood dynamics are learned and any returns sacrificed for experimentation are repaid by improved management over the remaining time horizon. However, a manager is unlikely to weight outcomes in the distant future equally against outcomes in the present. Furthermore, the most appropriate model of system dynamics may not remain constant over the time‐frame required to experiment, learn and improve management. In these cases the use of discounting and/or a finite time horizon fit the manager's assumptions and goals more effectively, and the value of experimentation is likely to be diminished. In this paper we construct a simple model of a hypothetical population and compare optimal passive and active adaptive harvest strategies over a range of time horizons. This allows us to determine the optimal level of experimentation for short‐, medium‐ and long‐term goals. We discover that the optimal active adaptive harvest strategy may be precautionary over short to medium time horizons, rather than experimental. That is, an action with known moderate benefits is preferred over an action with uncertain but marginally larger expected benefits. This runs counter to the widespread assumption in the adaptive management literature that incorporating learning into an optimization of management will encourage experimentation. Synthesis and applications. The general results of this paper have potential application to any environmental management problem where adaptive management might be applied; for example, conservation, pest control, harvesting and management of water flows. We examine adaptive management over a range of finite time horizons to reflect a variety of possible management goals and assumptions. Our simple example demonstrates that in the face of model uncertainty, the management strategy that maximizes benefits does not necessarily include deliberate experimentation and learning. Optimal active adaptive management weighs experimentation against all its potential consequences, and this can yield a precautionary approach.

Applying portfolio optimisation to the harvesting decisions of non-industrial private forest owners

The non-industrial private forest owner's optimal harvesting and investment strategies are studied at forest holding level by including individual forest stands in an asset class portfolio. The forest owner can either clearcut mature stands and invest the capital in financial or real asset classes (bank deposits, government bonds, stocks, apartments) or postpone clearcutting and retain capital in standing trees. Forest inventory data from actual forest holdings in Southwest Finland, the simulation–optimisation software MELA, and statistics on timber prices are utilised to compute the return series for forest stands. The numerical results show that the optimal level of clearcutting decreases markedly with initial non-forest wealth, especially at low risk-free rates of interest. It may therefore be rational for non-industrial private forest owners to consider shorter rotation periods than those of investors with diversified portfolios. The correlations between returns from forest stands are high, implying that increasing the variety of stand structures achieved by planting different species is not likely to bring substantial diversification benefits. The favoured investment outlet for harvesting revenues (apartments, government bonds or stocks) is sensitive to the period of historical data used to compute the return series and risk-free rate of interest. The value growth of forest stand can be used to estimate annual returns only for those stands that are readily mature. An alternative method of computing returns on stands in any development phase is proposed, based on net present value of stand adjusted for fluctuations in forest land prices. This method applies if selling forest land is considered an option. If selling is not an option, the ratio of maximised net present value to value at immediate harvest can be used as a ‘maturity index’ for ranking the stands for portfolio optimisation.

The Effect of Temporary Certified Emission Reductions on Optimal Forest Rotations and the Supply of Sequestered Carbon

This paper examines the effect of the regulations under the Clean Development Mechanism (CDM) in creating temporary certified emission reductions (tCERs) on optimal harvesting decisions and supply of carbon removal services in forest plantations. The paper develops a theoretical model examining optimal harvesting strategies when revenues from sequestered carbon dioxide are considered under the CDM guidelines. We find that the current CDM rules with 5-year verification intervals of tCERs may result in socially inefficient timber rotations because they do not fully internalize the carbon sequestration function of trees. Decreasing the intervals between carbon credit verification periods increases the optimal rotation lengths. Other factors that lengthen rotation intervals, such as decreasing timber price and increasing harvesting cost, will increase the supply of tCERs. Fast growing tree species with shorter rotation intervals have relatively more inelastic carbon credit supply curves than slow growing tree species with longer rotation intervals.