Optimal Harvesting Policy Research Articles

Experimental Harvesting of Cyclic Stocks in the Face of Alternative Recruitment Hypotheses

Cyclic fluctuations in year-class abundance have been recorded for several fish populations. Historical patterns are generally consistent with several hypotheses about underlying mechanisms, which involve (a) strong density dependence or (b) environmental forcing. Optimal harvesting policies differ depending on which hypothesis is deemed true. Not only does the harvesting policy affect the amount of catch taken, but it can strongly affect our ability to discriminate between alternative hypotheses. Fully-adaptive feedback policies, which explicitly account for the information content of harvest controls, were computed with dynamic progamming for some model prototypes of the problem. Results indicate that deliberate experimentation with escapement levels, oriented to reduce the uncertainty, may be worthwhile under some conditions. In most cases, however, optimal passive policies (in which learning occurs passively) were a good approximation to actively adaptive policies. The optimal passive controls for maximizing a risk-neutral objective, such as total catch, were generally very informative. Although passive and active controls markedly differed in some cases, expected discounted yields under the two types of policies were very similar (differences less than 2%). The extreme risk-averse presciption of managing a stock according to the more pessimistic recruitment model may lead to considerable yield losses.

Approximately Optimal Recovery of a Multicohort Fishery from Depleted Stocks and Excess Vessel Capacity

The effect of current harvesting on future fish stocks is best captured with a multicohort model. In principle, numerical dynamic programming can be used to determine optimal harvesting for any level of fish stocks. In practice, applications to long-lived species of fish have been limited because of the need to have a state variable for each cohort. The problem is further increased if vessel capacity is included as a state variable. Ignoring excess vessel capacity in a fishery with depleted stocks is likely to lead to recommendations for overly drastic reductions in catch. A method is proposed for finding approximately optimal harvesting policies for a multicohort fishery, taking account of changing harvesting capacity. The method is illustrated for the southern bluefin tuna fishery.

Approximately Optimal Recovery of a Multicohort Fishery from Depleted Stocks and Excess Vessel Capacity

The effect of current harvesting on future fish stocks is best captured with a multicohort model. In principle, numerical dynamic programming can be used to determine optimal harvesting for any level of fish stocks. In practice, applications to long-lived species of fish have been limited because of the need to have a state variable for each cohort. The problem is further increased if vessel capacity is included as a state variable. Ignoring excess vessel capacity in a fishery with depleted stocks is likely to lead to recommendations for overly drastic reductions in catch. A method is proposed for finding approximately optimal harvesting policies for a multicohort fishery, taking account of changing harvesting capacity. The method is illustrated for the southern bluefin tuna fishery.

Optimal management of renewable economic resources in a model with Bertalanffy growth law

Two methods for obtaining economic optimality in renewable resource exploitation are examined. The issue of biological optimality (conversation of the resource base) is also examined. In the first part of the article, the effectiveness of two realistic harvesting strategies are examined when management objective is the maximization of economic rent. A new optimal harvesting policy which depends on the market price is derived when maximization of total present value of economic rent is the resource management objective.

Optimal harvesting of a renewable economic resource in a model with Bertalanffy growth law II

An optimal harvesting policy which depends on the market price is derived when maximization of present value of economic rent is the management objective. An equation is derived whose solution represents the optimal age of harvest. The sensitivity of the optimal age of harvest to biological and economic parameters is also studied.

Review article : Effort fluctuations in a harvest model with random prices

The effect of a single increase in the unit price of biomass on the optimal harvest policy for an exploited population is studied numerically. The price of a unit is assumed constant until a random time, when the price increases by a given amount. The optimal policy coresponding to the expect return is computed from the Bellman equation of dynamic programming. The results are compared with a model in which prices remain constant as well as a “well-timed” model in which the price increses at the expected increase time of the random case. Both optimal expected return and optimal policy computed from the deterministic models may differ substantially from that calculated from the random model, particularly if marginal costs are large. The emphasis is on numerical computation.

OPTIMAL HARVESTING WITH DENSITY DEPENDENT RANDOM EFFECTS

We consider the effect of sudden large, randomly occurring density dependent disasters on the optimal harvest policy and optimal expected return for an exploited population. The population is assumed to grow logistically with disasters occurring on a time scale very short compared to the natural growth scale. The case of a density dependent disaster frequency is also treated. Stochastic dynamic programming is used in the optimization. For a set of realistic field data it is found that random effects typically have a significant effect on both optimal return and optimal effort levels. The effect of density dependence is far more pronounced for optimal return than for optimal effort levels.

Socially optimal forestry

The Faustmann rule is the major contribution of economic theory to the analysis of forestry management. It is typical to consider the Faustmann rule in the context of a model of a forestry firm in which there is some periodicity in the rate of harvesting over time. This paper on the other hand shows the Faustmann rule to be associated with socially optimal sustained yield or steady-state regimes. In the course of so doing, attention is placed on the role of the shadow price of a tree in the determination of an optimal harvesting policy.

Optimal harvesting of renewable resources

The aim of the paper is to investigate different types of calculus of variations solutions maximizing the present value of a renewable resource. It is found that there are two types of optimal stationary harvesting policies. For certain cost functions, bang-bang harvesting may be more profitable than either of these.

IRREVERSIBLE INVESTMENT AND OPTIMAL FOREST EXPLOITATION

A forest harvest scheduling model which includes as activities the level of investment in harvest capacity and the accumulated harvest capacity in each period, is presented. The inclusion of these activities, in addition to the harvest activities, allows for the removal of harvest‐flow constraints found in more typical Model II formulations of the harvest scheduling problem. The optimal harvest and investment policy can be determined by linear programming or quadratic programming methods, depending on whether prices are constant or supply‐dependent. The new model better reflects economic reality than existing models, and provides a method for determining the optimal economic development of a forest industry, and the optimal draw‐down of old growth forest. Numerical examples are given.

Forest-level analysis of stability under exploitation: depensation responses and catastrophe theory

Stability analysis of whole forests is proposed as a qualitative tool for the study of forest responses to partial or patchy harvests or mortality. Instead of modeling every tree or stand, aggregate tree biomass is modeled. In order to aggregate stands, spatial effects must be incorporated. It is shown that depensation growth responses (reduced growth at low biomass) are common because forests often modify harch environments to be more suitable for their growth. Depensation can result from thinning, partial mortality, patchy cutting, or clearcutting, depending on forest type and abiotic factors. Examples of these types of behaviors are given. Stability analysis of different growth regimes under exploitation are related to catastrophe theory and to optimal harvesting policies. Such qualitative analysis is shown to be applicable to data-poor regions such as the tropics where there is great concern over responses of forests to exploitation.

Fixed and Equilibrium Endpoint Problems in Uneven-Aged Stand Management

Abstract Studies in uneven-aged management have concentrated on the determination of optimal steady-state diameter distribution harvest policies for single and mixed species stands. To find optimal transition harvests for irregular stands, either fixed endpoint or equilibrium endpoint constraints can be imposed after finite transition periods. Penalty function and gradient methods are presented to solve these problems. The methods are demonstrated with a stage-structured model for projecting stands that contain mixtures of California white fir (Abies concolor [Gord. & Glend.] Lindl. (Iowiana [Gord.])) and red fir (Abies magnifica A. Murr.). With present value as the efficiency criterion, optimal transition strategies are computed for three kinds of target steady states: the extremal steady state associated with an infinite time horizon dynamic optimization problem, an investment-efficient steady state, and a maximum sustainable rent steady state. Harvest regimes that convert to investment-efficient or maximum sustainable rent steady states are dominated by red fir and are suboptimal compared to transition regimes that convert to the extremal steady state, which includes only white fir. The fixed endpoint regimes are compared with transition strategies that are obtained with equilibrium endpoint constraints that do not require a particular steady-state stand structure. Transition regimes that convert to the extremal steady state are suboptimal compared to regimes that solve the more general equilibrium endpoint problem, and the present values of these two kinds of regimes converge as the transition period lengthens. The species composition and structure of the steady states found by solving the equilibrium endpoint problem depend on the transition period length. For. Sci. 33(4):908-931.

Effort fluctuations in a harvest model with random prices

The effect of a single increase in the unit price of biomass on the optimal harvest policy for an exploited population is studied numerically. The price of a unit is assumed constant until a random time, when the price increases by a given amount. The optimal policy corresponding to the expected return is computed from the Bellman equation of dynamic programming. The results are compared with a model in which prices remain constant as well as a “well-timed” model in which the price increases at the expected increase time of the random case. Both optimal expected return and optimal policy computed from the deterministic models may differ substantially from that calculated from the random model, particularly if marginal costs are large. The emphasis is on numerical computation.

Optimal catch capacity and fishing effort in deterministic and stochastic fishery models

This paper is a survey of fisheries economics, aimed mainly at fisheries biologists. The paper begins by reviewing the static theory, which established two major results. (i) Free access leads to over-exploitation, and (ii) the optimal rate of exploitation is less than the maximum sustainable yield rate. The latter could be regarded as an antithesis to the biological doctrine that fish stocks should be managed to give maximum sustainable yield ( MSY). Dynamic theory, which is considered next, showed that the optimal rate of exploitation could be either less or greater than the MSY rate. In particular, a higher discount rate was shown to imply a higher rate of exploitation. This, however, ignores the role of capital invested in the harvesting sector. Once it is recognized that a higher discount rate implies a higher required rate of return on capital, the impact of the discount rate on the optimal rate of exploitation becomes ambiguous. The paper examines the impact of the discount rate with and without stock-dependent harvesting costs. This leads on to the question of how the risk of extinction under free access depends on the sensitivity of unit harvesting costs, or catch per unit of effort, to the size of the exploited stock. Finally, stochastic fishery models are briefly considered. The main purpose of this part of the paper is to demonstrate that deterministic fishery models may give poor guidance for managing the stochastic fisheries of the real world, even if risk neutrality and constant prices are assumed. To demonstrate this as clearly as possible, the unit cost of harvesting is assumed to be constant, implying that the optimal rate of exploitation is constant in a deterministic model. First we consider the simple case of time-invariant stochastic catch quotas (no population dynamics), and demonstrate how optimal catch capacity depends on the cost of investing in the necessary equipment. Then we consider population dynamics, where expected future catch quotas depend on how much is being taken presently. Optimal catch capacity depends on the cost of investment in this case as well, but the derivation of optimal harvesting and investment policies becomes more complicated.

Optimal Policies for Rehabilitation of Overexploited Fish Stocks Using a Deterministic Model

Traditional fisheries models are of limited use during the transitional period when effort is reduced to permit recovery of an overexploited stock. We used a generalized age-structured model to represent stock dynamics during this transitional period and obtained optimal harvesting policies for three overexploited fish stocks using a first-order gradient procedure. The length of the rehabilitation period was affected by (1) the demographic characteristics of the stock, (2) the historical level of exploitation, and (3) the form of the objective function. When a target stock biomass or spawning stock was specified, rehabilitation was relatively rapid due to the sharp initial reduction in fishing effort. Fishing began earlier in the planning horizon when a target harvest was specified; however, stocks recovered more slowly and fishing effort and harvest did not stabilize at the desired levels as rapidly. Policies for maximizing harvest did not usually result in closure of the fishery; however, fishing effort usually exceeded the desired level and sometimes fluctuated considerably from year to year. Our results should aid in the development of rehabilitation policies tailored to specific fisheries or specific management goals.

A control theoretic model of multispecies fish harvesting

A mathematical model of the growth of mass of a multispecies fish community is constructed taking into account natural growth, mortality and breeding. The Sterile Male Technique (STM) propounded Taylor and Costello (1973) is applied with a view to controlling ecological resources which are essential for the growth of fish populations. The optimal harvest policy is studied by invoking Pontryagin's Maximal Principle. Dynamical behaviour of the system is discussed at length.

比例制御入力を受ける離散型捕食-被食者系のカオス的挙動

By motivating the fact that discrete predator-prey systems often exhibit chaotic behavior, in this paper, control problems of a class of discrete predator-prey systems are studied.By examining the stability of an equilibrium associated with the predator-prey system, it is first shown that the harvesting or supplying of predators, whose amount is proportional to the number of predator, is effective for preventing oscillations of populations. It is also shown that if the growth rate of predators is too large and the population of predators at the equilibrium is too large, then populations oscillate and these oscillations are stabilized by the harvesting of predators. On the other hand, if the growth rate of predators is too small, the supplying of predators is effective. The optimal harvesting policy yielding the maximum average harvest of predators is also derived.Furthermore, by introducing the concept of the invariant domain, the constant rate harvesting investigated here is compared with the constant harvesting, and the former is shown to have an advantage from viewpoints of the conservation of ecosystems.The validity of theoretical results presented here is demonstrated by numerical experiments with various values of parameters.

On uncertain renewable resource stocks: Optimal harvest policies and the value of stock surveys

Annual harvest quotas are commonly employed in the management of renewable resource stocks, commercial fisheries being a prime example. Such resource stocks often undergo quite significant natural fluctuations, to which quotas must be adapted. A further complication arises from the fact that estimates of stock abundance are often highly uncertain. In this paper a Bayesian approach is used to model optimal quota decisions for an uncertain, fluctuating, renewable resource stock.

A bioeconomic model of harvesting a multispecies fishery

The paper deals with the problem of combined harvesting of two competing fish species, each of which obeys the law of logistic growth. It is shown that the open-access fishery may possess a bionomic equilibrium which drives one species to extinction. An analysis of the dynamic behaviour of the system reveals that its non-trivial critical point is either an asymptotically stable node or an unstable saddle point depending on the values of the biological parameters. Further, the nature of the trivial critical point (origin) is found to depend on the biotechnical productivity (btp) of each species. It is also proven that the dynamic system does not possess any limit cycles. Mathematical formulation of the optimal harvest policy is given and its solution is derived in the equilibrium case by using Pontryagin's maximal principle. Biological and economic interpretations of the results associated with the optimal equilibrium solution are explained. The significance of the results derived in the paper are then discussed.

The Multicohort Fishery Under Uncertainty

The multicohort fishery subject to random environmental disturbances is examined within a market framework. The free access problem is considered and optimal selective and proportional harvesting policies are discussed.