Optimal Harvesting Strategy Research Articles

Harvesting and Replenishment Policies for Renewable Natural Resources

The current paper links the optimal intertemporal use of renewable natural resources to the harvesting activities of various economic agents. Previous contributions cite market forces as a causative factor inducing the extirpation of renewable natural resources. The analysis given here discusses investment in the stock of renewable resources and cites important examples of this activity. By introducing joint harvesting and replenishment strategies into a model of renewable resource use, the analysis adds descriptive reality and relevance to positive and normative discussions of renewable natural resource use. A high price for the yield or a high discount rate tend to diminish the size of the optimum stationary stock of the resource with a non-replenishment harvesting strategy. Optimal non-replenishment harvesting strategies for renewable natural resources will exhaustion or extirpation of the resource if the price of the yield or the discount rate are sufficiently large. However, the availability of a replenishment technology and the use of replenishment activities tends to buffer the resource against exhaustion or extirpation.

Shrimp growth functions and their economic implications

Obtaining a reliable growth function is an integral part of deriving the optimal harvesting strategy for any aquaculture operation. This paper examines the common functional forms of fitting growth equations for fish and shrimps. The following functional forms are considered: linear, polynomial, log reciprocal, Von Bertalanffy, Gompertz, logistic and exponential. Results of fitting these various functional forms with experimental data for Penaeus vannamei are compared and evaluated using standard statistical goodness-of-fit tests. The implications of these estimated growth functions in determining the optimal harvest schedule is compared and discussed. Results indicate that Gompertz and Von Bertalanffy functions are statistically the best fit to the experimental data and the harvesting schedule calculated based on these two functions well reflect the actual shrimp farm operation. Therefore, the Gompertz and Von Bertalanffy function may be the best functions describing shrimp biological growth and hence might be useful for economic evaluation.

A simple model for seaweed growth and optimal harvesting strategy

In this paper, a logistic type of model with periodic coefficients (time-dependent periodic growth and death rates) is used to simulate the growth and optimal harvesting of a type of seaweed. Applying a result of the optimal periodic control theory, we obtain an optimal annual harvesting strategy which has the same period as that of the seaweed growth and death rates.

Evolution of yields from populations with age-specific cropping

Age-specific exploitation of a natural population acts as a selective force on genetic variation in life history traits. Evolution arising from this selection may bring about evolutionary changes in the total yield which the population is able to sustain. An analysis of this process is given for a harvested population with densitydependent recruitment, in which selection of life history traits by cropping is independent of density and frequency. Evolution of the total yield depends on an interplay between the yield from an individual over the course of its life and recruitment; whether the total yield increases or decreases depends on the properties of particular populations. Evolution brought about by harvesting does not, in general, lead to the maximization of the total yield. Nonetheless, by appropriate choice of an age-specific harvest pattern, it is possible in principle to select the life history which gives the maximum total yield following evolution; this harvest pattern is called the ‘evolutionarily stable optimal harvesting strategy’ (ESOHS). Results of the analysis are illustrated with data on the Arcto-Norwegian cod.

Effect of Stochasticity on Optimal Harvesting Strategies in Some Lumped-Parameter Fishery Models

This paper introduces some methods for anticipating the difference between optimal harvesting strategies in a fishery model with stochastic recruitment and in the corresponding deterministic model with recruitment equal to its expected value. It extends known results on the sign of the difference and presents ways to estimate the magnitude. Two classes of lumped-parameter models are discussed. In myopic models, the policy difference is likely to be insignificant. In more general models with downward sloping demand for fish and increasing marginal cost of fishing effort, a heuristic measure is introduced that can suggest the direction and magnitude of the policy shift.

Mass Rearing and Harvesting Based on an Age-Stage, Two-Sex Life Table: A Potato Tuberworm (Lepidoptera: Gelechiidae) Case Study

Traditional age-specific life table analysis does not take variable development rates into account and deals only with the female population. In this paper, rearing and harvesting of specific life stages are analyzed in the context of a general age-stage, two-sex life table. The question of selecting optimal harvest and discard strategies for the design of insect mass rearing facilities is discussed. The method is demonstrated using data collected from a culture of the potato tuberworm, Phtharimaea aperculella (Zeller).

How to avoid extinction of populations optimally exploited

A stochastic optimal control approach is introduced which quantifies the risk of extinction of the population associated with the optimal exploitation. Optimal harvesting strategies can be determined subject to the constraint that the risk of extinction does not exceed a given limit. By the example of a logistic growth it is demonstrated that the purely economic optimization delivers an unnecessarily high risk of extinction which can be lowered considerably without a substantial loss of profit.

Optimization theory and pre-columbian hunting in the Tehuacan Valley

Previous analyses of faunal remains from highland Mesoamerican sites have viewed implied changes in animal exploitation patterns as a secondary consequence of early agricultural practices. This paper argues that faunal data from the Tehuacan Valley, when interpreted within an optimization framework provide evidence for the alteration of optimal meat harvesting strategies through time by communities responding to a variety of socioenvironmental factors: seasonal and long-term availability of game, access to domestic meat resources, human meat demand levels, and scheduling constraints.

Optimal harvesting of a logistic population in an environment with stochastic jumps.

Dynamic programming is employed to examine the effects of large, sudden changes in population size on the optimal harvest strategy of an exploited resource population. These changes are either adverse or favorable and are assumed to occur at times of events of a Poisson process. The amplitude of these jumps is assumed to be density independent. In between the jumps the population is assumed to grow logistically. The Bellman equation for the optimal discounted present value is solved numerically and the optimal feedback control computed for the random jump model. The results are compared to the corresponding results for the quasi-deterministic approximation. In addition, the sensitivity of the results to the discount rate, the total jump rate and the quadratic cost factor is investigated. The optimal results are most strongly sensitive to the rate of stochastic jumps and to the quadratic cost factor to a lesser extent when the deterministic bioeconomic parameters are taken from aggregate antarctic pelagic whaling data.

Optimal Thinning of a Year-Class with Density-Dependent Growth

I consider the impact of density-dependent growth on the optimal harvesting of a year-class of fish. In general, density dependence makes "thinning" of the year-class a desirable strategy. Moderate density dependence implies that thinning should be gradual, even in the case of zero harvesting costs where the optimal harvesting strategy would otherwise be instantaneous harvesting. Strong density dependence calls for an immediate thinning at an early date, in the case of zero harvesting costs.

Optimal management of replenishable resources in a predator-prey system with randomly fluctuating population

An ecosystem of two species with predator-prey behavior and stochastic growth is formulated. The steady state distribution of the population levels of the species is generated and examined. Optimal harvesting strategies based on a social welfare function are studied. The results derived from constant effort harvesting and an effort adjustment policy are discussed. Qualitative results and interpretations are provided.

Optimal and feedback strategies for managing multicohort populations

A Beverton and Holt type linear cohort dynamics model is integrated and combined with a nonlinear stock-recruitment relationship to obtain a discrete-time multicohort harvesting model. Assuming that each age class is individually controllable, it is shown, subject to certain assumptions, that the optimal harvesting strategy is to drive the population to the maximum sustainable yield solution in one time step. In most fisheries, this controllability assumption is not met and harvesting is agewise nonselective. In this case, it may be preferable to implement a harvesting policy based on suboptimal constant effort or stock level feedback strategies, rather than implement a more complicated optimal policy. This question is addressed through numerical studies on the management of an anchovy fishery.

Dynamics of a vegetation-ungulate system and its optimal exploitation

Optimal harvest strategies for a vegetation-ungulate system are estimated using stochastic dynamic programming. Effects of a randomly fluctuating mortality rate and alternative assumptions about vegetation production are considered in the estimation. In the contex used here, optimal strategy refers to a sequential decision rule, optimal with respect to maximizing harvest. Optimal control laws are intensitive to the probability distribution of the mortality rate. They are, however, sensitive to assumptions regarding vegetation production. Values of information were computed, and these indicated that considerably higher returns can be produced by using optimal policies as compared to traditional approaches. Implications for ungulate population management are discussed.

An economic model of short-rotation forestry

This paper presents an economic model of short-rotation forestry and shows that Lemke's linear complementarity algorithm can be used to compute optimal sustainable harvesting strategies. As an example, we apply our method, using existing data, to calculate optimal harvesting strategies for a plantation consisting of two interdependent species of trees.

Ungulate population dynamics and optimization models

Optimal harvesting strategies for an ungulate population are estimated using stochastic dynamic programming. Data on the Llano Basin white-tailed deer (Odocoileus virginianus) population were used to construct a 2-variable population dynamics model. The model provided the basis for estimating optimal harvesting strategies as a feedback function of the current values of the state variables (prefawning older deer and juveniles). Optimal harvest strategies were insensitive to assumptions about the probability distributions of the stochastic variable (rainfall). The response of the population components to harvesting and the returns obtained from applying optimal strategies were explored through simulation. Mean annual harvest is about 15% of the population. Simplified harvesting strategies based on age-ratios as well as a simplified version based on optimal strategies—but assuming persisting equilibrium juvenile deer density—were compared to optimal strategies through examining values of information. Simplified harvesting strategies lead to a lower harvest over a 50-year simulation period.

Rock-lobsters, mussels and man: A mathematical model

The palinurid rock-lobster Jasus lalandii (H. Milne-Edwards), which forms the basis of an important South African fishery, feeds mainly on the mussel Aulacomya ater (Molina). Natural populations of A. ater exhibit a bimodal size frequency distribution, believed to be caused by intense predation pressure upon medium-sized mussels. This may lead to situations in which rock-lobster productivity is severely restricted by food availability even in the presence of a large standing crop of prey. The present rock-lobster harvesting strategy is based on a minimum size limit; however, by not catching small rock-lobsters, an imbalance may be created in the lobster size distribution, resulting in an overabundance of small rock-lobsters which have insufficient food to grow fast. The need to predict an economically and biologically optimal harvesting strategy provided motivation for the present model, in which an alternative harvesting strategy, involving decrease of the minimim size limit, was compared with the present strategy. It appears that the mussel biomass could be increased by 87% and the rock-lobster yield by 19%. Simultaneously, the rock-lobster density and egg production are seen to decrease by 24 and 35%, respectively. The model assumes that rock-lobster populations have constant recruitment; therefore, the effect of the decline in fecundity cannot be predicted. Therefore, any major policy change should be delayed until the larval biology of J. lalandii has been researched more fully.

Discount Factors and Risk Aversion in Managing Random Fish Populations

The effects of changes in the discount factor as compared with the effects of changes in risk aversion are examined for a simple stochastic model of fish population dynamics. Numerical results suggest that both optimal harvesting strategies and the resulting population dynamics are insensitive to changes in the discount factor, whereas changes in the degree of risk aversion in the utility function do cause significant changes in both. When risk averse utility functions are viewed as total revenue curves with marginal prices that decrease with supply, the results suggest that the more sensitive price is to supply, then the resulting optimal harvesting policy is smoother. Theoretical results are presented which suggest these results are robust beyond the specific model.Key words: discount factors, risk aversion, population dynamics, randomness

Models for fisheries management

Realization of the massive potential harvests from the oceans, coupled with disastrous collapses of substantial fisheries has seen the development over the last 25 years of a quantitative fisheries management science. As an aid to management, models are used to represent fish populations and the effects of exploitation on them. Basic models currently used for fisheries management are reviewed. The models discussed range from the simple surplus production model through to the analytical model of Beverton and Holt incorporating age structure and finally to Kicker's stock-recruitment model. The models are used to examine the dynamics and stability of fish stock when subjected to different exploitation policies. Some of the problems for management in interfacing real fisheries data with the mathematical models are discussed. The goals of management, including catch, fishing effort and economics (e.g. price, cost and inflation) are quantified to produce an objective function which may be used to determine optimal strategies. The optimal harvesting strategies are examined for each model, with a view to developing a general workable robust harvesting policy, independent of the model used.

Optimization model for a wolf-ungulate system

Public outcries against predator control create a need to devise management policies that optimally balance the cost (managerial and environmental) of predator control against the benefit of ungulate harvesting. To address this problem, an optimization procedure utilizing stochastic dynamic programming is described. Through this approach, optimal feedback strategies for a wolf-ungulate system in Alaska are estimated. The dynamic predator-prey model used in the analysis is based on parameter estimates from data collected over an eight-year period in Denali (Mt. McKinley) National Park. Stability analysis of the system revealed that stability properties depend on predator search efficiency. The effects of random fluctuations in winter severity and alternative objective functions are considered in the estimation of optimal feedback strategies. Optimal moose harvesting strategies appear to be dependent on wolf control costs. If no wolf control cost is assessed, optimal moose harvest is independent of wolf density. Optimal wolf control strategies are completely insensitive to moose density. The strategies are compared to current and simplified management policies.

The ultimate-sustainable-yield problem in nonlinear age-structured populations

The Beverton-Holt theory of harvesting a multicohort fishery subject to constant recruitment, and the Leslie matrix harvesting model modified to include a nonlinear stock-recruitment relationship, are extended and shown to be related through the ultimate-sustainable-yield problem for an age-structured population. The well-known result that the optimal harvesting policy for the Leslie matrix model is bimodal is shown to hold for the Leslie matrix model modified to include an arbitrary stock-recruitment relationship. This conclusion extends a recent result of Reed (1979), who proved biomodality of the optimal harvesting strategy for the Leslie matrix model modified to include only compensatory stock-recruitment relationships. The paper concludes with a numerical example which demonstrates how the ultimate sustainable yield can be used as a standard of comparison for any sustainable-yield harvesting policy.