Optimal Harvesting Strategy Research Articles

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.

Harvesting Strategies and Parameter Estimation for an Age-Structured Model

An age-structured model with knife-edge recruitment describes the dynamics of exploited, seasonally breeding populations. For management strategy, an equation is derived that characterizes the economic optimal state of exploitation of a modeled stock. A further generalization is derived to account for those species where recruitment to the mature stock occurs over many age-categories. Since the parameters all have phenomenological definitions, they can be estimated from information independent of the model. These parameters can also be estimated by regression of the model to catch and effort data. Test regressions of the general model are made on catch and effort data from three exploited fish stocks: the yellowtail flounder of New England, the Pacific halibut of Area II, and the haddock of Georges Bank; the corresponding R2 values are 0.75, 0.87, and 0.86. Although the confidence intervals for individual parameter estimates are very large, the estimates compare favorably with published parameter values. Since only certain combinations of parameters from the general model appear to have low sensitivity to small perturbations to the data, some guiding suggestions are made that may lead to an improved robustness in the statistical procedures.Key words: age-structured model, optimal harvesting strategy, spawner–recruit curves, parameter estimation

Non-Convexity and Optimal Harvesting Strategies for Renewable Resources

Non-Convexity and Optimal Harvesting Strategies for Renewable Resources

Optimal Harvesting of a Randomly Fluctuating Resource. I: Application of Perturbation Methods

The effect of noise upon optimal harvesting strategies is considered. Whereas deterministic optimal strategies are based upon local considerations, the stochastic strategies must account for global effects. Perturbation methods are applied to obtain approximate solutions to the resulting boundary value problems, for small amounts of noise. Three problems are considered: (1) a single switching point (optimal escapement level), (2) three switching points, and (3) a switching point near a zero of the net growth rate. Approximate formulas are found for the perturbation of the optimal switching points. Qualitative results and interpretations are also provided.

The effects of information in a resource management problem: A social trap analog

A resource management simulation was devised in which players could harvest points for individual short-term gain, causing the premature destruction of the resource pool, or they could curb their own individual harvesting to preserve the pool for a longer overall supply. Although the first strategy was explained to be self-defeating, most groups opted for it, as they did even when an optimal harvesting strategy was provided that would avoid pool destruction. Groups whose members were allowed to communicate generally made better resource managers and achieved larger individual harvests.

The commons dilemma: A simulation testing the effects of resource visibility and territorial division

In a commons dilemma laboratory analog subjects were allowed individually to draw valuable points from a slowly regenerating pool. Subjects participated in groups of four and faced the dilemma of either rapidly drawing a large number of points for themselves (but thereby destroying the pool), or limiting their own harvesting so that the pool would regenerate, benefiting the group. All subjects were, in addition, informed of the optimum strategy for harvesting before the game began, but results showed that this strategy was rarely used. Two factors were added to the basic game: (1) dividing the resource pool into individual harvesting territories, and (2) making the varying levels of resources visible. Each of these increased the harvest and production of the resource, but only territoriality increased the supply. Only when both factors were applied together did the groups approach the optimal harvesting strategy earlier spelled out to them. Possible mediating variables and applications are discussed.

Optimal harvesting strategies for stochastic single-species, multiage class models

Qualitative properties of optimal harvesting policies for stochastic, single-species, multiage class models are described. For many problems the k-dimensional problem ( k is the number of age classes) can be reduced to k one-dimentional problems, which can be solved far more readily. When such separability does not occur, bounds can be put on the derivatives of an optimal policy function which can greatly increase computational efficiency.

Population growth with stochastic fluctuations in the life table

Monte Carlo simulations with the Leslie matrix and similar population models show that as the variance in survivorship or fecundity increases, the expected population growth rate decreases. This is attributed to Jensen's inequality with the observation that the rate of increase is a concave function of age-specific survivorship and fertility rates. Applications of this observation are advised for demographic studies, population simulation, optimal harvest strategies, and natural selection for variance in fertility and survivorship rates.

A Dynamic Model of the Western Lake Erie Walleye (Stizostedion vitreum vitreum) Population

A simple population model of western Lake Erie walleye was constructed using empirical relationships linking growth to population density and recruitment to breeding stock size and the spring water temperature regime. Given a reasonable set of values for annual rates of natural and fishing mortalities, consistent with empirical estimates of total survival for the period from 1947 to 1975, the model generated a pattern of behaviour similar, both qualitatively and quantitatively, to that exhibited by the real population. Two types of stochastic model, based on the initial population model, were used to derive optimal harvest strategies for the population. Optimal strategies were not sensitive to variations in catchability and natural mortality. Yields produced were highly sensitive to variations in both these factors. A refined and extended version of this model may serve as a useful tool in developing realistic management policies for this population. Key words: Percidae, dynamic model, population model, Stizostedion, Lake Erie walleye, growth, density, survival, management implication

Optimization Problems Associated with a Leslie Matrix

Since Leslie (1945, 1948) suggested the use of a matrix model to project through time the expected size of a population by age class, several related problems have been posed in the ecological literature: optimal age-specific harvesting strategies for such a population subject to a variety of ecological constraints, and the so-called problem of optimizing life-history strategies-that is, what use of energy for reproductive effort and for survivorship effort will maximize the individual's contribution over its expected lifetime to the growth of the population. The density-independent Leslie model is viewed in the literature as a first approximation to the real situation, appropriate perhaps for an expanding population that has not yet approached its resource limitations. This paper reviews some of the literature on these subjects and presents several new solutions (or solution techniques) to these problems. Finally, I hope to draw some conclusions on the practicality of the Leslie model for real-life problems.

Optimal Harvest Strategies for Salmon in Relation to Environmental Variability and Uncertain Production Parameters

A method is developed for incorporating the effects of environmental variability and judgmental uncertainty about future production parameters into the design of optimal harvest strategies; these are expressed as curves relating stock size and exploitation rate. For the Skeena River sockeye, the method suggests that optimal strategies are insensitive to judgmental uncertainty about the Ricker stock production parameter, but are very sensitive to management objectives related to the mean and variance of catches. Best possible tradeoffs between mean and variance of catches for the Skeena River are developed, and a simplified strategy is suggested for improving mean catch while reducing year to year variation.