Harvesting a population sustainably as a resource is a common problem in wildlife and fisheries management. In a typical situation population size and other state variables are monitored at fixed intervals and the resulting estimates are used to determine a quota or harvest effort. Such decisions must be made in the face of a range of uncertainties: environmental variation, an imperfect ability to observe state variables, an imperfect ability to implement management decisions and imperfect knowledge about how the population fluctuates dynamically in response to management actions.
In this thesis I explore the effect of these uncertainties on the optimal management of wild populations. In chapters 2 and 3, populations with significant age or stage structure are examined. When individuals of different maturity within a population have significantly different life history traits, the structure of the population and of the harvest taken can have a large effect on the growth rate of the population. In chapter 2 a simple matrix model is used to make observations about the role of demographic structure when the objective is to maintain the population below its carrying capacity. Uncertainty in the structure of the population and the manager's ability to select the harvest structure complicate optimal harvesting. In chapter 3 plausible models are developed for the maintenance of the Atlantic population of Canada geese (Branta canadensis) within acceptable population bounds, given uncertainty about the strength of density dependent population regulation and the limited ability of managers to achieve large harvests. Stochastic dynamic programming is used to determine the optimal harvest strategy under each of the plausible models. It is found that the target long-term population size depends critically on the strength of density dependence. Under the density-independent model, limits to harvest also influence the target long-term population size.
Chapter 4 explores the theory of adaptive management. In adaptive management we seek the optimal harvest decision in the presence of model uncertainty. Plausible models are weighted according to the amount of evidence currently supporting them. The optimal harvest decision is obtained by weighting the expected returns under each model. When the population is monitored subsequent to harvesting, the evidence supporting each model can be re-evaluated. In this way the model best describing the system dynamics can be learnt over time (passive adaptive management). Particular harvest decisions may accelerate learning and provide better management in the long term. However these actions are often perceived as risky and so short-term losses must be balanced by long-term benefits (active adaptive management). To test these ideas, a simple population model with an uncertain parameter is constructed. Fixed, passive adaptive and active adaptive harvest strategies are developed using stochastic dynamic programming. It is found that the passive adaptive strategy is `certainty-equivalent', meaning that the current best estimate of the uncertain parameter is used as if it were the true parameter value. Over very long time horizons, the active adaptive strategy probes for information but in the short-term it is actually more precautionary than the certainty-equivalent strategy. The passive and active adaptive strategies perform similarly well in maximising harvest, and both outperform fixed non- adaptive strategies. Two different sets of plausible models produce consistent results, leading to the conclusion that it is important to incorporate model uncertainty, but the specific approach does not critically affect the results.
In chapter 5 the problem of optimal adaptive monitoring is considered. The most common approach to harvest management is to use the same monitoring effort at regular intervals to estimate state variables. This approach neglects the large costs often involved in population monitoring, assuming that the level of accuracy achieved is both necessary and sufficient to make the appropriate harvest decision. I take an alternative approach, combining the costs of monitoring and the expected benefits for management in a single framework to determine the level of monitoring accuracy required. Monitoring effort becomes a state-dependent decision at each time interval, determined by prior information about the state variables. This approach is demonstrated using data for a red kangaroo (Macropus rufus) population in South Australia.
This document is not a comprehensive treatment of optimal harvesting under uncertainty. However it does indicate the ways in which uncertainty complicates the harvest of wildlife, and its potential effect on optimal harvesting and monitoring decisions.