Managing populations in the face of uncertainty: adaptive management, partial observability and the dynamic value of information

The work presented in this thesis falls naturally into two parts. The first part (Chapter 2), is concerned with the benefit of perturbing a population into an immediately undesirable state, in order to improve estimates of a static probability which may improve long-term management. We consider finding the optimal harvest policy for a theoretical harvested population when a key parameter is unknown. We employ an adaptive management framework to study when it is worth sacrificing short term rewards in order to increase long term profits. Active adaptive management has been increasingly advocated in natural resource management and conservation biology as a methodology for resolving key uncertainties about population dynamics and responses to management. However, when comparing management policies it is traditional to weigh future rewards geometrically (at a constant discount rate) which results in far-distant rewards making a negligible contribution to the total benefit. Under such a discounting scheme active adaptive management is rarely of much benefit, especially if learning is slow. In Chapter 2, we consider two proposed alternative forms of discounting for evaluating optimal policies for long term decisions which have a social component. We demonstrate that discount functions which weigh future rewards more heavily result in more conservative harvesting strategies, but do not necessarily encourage active learning. Furthermore, the optimal management strategy is not equivalent to employing geometric discounting at a lower rate. If alternative discount functions are made mandatory in calculating optimal management policies for environmental management, then this will affect the structure of optimal management regimes and change when and how much we are willing to invest in learning. The second part of this thesis is concerned with how to account for partial observability when calculating optimal management policies. We consider the problem of controlling an invasive pest species when only partial observations are available at each time step. In the model considered, the monitoring data available are binomial observations of a probability which is an index of the population size. We are again concerned with estimating a probability, however, in this model the probability is changing over time. Before including partial observability explicitly, we consider a model in which perfect observations of the population are available at each time step (Chapter 3). It is intuitive that monitoring will be beneficial only if the management decision depends on the outcome. Hence, a necessary condition for monitoring to be worthwhile is that control polices which are specified in terms of the system state, out-perform simpler time-based control policies. Consequently, in addition to providing a benchmark against which we can compare the optimal management policy in the case of partial observations, analysing the perfect observation case also provides insight into when monitoring is likely to be most valuable. In Chapters 4 and 5 we include partial observability by modelling the control problem as a partially observable Markov decision process (POMDP). We outline several tests which stem from a property of conservation of expected utility under monitoring, which aid in validating the model. We discuss the optimal management policy prescribed by the POMDP for a range of model scenarios, and use simulation to compare the POMDP management policy to several alternative policies, including controlling with perfect observations and no observations. In Chapter 6 we propose an alternative model, developed in the spirit of a POMDP, that does not strictly satisfy the definition of a POMDP. We find that although the second model has some conceptually appealing attributes, it makes an undesirable implicit assumption about the underlying population dynamics