A ubiquitous problem for all foragers is the trade-off between acquiring food energy while simultaneously avoiding the risk of predation. In central montane Alberta I modelled how ungulate forage changes with succession within cutblocks and the implications for forage availability to ungulates under current harvest regimes. Because cutblocks are discrete patches in space, I developed a dynamic state variable model for an ungulate to explore under what conditions an individual forager could (1) behaviourally avoid predation within a patch through inactivity, (2) overcome patch isolation when confronted with predation during transit between patches, and (3) alter patch use across a home range to optimize fitness. The model includes the requirement to process forage into energy through rumination behaviour that constrains foraging, and compares outcomes under a time-minimizing (sigmoid) and energy maximizing (linear) fitness functions. When an ungulate is in high energetic state, inactivity provides an effective behavioural refuge, or animals prioritize safety over energy gain, individuals avoid predation within patches reducing the need to move between patches. When energy acquisition is prioritized, individuals are at a low energetic state, or within patch anti-predator behaviours are ineffective, individuals move among patches to avoid predators in space, and configuration of the patches influences fitness. When model results were qualitatively compared to activity patterns and cutblock use of female, GPS-collared elk appear to follow a time minimizing strategy in their patch use across the home range and with their activity within riskier patches. I discuss the implications of these findings for the management of elk and cutblocks in west central Alberta.

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Significant research efforts have been devoted to large-scale dynamical systems, with the aim of understanding their complicated behaviors and managing their responses in real-time. One pivotal technological obstacle in this process is the existence of uncertainty. Although many of these large-scale dynamical systems function well in the design stage, they may easily fail when operating in realistic environment, where environmental uncertainties modulate system dynamics and complicate real-time predication and management tasks. This dissertation aims to develop systematic methodologies to evaluate the performance of large-scale dynamical systems under uncertainty, as a step toward real-time decision support. Two uncertainty evaluation approaches are pursued: the analytical approach and the effective simulation approach. The analytical approach abstracts the dynamics of original stochastic systems, and develops tractable analysis (e.g., jump-linear analysis) for the approximated systems. Despite the potential bias introduced in the approximation process, the analytical approach provides rich insights valuable for evaluating and managing the performance of large-scale dynamical systems under uncertainty. When a system’s complexity and scale are beyond tractable analysis, the effective simulation approach becomes very useful. The effective simulation approach aims to use a few smartly selected simulations to quickly evaluate a complex system’s statistical performance. This approach was originally developed to evaluate a single uncertain variable. This dissertation extends the approach to be scalable and effective for evaluating large-scale systems under a large-number of uncertain variables. While a large portion of this dissertation focuses on the development of generic methods and theoretical analysis that are applicable to broad large-scale dynamical systems, many results are illustrated through a representative large-scale system application on strategic air traffic management application, which is concerned with designing robust management plans subject to a wide range of weather possibilities at 2-15 hours look-ahead time.

This thesis presents a methodology to incorporate reservoir uncertainties and estimate the loss in project value when facility planning decisions are based on erroneous estimates of input variables. We propose a tank model along with integrated asset development model to simulate the concept selection process. The model endogenizes drilling decisions and includes an option to expand. Key decision variables included in the model are number of pre-drill wells, initial facility capacity and number of well slots. Comparison is made between project value derived under erroneous estimates for reserve size and under an alternate hypothesis. The results suggest loss in project value of up to 40% when reservoir estimates are erroneous. Moreover, both optimistic and pessimistic reserve estimates results in a loss in project value. However, loss in project value is bigger when reserve size is underestimated than when it is overestimated. / text

Operating and interacting in an environment requires the ability to manage uncertainty and to choose definite courses of action. In this thesis we look to Bayesian probability theory as the means to achieve the former, and find that through rigorous application of the rules it prescribes we can, in theory, solve problems of decision making under uncertainty. Unfortunately such methodology is intractable in realworld problems, and thus approximation of one form or another is inevitable. Many techniques make use of heuristic procedures for managing uncertainty. We note that such methods suffer unreliable performance and rely on the specification of ad-hoc variables. Performance is often judged according to long-term asymptotic performance measures which we also believe ignores the most complex and relevant parts of the problem domain. We therefore look to develop principled approximate methods that preserve the meaning of Bayesian theory but operate with the scalability of heuristics. We start doing this by looking at function approximation in continuous state and action spaces using Gaussian Processes. We develop a novel family of covariance functions which allow tractable inference methods to accommodate some of the uncertainty lost by not following full Bayesian inference. We also investigate the exploration versus exploitation tradeoff in the context of the Multi-Armed Bandit, and demonstrate that principled approximations behave close to optimal behaviour and perform significantly better than heuristics on a range of experimental test beds.