Optimal foraging theory provides a suite of tools that model the best way that an animal will <br/>structure its searching and processing decisions in uncertain environments. It has been <br/>successful characterizing real patterns of animal decision making, thereby providing insights<br/>into why animals behave the way they do. However, it does…
Optimal foraging theory provides a suite of tools that model the best way that an animal will <br/>structure its searching and processing decisions in uncertain environments. It has been <br/>successful characterizing real patterns of animal decision making, thereby providing insights<br/>into why animals behave the way they do. However, it does not speak to how animals make<br/>decisions that tend to be adaptive. Using simulation studies, prior work has shown empirically<br/>that a simple decision-making heuristic tends to produce prey-choice behaviors that, on <br/>average, match the predicted behaviors of optimal foraging theory. That heuristic chooses<br/>to spend time processing an encountered prey item if that prey item's marginal rate of<br/>caloric gain (in calories per unit of processing time) is greater than the forager's<br/>current long-term rate of accumulated caloric gain (in calories per unit of total searching<br/>and processing time). Although this heuristic may seem intuitive, a rigorous mathematical<br/>argument for why it tends to produce the theorized optimal foraging theory behavior has<br/>not been developed. In this thesis, an analytical argument is given for why this<br/>simple decision-making heuristic is expected to realize the optimal performance<br/>predicted by optimal foraging theory. This theoretical guarantee not only provides support<br/>for why such a heuristic might be favored by natural selection, but it also provides<br/>support for why such a heuristic might a reliable tool for decision-making in autonomous<br/>engineered agents moving through theatres of uncertain rewards. Ultimately, this simple<br/>decision-making heuristic may provide a recipe for reinforcement learning in small robots<br/>with little computational capabilities.
Biodiversity has been declining during the last decades due to habitat loss, landscape deterioration, environmental change, and human-related activities. In addition to its economic and cultural value, biodiversity plays an important role in keeping an environment’s ecosystem in balance. Disrupting such processes can reduce the provision of natural resources such…
Biodiversity has been declining during the last decades due to habitat loss, landscape deterioration, environmental change, and human-related activities. In addition to its economic and cultural value, biodiversity plays an important role in keeping an environment’s ecosystem in balance. Disrupting such processes can reduce the provision of natural resources such as food and water, which in turn yields a direct threat to human health. Protecting and restoring natural areas is fundamental to preserve biodiversity and to mitigate the effects of ongoing environmental change. Unfortunately, it is impossible to protect every critical area due to resource limitations, requiring the use of advanced decision tools for the design of conservation plans. This dissertation studies three problems on the design of wildlife corridors and reserves that include patch-specific conservation decisions under spatial, operational, ecological, and biological requirements. In addition to the ecological impact of each problem’s solution, this dissertation contributes a set of formulations, valid inequalities, and pre-processing and solution algorithms for optimization problems with spatial requirements. The first problem is a utility-based corridor design problem to connect fragmented habitats, where each patch has a utility value reflecting its quality. The corridor must satisfy geometry requirements such as a connectivity and minimum width. We propose a mix-integer programming (MIP) model to maximize the total utility of the corridor under the given geometry requirements as well as a budget constraint to reflect the acquisition (or restoration) cost of the selected patches. To overcome the computational difficulty when solving large-scale instances, we develop multiple acceleration techniques, including a brand-and-cut algorithm enhanced with problem-specific valid inequalities and a bound-improving heuristic triggered at each integer node in the branch-and-bound exploration. We test the proposed model and solution algorithm using large-scale fabricated instances and a real case study for the design of an ecological corridor for the Florida Panther. Our modeling framework is able to solve instances of up to 1500 patches within 2 hours to optimality or with a small optimality gap. The second problem introduces the species movement across the fragmented landscape into the corridor design problem. The premise is that dispersal dynamics, if available, must inform the design to account for the corridor’s usage by the species. To this end, we propose a spatial discrete-time absorbing Markov chain (DTMC) approach to represent species dispersal and develop short- and long-term landscape usage metrics. We explore two different types of design problems: open and closed corridors. An open corridor is a sequence of landscape patches used by the species to disperse out of a habitat. For this case, we devise a dynamic programming algorithm that implicitly enumerates possible corridors and finds that of maximum probability. The second problem is to find a closed corridor of maximum probability that connects two fragmented habitats. To solve this problem variant, we extended the framework from the utility-based corridor design problem by blending the recursive Markov chain equations with a network flow nonlinear formulation. The third problem leverages on the DTMC approach to explore a reserve design problem with spatial requirements like connectivity and compactness. We approximate the compactness using the concept of maximum reserve diameter, i.e., the largest distance allowed between two patch in the reserve. To solve this problem, we devise a two-stage approach that balances the trade-off between reserve usage probability and compactness. The first stage's problem is to detect a subset of patches of maximum usage probability, while the second stage's problem imposes the geometry requirements on the optimal solution obtained from the first stage. To overcome the computational difficulty of large-scale landscapes, we develop tailored solution algorithms, including a warm-up heuristic to initialize the branch-and-bound exploration, problem-specific valid inequalities, and a decomposition strategy that sequentially solves smaller problems on landscape partitions.
