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ItemOptimal resource allocation for invasive species managementBaker, Christopher M. ( 2016)Invasive species are responsible for enormous ecological and economic damage worldwide, and resources for managing them are severely limited. Allocating these resources efficiently is therefore a key concern for conservation managers. Unfortunately, the complexity of the problem makes developing cost-effective strategies for managing invasive species extraordinarily difficult. The scale and difficulty of the problem highlights that quantitative approaches are needed to both understand the general properties of a good control strategy and to assist in developing invasive species management plans in specific cases. In this thesis I use mathematical modelling to find optimal strategies for invasive species control. The theoretical work contained here focuses on solving for the optimal resource allocation in spatial, temporal and spatiotemporal systems. This gives insight into the qualitative features of optimal management. Moving from purely spatial or temporal optimal solutions to the full spatiotemporal solution increases the complexity of the models and solutions. However, key ideas about invasive species control in the spatial and temporal sections translate to the spatiotemporal problem, and a good understanding of these results in this thesis allow one to better understand solutions in the more complex spatiotemporal case. As well as general insights, I want to offer specific support to environmental managers; mathematical modelling is applied to three case studies in this thesis. The first two are applications of optimal control theory to feral cat (Felis catus) control in arid Australia and to orange hawkweed control (Hieracium aurantiacum). The third case is about the proposed eradication of tropical fire ants (Solenopsis geminate) from the islands of Ashmore Reef Commonwealth Marine Reserve in the Timor Sea, which is off the Northwest coast of Australia. This work focuses on providing quantitative advice about the management of tropical fire ants. Linked models for the population dynamics and detectability of tropical fire ants are developed. These models quantify how different control methods and schedules affect the probability of eradicating ants and allow the resource allocation for surveillance to be optimised.