Mathematical models of species' responses to habitat destruction
Labrum, Matthew J.
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Anthropogenic habitat destruction is the leading cause of the high rate of extinctions of species observed around the world today. With a growing human population, it is vitally important for conservationists to understand how species will respond to such destruction. This work aims to contribute to this knowledge by way of a theoretical approach. Within the framework of habitat destruction models, metapopulation Allee effects (the phenomenon of species experiencing a net loss in patch occupancy below a certain threshold) are the focus of the first two chapters. The third chapter then examines the effects of intransitive competition (e.g., a rock-scissors-paper type relationship) and spatial structure on species' responses. The first chapter discusses analyses and results that differed from a previous study and highlight a need for a better understanding of metapopulation Allee effects. Results here suggest that if sufficiently large thresholds are present, habitat restoration as a conservation plan may be futile. A new model for studying the dynamics of species subject to habitat destruction and metapopulation Allee effects is presented in the second chapter. This new model addresses anomalies discovered in earlier models. It is shown here that higher metapopulation Allee effect thresholds lead to more extinctions in less time as well as possible differences in the order of extinctions when compared to lower thresholds. The final chapter steps back from metapopulation Allee effects and investigates the consequences of modifying the underlying assumptions of a standard habitat destruction model. The focus here is the inclusion of spatial structure as well as intransitive competition, thus relaxing the assumptions of a well-mixed environment and a strict hierarchy of species in regards to competitive abilities. The predictions derived suggest the effect of spatial structure on biodiversity depends on the degree of habitat destruction, intransitive competition may not influence results as much as other factors, and the measure used to quantify biodiversity has a significant impact on how predictions are applied in conservation plans.