2011 Summer.Includes bibliographical references.Despite the obvious threats invasive species pose to ecosystem health, studying the characteristics that influence their colonization can provide valuable insight on fundamental issues in ecology, evolution, and biogeography. The aim of this research has been focused on the implications of mechanisms likely to affect persistence of small founder populations. Individuals can suffer a reduction in one or more components of fitness when population growth and spread are constrained at low density. This dynamical relationship between fitness and population size (i.e., positive density dependence) can be driven by a myriad of mechanisms, broadly termed Allee effects. In this dissertation, I have theoretically explored how small founder populations faced with Allee effects can overcome the demographic challenges that heighten the risk of extinction. I have developed models of increasing complexity to better understand the ecological and evolutionary consequences of Allee effects. I begin by exploring ways in which intraspecific interactions influence population dynamics and invasiveness through a review of the literature. The mechanisms that impact individual fitness at low density suggest that there are benefits to being in a large population; however, there are abundant examples of adaptations that might have evolved in small or sparse populations in response to Allee effects. Using a reaction-diffusion framework with a quantitative genetics approach, I have derived conditions and explored the dynamics for rapid adaptive evolution rescuing the population from extinction. This deterministic modeling approach broadly describes population dynamics through diffusive dispersal and density dependent growth, where the response to population density can evolve through a genetic subsystem that incorporates the intensity of selection and genetic variance. For both the spatial and non-spatial cases, invasion criteria were determined across the range of parameter space. The results emphasized that a sufficient amount of genetic variance is a crucial component for evolutionary rescue to occur. I developed a spatially explicit, individual-based stochastic simulation in order to more realistically capture the complexity of intraspecific interactions. I found that with limited dispersal and local perception, the emergence of spatial structure impacted individual fitness and could enable population persistence. Departures from the population-level model predictions demonstrate the importance of considering individual variation in assessing the consequences of Allee effects. I further incorporated immigration and genetic variation into the simulation in order to explore the relative importance of evolutionary, demographic, and genetic rescue for establishment. Additional immigration was more effective than adaptive evolution in contributing to successful invasions due to the intensity of ecological constraints on population growth and time to extinction. Without multiple introductions, evolutionary processes can contribute to recovery through genetic variation maintained and enhanced by mutation and recombination. Overall, I have demonstrated that it is possible for a small founder population to overcome a suite of ecological, evolutionary, and genetic obstacles upon introduction into a novel environment despite the paradox of invasion
