DescriptionExotic species and collapses of native species pose equivalently severe threats to global biodiversity and ecological health. Much work has been done to improve our understanding of the patterns and processes associated with biological invasions and population declines. However, due to the complexity of the issues posed to conservation and management, we still lack fundamental knowledge about their population dynamics. Early-action is often recommended to deal with both situations, which, as has been argued, requires minimal detail about the population biology of the target species. While this holds true in many cases, it does not justify ignoring population biology as a whole. Indeed, by analyzing data about past events we can greatly improve our ability to manage future ones. Furthermore, applying powerful tools and concepts from other disciplines can help develop expectations for general trends across taxa and systems. In this dissertation I explore statistical methods to identify and describe poorly explained population growth patterns, using both exotic and native species. I used a large, uncommonly complete database of citizen-collected data and developed efficient, robust methods to quantify population lag phases and collapses. I found lags—periods of low population growth rates relative to future growth—to be common in exotic birds in Hawaii. I found seemingly spontaneous population collapses—>90% declines in abundance within a specified timeframe—in nearly half of the populations investigated. I expand on the details of the method I developed for collapses to account for variation about important portions of any population’s growth patterns; specifically estimated maximum abundances and the duration of observed declines. I applied this method to endemic Hawaiian forest birds to display its utility and assess limitations. These results have important implications for conservation management, and yield novel conclusions about the population biology of exotic and native species. By establishing methods to classify populations experiencing lags or collapses, we can begin to develop models to anticipate their occurrence prescribe well prepared management actions and conservation strategies. With more knowledge of the spatial dynamics of exotic populations we can strategically apply targeted control measures in efficient, cost-effective ways.