This thesis is about the demography of the tunicate Styela clava, a species of some notoriety because of its invasiveness and impacts in many parts of the world. Species assemblages have continuously changed throughout evolutionary history, but the rate of today’s anthropogenically facilitated dispersal is unparalleled in history. Non-indigenous species (NIS) are now considered one of the most important risks to native biodiversity. NIS become invasive by becoming both widespread and locally dominant. This requires that a species becomes established, spreads locally, and increases in abundance. In the early stages of invasion, its demography and life history characteristics are of crucial importance. In New Zealand, Styela has established populations in several places, but none of these populations has yet reached the high densities found in other countries. In Lyttelton Port, where this study was located, Styela was first noticed in 2005. It therefore presented an ideal situation to study an invasive species in its early stages of establishment and provided a potentially good model for understanding how invasive species get local traction and spread from initial infestation points. Therefore, I set out to determine demographic features of Styela to understand the numbers game of population dynamics. This study used empirical data on growth rates, size-frequencies through time, and size and age to maturity to test several models, including von Bertalanffy, Logistic dose-response, Ricker and power models of individual growth. The most useful proved to be the von Bertalanffy model. Styela individuals shrink frequently, so average growth rates were often quite low, even though some individuals reached 160 mm or more in total length. Mortality was greatest in summer, presumably after reproduction, and lowest in winter. Fewer than 5% of individuals survived 12 months, and most or all of these died soon afterwards. Populations were, therefore, essentially annual. Recruitment was difficult to determine because of the cryptic nature of small juveniles. However, size-frequency, abundance and mortality data indicated that recruitment most likely occurred in early spring (late-October), and then again in late summer, with growth to maturity (at c. 50 mm total length) within < 5 months. Several manipulative experiments showed that Styela did not readily capitalise on provision of free space but the other non-native ascidian, Ciona intestinalis, rapidly recruited. Transplants of Styela were greatly affected by C. intestinalis, which overgrew them, similar to a localised replacement of Styela by Ciona seen overseas. Lefkovitch modelling was used to test whether Styela had an “Achilles heel” in its life history, whereby managed removal could impact future populations. This showed that under several scenarios intervention would most likely be ineffectual. Overall, this study showed that the original populations in Lyttelton Port are either static or in decline, somewhat contrary to original expectations. Nevertheless, it appears that these small populations may be acting as stepping stones for spread of this species outside of the port.