Managing competing endangered and invasive species in spatially structured environments is challenging because it is often difficult to control invasive species without negatively impacting the endangered species. Effective management action requires an understanding of the factors affecting the presence and absence of each species so that promising sites for relocation of endangered species combined with eradication of invasive species can be identified. We investigate competing hypotheses about the factors affecting occupancy of the critically endangered red-finned blue-eye (Scaturiginichthys vermeilipinnis; hereafter ‘RFBE'), a native Australian fish with a global distribution that is restricted to a group of shallow artesian springs. RFBE are threatened by competition with invasive mosquito fish (Gambusia holbrooki), which are steadily colonizing the springs, resulting in local extinctions of RFBE in most cases. While hypotheses about the influences of Gambusia on RFBE exist, none have been tested with a quantitative model. We used a spatially-structured two-species occupancy modeling approach to examine the occupancy dynamics of these fish and tested competing hypotheses on how Gambusia occupancy affected RFBE. Gambusia occupancy had a strong negative effect on RFBE occupancy and colonization potential; increasing the probability of local extinction at a spring and decreasing the persistence probability of RFBE in a spring by 8.0% ± 2.7% (mean ± 1 SE). We found strongest support for the hypotheses that elevation and spring area influence colonization, and that spring area influences patch extinction probability. Using colonization and local extinction estimates for both species, we identify promising sites for eradication of Gambusia and relocation of RFBE.