Significant efforts in conservation are devoted to the management and study of ungulates, due to their significant roles in ecosystems as well as their potential economic value. This is especially true for species considered exotic, such as mouflon sheep (Ovis musimon) in Hawaii. Effective management of an exotic species requires an understanding of ecological metrics such as space use, survival, and population size. We provided these metrics for a population of mouflon that have hybridized with feral sheep (Ovis aries) on the island of Hawaii. In Chapter 1, we quantified space use and annual survival of sheep in an area where sheep are managed for hunting opportunity. We determined that sheep have relatively small home-ranges and high rates of annual survival (>90%). In Chapter 2, we provided the first estimate of population size for the same study area while simultaneously testing the viability of a novel method of estimating population size, currently known as Instantaneous Sampling. Using photographic capture recapture as a comparison method, we compared estimates derived from both techniques and provided support for Instantaneous Sampling as an alternative method for estimating population size.