Population models, such as those used for Population Viability Analysis (PVA), are valuable for projecting trends, assessing threats, guiding environmental resource management, and planning species conservation measures. However, rarely are the needed data on all aspects of the life history available for cetacean species, because they are long-lived and difficult to study in their aquatic habitats. We present a detailed assessment of population dynamics for the long-term resident Sarasota Bay common bottlenose dolphin (Tursiops truncatus) community. Model parameters were estimated from 27 years of nearly complete monitoring, allowing calculation of age-specific and sex-specific mortality and reproductive rates, uncertainty in parameter values, fluctuation in demographic rates over time, and intrinsic uncertainty in the population trajectory resulting from stochastic processes. Using the Vortex PVA model, we projected mean population growth and quantified causes of variation and uncertainty in growth. The ability of the model to simulate the dynamics of the population was confirmed by comparing model projections to observed census trends from 1993 to 2020. When the simulation treated all losses as deaths and included observed immigration, the model projects a long-term mean annual population growth of 2.1%. Variance in annual growth across years of the simulation (SD = 3.1%) was due more to environmental variation and intrinsic demographic stochasticity than to uncertainty in estimates of mean demographic rates. Population growth was most sensitive to uncertainty and annual variation in reproduction of peak breeding age females and in calf and juvenile mortality, while adult survival varied little over time. We examined potential threats to the population, including increased anthropogenic mortality and impacts of red tides, and tested resilience to catastrophic events. Due to its life history characteristics, the population was projected to be demographically stable at smaller sizes than commonly assumed for Minimum Viable Population of mammals, but it is expected to recover only slowly from any catastrophic events, such as disease outbreaks and spills of oil or other toxins. The analyses indicate that well-studied populations of small cetaceans might typically experience slower growth rates (about 2%) than has been assumed in calculations of Potential Biological Removal used by management agencies to determine limits to incidental take of marine mammals. The loss of an additional one dolphin per year was found to cause significant harm to this population of about 150 to 175 animals. Beyond the significance for the specific population, demographic analyses of the Sarasota Bay dolphins provide a template for examining viability of other populations of small cetaceans.