Laysan ducks (Anas laysanensis) are restricted to approximately 9 km2 in the Northwestern Hawaiian Islands, USA. To evaluate the importance of density dependence for Laysan ducks, we conducted a Bayesian analysis to estimate the parameters of a Gompertz model and the magnitude of process variation and observation error based on the fluctuations in Laysan duck abundance on Laysan Island from 1994 to 2007. This model described a stationary distribution for the population at carrying capacity that fluctuates around a long-term mean of 456 ducks and is between 316 to 636 ducks 95% of the time. This range of expected variability can be used to identify changes in population size that warn of catastrophic events. Density-dependent population dynamics may explain the recovery of Laysan duck from catastrophic declines and allow managers to identify population monitoring thresholds.