A variety of mechanisms have been proposed to explain the renowned British Columbia sockeye salmon (Oncorhynchus nerka) cycles, most of which invoke between-brood interactions (delayed density dependence) or depensatory harvest practices. We examine the dynamics of the Ricker model with realistic parameter values and suggest that the cycles could result from a stable mode excited by stochastic forcing. The previously proposed mechanisms are not required to generate cyclic patterns, although they could play a role in reinforcing cycles. Our results suggest that relaxing harvest rates will increase yields and decrease variability in sockeye abundances.