Neurogenesis in the adult hippocampal dentate gyrus (DG) is demonstrated to facilitate behavioral discrimination between similar contexts or objects, referred to as pattern separation. The vast majority of adult-born cells die, and the adult DG retains approximately the same total number of granule cells throughout the lifetime of the animal. Meanwhile immature cells compete with each other and with mature cells for survival. The DG is among the few restricted layers of the central nervous system in which neurogenesis occurs appreciably in the adult. The DG is also notoriously sparse in its activity. However the computational implications of extreme sparseness co-localized with neurogenesis has not yet received significant attention. We therefore evaluate pattern separation in networks with competitive neuronal turnover across varying degrees of sparseness. We find that neuronal turnover enhances pattern separation by selecting an efficient dentate population code in which the dimensionality of contextual discrimination is reduced. Ultrasparse coding emerges from the model as the optimally performing case in which the dimensionality of the pattern separation problem is most rapidly reduced in the dentate representation. Furthermore, the optimal neurogenesis rate is proportional to the novelty of the environment, and this value remains less than 0.5% of the total DG population per day, corresponding with values that have been experimentally determined. Thus competitive neurogenesis represents an efficient biological strategy for pattern separation.