This paper extends existing models of frequency-dependent diet selection by considering the optimal diet selection of a predator feeding upon prey populations which can be depleted but are also capable of renewal (e.g. immigration, growth, or reproduction). This model and existing models which include prey depletion, predict partial-preference and a generic diet preference for the commonest prey types (apostatic selection). Unlike previous diet selection models, it is found that the optimal diet selection of an individual predator can be to favour the rarest prey type (anti-apostatic selection) when encounter rates are high, even if the individual prey do not differ in their nutritional value. Studies have demonstrated that predators generally show apostatic selection, even when all prey have the same nutritional value. Anti-apostatic selection has also been observed when prey are crowded, and therefore at high density, consistent with the idea of high encounter rates. This anti-apostatic diet selection has previously been proposed as evidence for the use of prey search images by a predator, or variation in individual prey preference. In this paper it is suggested that prey renewal is a further factor, often confounded in experiments, which could favour anti-apostatic selection.