Predator-prey dynamics of the spider mites and predatory phytoseiid mites (Acari: Tetranychidae, Phytoseidae) in horticultural crops Gómez-Moya, C.A. and Ferragut, F. ABSTRACT The spider mites are one of the most important pests in the production of horticultural crops in the Mediterranean area of Spain, both in greenhouse and open-air production systems. These mites are usually controlled with chemicals, with significant economic and ecological costs. Alternatively, predatory phytoseiid mites could be released to biologically control the tetranychids. However, basic information needed for effective biological control about the dynamic and the optimal predator-prey ratio is lacking. This study evaluated the predator-prey ratio of the native predatory phytoseiid mites Phytoseiulus persimilis Athias- Henriot and Neoseiulus californicus (McGregor) with the spider mites Tetranychus urticae Koch, Tetranychus turkestani Ugarov & Nikolski and Tetranychus evansi Baker & Pritchard. The study included laboratory and greenhouse trials on plants of bean (Phaseolus vulgaris L.) and potato (Solanum tuberosum L.), as well as simulations of the population dynamic of the phytoseiid predators and the phytophagous mites. In the laboratory, the feeding behaviour and the main biological and demographic parameters of the predators when feeding on T. urticae, were studied. Results indicated that the duration of growth stages, reproductive behaviour, and demographic parameters of the local populations of N. californicus and P. persimilis were similar to those observed in other geographical regions, and that their parameters reached optimal values when these predators fed on T. urticae. In the greenhouse, the effectiveness of three predator-prey ratios, 1:12, 1:8 and 1:4 for the trials with T. urticae, and 1:16, 1:8 and 1:4 for the trials with T. turkestani and T. evansi, were evaluated. The damage level, distribution of the spider mites on the plants, and their dispersive behaviour as a function of time and population density were also evaluated. In the greenhouse, P. persimilis was able to control T. urticae and T. turkestani with the three predator-prey ratios tested, while N. californicus significantly controlled T. urticae y T. turkestani only when the predator-prey ratio was 1:4. However, none of the two predators was able to control T. evansi. As the population density increased, also increased the level of damage, but this level of damage in the bean plants was more severe with T. turkestani than with T. urticae. T. evansi caused the maximum level of damage after three weeks in the potato plants. This study also found that, as in P. persimilis, T. urticae and T. turkestani tended to move towards the upper leaves as the population density increased, while N. californicus remained on the lower leaves. In addition to the laboratory and greenhouse trials, a simulation of the population dynamics of both predators with T. urticae and T. turkestani was conducted using a selection algorithm. The objective was to determine the optimal number of predators to release as a function of the growth rate, the extinction time of the prey, and the level of damage caused by the phytophagous mites on the host plant. There was a good agreement between the model predictions and the empirical data obtained in the greenhouse trials; thus, trial results validated the mathematical model. If the initial population of the pest was 25 mites per plant, the minimum release dose of N. californicus was estimated in 12 and 20 mites per plant to control T. urticae and T. turkestani, respectively. In of P. persimilis the minimum release dose would be from 6 to 8 mites per plant to control T. urticae, or 12 mites per plant if the pest was T. turkestani. Keywords: Phytoseiulus persimilis, Neoseiulus californicus, Tetranychus urticae, Tetranychus turkestani, Tetranychus evansi, biological control, predator-prey ratio, damage level, simulation.