The study of pest distributions in space and time in agricultural systems provides important information for the optimization of integrated pest management programs and for the planning of experiments. Two statistical problems commonly associated to the space-time modelling of data that hinder its implementation are the excess of zero counts and the presence of missing values due to the adopted sampling scheme. These problems are considered in the present article. Data of coffee berry borer

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... station collected under Colombian field conditions are used to study the spatio-temporal evolution of the pest infestation. The dispersion of the pest starting from initial focuses of infestation was modelled considering linear and quadratic infestation growth trends as well as different combinations of random effects representing both spatially and not spatially structured variability. The analysis was accomplished under a hierarchical Bayesian approach. The missing values were dealt with by means of multiple imputation. Additionally, a mixture model was proposed to take into account the excess of zeroes in the beginning of the infestation. In general, quadratic models had a better fit than linear models. The use of spatially structured parameters also allowed a clearer identification of the temporal increase or decrease of infestation patterns. However, neither of the space-time models based on standard distributions was able to properly describe the excess of zero counts in the beginning of the infestation. This overdispersed pattern was correctly modelled by the mixture space-time models, which had a better performance than their counterpart without a mixture component.