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The inadvertent introduction of the brown tree snake (Boiga irregularis) to Guam has resulted in the extirpation of most of the island’s native terrestrial vertebrates, has presented a health hazard to small children, and also has produced economic problems. Trapping around ports and other cargo staging areas is central to a program designed to deter dispersal of the species. Sequential trapping of smaller plots is also being used to clear larger areas of snakes in preparation for endangered species reintroductions. Traps and trapping personnel are limited resources, which places a premium on the ability to plan the deployment of trapping efforts. In a series of previous trapping studies, data on brown tree snake removal from forested plots was found to be well modeled by exponential decay functions. For the present article, we considered a variety of model forms and estimation procedures, and used capture data from individual plots as random subjects to produce a general random coefficients model for making predictions of brown tree snake capture rates. The best model was an exponential decay with positive asymptote produced using nonlinear mixed model estimation where variability among plots was introduced through the scale and asymptote parameters. Practical predictive abilities were used in model evaluation so that a manager could project capture rates in a plot after a period of time, or project the amount of time required for trapping to reduce capture rates to a desired level. The model should provide managers with a tool for optimizing the allocation of limited trapping resources. Copyright # 2003 John Wiley & Sons, Ltd.