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Strategies for the control of vertebrate pest are identified using mathematical models of poisoning. The models integrate aspects of foraging ecology and toxicology in a probabilistic framework. The structure, assumptions and control implications of the models are presented. Variables (control parameters) influencing the probability that a pest animal dies in a poison program are identified and classified according to their degree of operator control. Control strategies suggested by the models are identified, and practical means of applying them are discussed. The models suggest that the probability that an animal dies is a function of 15 to 17 control parameters, of which operators have direct control over a maximum of 4: poisoned bait abundance, poison bait dispersion, the time over which poisoned bait is available, and poison concentration.