How to control pest species: application of models from the theory of island biogeography in formulating pest control strategies.
Mathematical models for birth and death processes in local populations (within a local patch), and for migration between local patches in a heterogeneous habitat complex are analysed to arrive at optimal pest-control strategies. The type of pest control considered is to miminise the expected time to extinction of local populations starting out with a few immigrants only, and simultaneously to reduce the number of local populations. It is pointed out that these objectives are mathematically equivalent with other objectives such as to minimise the expected number of young born by an average female during its life-span. Various concepts relating to pest control are defined. In order to design optimal pest-control programmes it is, according to the analysis, necessary to know the relative costs of reducing dispersal, reproduction and survival. In addition it is essential to know the demography of the pest species before control (particularly the natural mortality and extinction rate of local populations) and the characteristics of the habitat complex such as the carrying capacity of an average patch in the complex. The following predictions emerge: if very efficient methods for reducing immigration into empty patches are available, these should be implemented as much as possible regardless of the demography of the pest species; the control treatment should be applied in the habitat with as great spatial variability as possible. If effective methods for reducing dispersal are not available, any reduction of immigrants is still likely to be optimal for control of K-selected species. For r-selected species it is predicted as optimal to increase the extinction rate of local populations as much as possible; in this case the control treatment should be applied in the habitat complex with as little spatial variability but with as much temporal variability as possible. The economic resources not used for reducing immigration should be allocated towards reducing reproduction or survival depending on the mortality rate of the uncontrolled population. The larger the mortality of the uncontrolled population, the more likely is reduction of reproduction to be the optimal pest control. If the equilibrium density of the pest species is low, the optimal pest-control strategy will most often be to increase mortality as much as possible. This is particularly so if the mortality rate of the uncontrolled population is low. It is pointed out that, although the concept of the r-K strategy continuum may be helpful, it can yield ambiguous predictions. Various modifications of the model have been considered. It is concluded that several apparent weaknesses in the model do not affect the basic conclusions reached.