| Three models are used to explore the relationship of spatial scale to theoretical and practical problems in understanding aspects of the evolution of pesticide resistance. In the first paper, the role that economic thresholds play in resistance is explored in a single field, and then multiple field, deterministic, two-dimensional cellular automata model. It is found that resistance develops in large patches and explains much of the regional variability found in field studies of Colorado potato beetle.; In the second, a stochastic, spatial model is developed to explore resistance of Heliothis virescens in transgenic cotton expressing the {dollar}delta{dollar}-endo toxin from Bacillus thuringiensis in its plant tissues. The model predicts that migration and the distribution of migration have a strong influence on the route to resistance. The model also shows that resistance can be delayed by using the same fields as refuges year after year.; The third paper attacks recent attempts to dismiss the third phase of the shifting balance that Sewall Wright proposed as a method to explain evolution of traits that must pass through an adaptive valley. The paper provides counter examples to current deterministic and non-spatially explicit models that predict that the third phase proceeds under a restrictive set of conditions. |
