The effect of harvesting on competing populations

For the simplest competition model for two species there are four nondegenerate possibilities for ultimate behavior, viz. (I) the first species alone survives, whatever be the initial populations, (II) the second species alone survives, whatever be the intial populations, (III) the two species coexist in stable equilibrium, (IV) the two species coexist in unstable equilibrium, and the survival of first or second species depends on the initial population sizes. We investigate here the harvesting policy which will transform a given possibility before harvesting into any one of these four possibilities after harvesting. We show that I and II can be transformed into either III ci IV, but III and IV cannot be transformed into each other. We determine the harvesting policies for all feasible transformations. In addition we determine the paths of these transformations through degenerate transformations. The results obtained here are compared with those of Yodzis [19]