Control and the management of a spreading invader

We consider the problem of management of an aquatic invader spreading in a lake system. We assume that each year the invader can be removed from a certain proportion of invaded lakes, which depends on the selected intensity of control. Control decisions are generated and compared for an optimally controlled system and for a static optimization across asymptotic steady states. Control close to eradication of the invasive species is always optimal for invasions with relatively high damages, low rates of density dependent spread and/or low chance of additional random introductions. Control to a highly invaded steady state is optimal for those invasions with low relative damages, high chances of random introduction and high levels of uncertainty in species location. In all other cases the optimal outcome depends upon initial conditions. Comparing the relative performance of the optimally controlled system and the static optimization demonstrates situations when the differences are small and when not. When invasions are acted upon in their later stages and across certain parameter combinations a static optimization provides a reasonable approximation of an optimally controlled system. The flip-side is that optimal policies directed at an invasion in its early stages tend to provide significantly savings. The savings vary across parameter combinations, yet in these situations little useful insight will be generated without consideration of a dynamically optimized system.