Cost-effective management of invasive species using linear-quadratic control

Abstract

The removal of invasive species is the first step toward restoring an ecosystem following invasion. We develop spatially-explicit, dynamic optimal control strategies for a large class of invasion problems using linear-quadratic control. This approach allows us to produce new insights that help guide policy that could not have emerged from existing models. We assume adults are sedentary, and heterogeneous patches are connected via dispersal of offspring. We develop a generalized approach to optimally manage species across time and space and apply the framework to several examples, primarily based on Spartina alterniflora. General conclusions are drawn and we show that strong connectivity makes invasive control much more costly, demonstrating that reducing connectivity can be a cost-effective part of invasive species control.