Optimal Management of a Native Species Facing Species or Pathogen Invasion Risks Involving Multi-Stable Outcomes

Many invaded ecosystems appear subject to regime shifts—abrupt changes from one state to another after crossing a threshold or tipping point. The stability landscapes of such multi-stable systems, including their associated thresholds, have been shown to be endogenously determined within a coupled socioeconomic-ecological system (SES) where human choices, including those of managers, are feedback responses. Which outcome arises within traditional SES models, for a given set of available policy options, is ultimately determined by exogenously-defined initial conditions. We examine optimal management when the initial conditions at the onset of an invasion are endogenous. This is accomplished by considering the economically optimal management of a non-invaded system at risk of invasion and subsequent multi-stability. Methodologically, this requires that we account for two uncertain processes: introduction and establishment of the invader, where establishment is defined by a random invader population level that serves as the initial condition for the invaded system. Both random processes are conditional on how the native population is managed, making them endogenous. We find multi-stability of the invaded system, as well as uncertainty regarding the initial established invader population, may create economic non-convexities that yield multiple candidate solutions to the ex ante optimization problem. Some candidate solutions may involve attempting to prevent invasion, while others may attempt to increase the likelihood that any invasion becomes contained within a “good” ex post state