Thomas Krishna Waring , Vera Somers, Michael McCarthy, Christopher Baker

Resource allocation for invasive species management requires information about the size of the invasive population, which may be expensive and time-consuming to obtain. The trade-off between investment in monitoring and control efforts is a challenging decision problem, and existing mathematical tools are often difficult to interpret, and / or limited to a specific case study. 

We propose a partially observable Markov decision process (POMDP) framework to help decision makers understand effective monitoring and control policy making. POMDPs can deal with uncertainty in both the model and state of the system, but are more challenging to solve due to the continuous and high-dimensional state space. Rather than limiting the possible states of the system, as do most previously proposed methods, we work through the development of a density projection approach, which reduces the dimensionality of the space of beliefs by restricting them to a parametrised family of probability distributions. This serves to align the mathematical representation of the problem with the real-world quantities relevant to human decision making. 

The result of our model is a sequence of actions which minimises the expected cost incurred in managing the invasive species, where the recommendation depends on an estimate of the species' abundance, and the uncertainty in this estimate. We demonstrate the effectiveness of our proposed framework with a case study on tropical fire ant (Solenopsis geminata) control and two generic case studies of varying complexity. Furthermore, we investigate sensitivity of the results to the choices of control cost and efficacy, and monitoring cost and error.

The framework proposed by this paper makes the powerful machinery of POMDPs available to environmental managers. It computes the optimal course of action to manage a growing population of an invasive species, incorporating a varying time horizon and multiple control interventions. We sidestep the computational difficulties of general POMDPs to provide a clear, visual overview of decision-making recommendations, and how these decisions change in new situations. Initial results and scenario based analysis show promising results, and the framework could be extended to the related field of disease management.