Thomas Krishna Waring

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 policymaking. 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.

The rise of globalization has led to a sharp increase in international trade with high volumes of containers, goods, and items moving across the world. Unfortunately, these trade pathways also facilitate the movement of unwanted pests, weeds, diseases, and pathogens. Each item could contain biosecurity risk material, but it is impractical to inspect every item. Instead, inspection efforts typically focus on high‐risk items. However, low risk does not imply no risk. It is crucial to monitor the low‐risk pathways to ensure that they are and remain low risk. To do so, many approaches would seek to estimate the risk to some precision, but increasingly lower risks require more samples. On a low‐risk pathway that can be afforded only limited inspection resources, it makes more sense to assign fewer samples to the lower risk activities. We approach the problem by introducing two thresholds. Our method focuses on letting us know whether the risk is below certain thresholds, rather than estimating the risk precisely. This method also allows us to detect a significant change in risk. Our approach typically requires less sampling than previous methods, while still providing evidence to regulators to help them efficiently and effectively allocate inspection effort.

For invasive species management, the trade-off between monitoring and control has high stakes,and existing decision-making methods are limited in this area. In particular, most current approachesare limited to a specific case study, or ignore the uncertainty and interaction between monitoring and control in the system. Hence, the field is missing an effective and general framework. We propose a partially observable Markov decision process (POMDP) framework to helpdecision makers understand effective monitoring and control policy making. POMDPs can deal withuncertainty in both the model and state of the system, but are more challenging to solve due tothe continuous and high-dimensional state space. We reduce the dimensionality of the state spaceby restricting the belief state to a parametrised family of probability distributions, aligning themathematical representation of the problem with quantities of the physical process linked to humandecision 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 in two generic case studies of varying complexity. Furthermore, we investigate sensitivityof 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 availableto 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.