Count or control? Optimal monitoring for invasive species management

There exists an extensive body of research on mathematical models for the optimal control of biological populations. The literature addresses such issues as: uncertainty in control success, stochasticity in population dynamics and the economics of control versus pest damage. However, in order to apply these models to real world situations monitoring is required (to parameterise models and track population size) and despite being far from trivial, monitoring costs are rarely included when comparing management regimes. We consider finding an optimal combined management strategy for an invasive fox population which specifies both when to monitor and when to control. In our model, the monitoring data are binomial observations of an index associated with the population size. We use bayesian updating to track the population index and embed this in a Markov decision process to investigate the value of monitoring. Preliminary results are somewhat counter-intuitive, and suggest that managers should only monitor when they believe the population is small, that is, in a desirable state. Preliminary results have also demonstrated that a seemingly sensible objective function can lead to somewhat counter-intuitive results, suggesting that it is difficult to intuitively predict optimal monitoring-control regimes. This highlights the need for mathematical rigour in designing management regimes.