Selecting simultaneous actions of different durations to optimally manage an ecological network

Summary Species management requires decision‐making under uncertainty. Given a management objective and limited budget, managers need to decide what to do, and where and when to do it. A schedule of management actions that achieves the best performance is an optimal policy. A popular optimisation technique used to find optimal policies in ecology and conservation is stochastic dynamic programming (SDP). Most SDP approaches can only accommodate actions of equal durations. However, in many situations, actions take time to implement or cannot change rapidly. Calculating the optimal policy of such problems is computationally demanding and becomes intractable for large problems. Here, we address the problem of implementing several actions of different durations simultaneously. We demonstrate analytically that synchronising actions and their durations provide upper and lower bounds of the optimal performance. These bounds provide a simple way to evaluate the performance of any policy, including rules of thumb. We apply this approach to the management of a dynamic ecological network of Aedes albopictus, an invasive mosquito that vectors human diseases. The objective is to prevent mosquitoes from colonising mainland Australia from the nearby Torres Straits Islands where managers must decide between management actions that differ in duration and effectiveness. We were unable to compute an optimal policy for more than eight islands out of 17, but obtained upper and lower bounds for up to 13 islands. These bounds are within 16% of an optimal policy. We used the bounds to recommend managing highly populated islands as a priority. Our approach calculates upper and lower bounds for the optimal policy by solving simpler problems that are guaranteed to perform better and worse than the optimal policy respectively. By providing bounds on the optimal solution, the performance of policies can be evaluated even if the optimal policy cannot be calculated. Our general approach can be replicated for problems where simultaneous actions of different durations need to be implemented.