Incorporating overhead costs and handling times into invasive species control

I have a new paper out, focused on optimising resource allocation with multiple control methods. Invasive species eradications involve complicated logistics and cost structures, and my PhD optimal papers didn’t really consider this (though see my Ashmore Reef & fire ant chapter for an application of overhead and start-up costs to optimal detection). I tried to break down some of these assumptions to understand their effect on optimal management, with the help of Paul Armsworth and Suzanne Lenhart from the University of Tennessee and the National Institute for Mathematical and Biological Synthesis. In my PhD I looked at how to allocate resources for a single control method, but there are usually multiple options available, and it is common to use several in a single eradication. Hence, we asked: how do you split your budget between two different control methods.

The key difference between the control methods was that one had an overhead cost and the other had a handling time. Overhead costs are costs that must be constantly paid to have a control method available. These differ from start-up costs. A start-up cost is a once-off payment that allows a method to be used in the future; this models initial training or purchase costs. Overhead costs model things like aircraft rental for aerial baiting. The cost of the aircraft does not change with how much you use it (only fuel, bait and personnel costs). Handling times impose a limit to how quickly species can be removed, and they typically apply to ground-based control methods, such as trapping. If traps are checked daily, then a single trap cannot remove more than one individual per day, even if many more individuals encounter the trap. There is a fixed amount of time associated with each removal.

One of the reasons that I started this work was that I had understood that the standard wisdom was to start eradications with expensive broad-scale methods and then switch towards the end. While this makes some intuitive sense, I wondered why and whether it is the best strategy or not. Essentially, should you start by using methods with high overhead costs and switch at the end? The results from this paper would say ‘yes’, but there is some nuance. We always found that the high overhead cost method should be used from the start, and, depending on the magnitude of the overhead cost, be phased out at some stage. Though, for small overhead costs, the effort is just reduced towards the end, rather than a complete stop. The other result is that we found that the ground-based method with handling time should commence before the overhead cost method is ceased. So, rather than a direct switch, a gradual change from one method to the other is optimal.

overheads_finalplot

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