Using maths to guide conservation law enforcement

In this post Kiran Dhanjal-Adams discusses her recent paper ‘Optimizing disturbance management for wildlife protection: the enforcement allocation problem

For International Women’s Day, we asked Kiran about her career in science and the challenges and improvements she is seeing in STEM. You can read all of our posts for International Women’s Day here.

Determining where and when to carry out enforcement patrols can be a complex issue. Imagine for instance that you have 10 sites that you want to visit between 0 and 5 times…There would be a grand total of 60,466,176 possible combinations of site visits. So how do you figure out which one of these 60,466,176 possible combinations works best for you?

Then of course there is the issue of how effective the enforcement actually is. Maybe people are stubborn and don’t want to change their behaviour to follow regulations. Or maybe they are very fearful, and go somewhere else to avoid patrols. If people are fearful and avoid patrols, it is both expensive and useless to keep patrolling the same site when no one is there. There is therefore a sweet spot, in other words an optimal number of visits, which ensures a site is not being visited so little that enforcement has no effect, or visited so much that money is wasted.

Our recent paper in the Journal of Applied Ecology examines these trade-offs and investigates where managers should patrol, and how often. The problem can be broken into two parts. Firstly, what is the benefit of enforcing regulations? And secondly, what is the cost of enforcing regulations?

Dogs playing in the waves
Dogs playing in the waves – a common site on Australian coastlines

Because we are birders and we live in Australia, we use the case study of declining migratory shorebirds and dogs on beaches to illustrate our approach. Indeed, the shorebirds that we see here migrate 11,000 kilometres, all the way from Alaska and Russia, to spend the summer feeding on worms, shells and crabs in the intertidal zone. Dogs, though cute, have a tendency to chase birds. One dog can cause hundreds of birds to take flight, and if this occurs regularly, the birds cannot feed and gain the weight necessary to complete their long-distance migrations.

Enforcement is very simple. It involves increasing the number of dogs on leashes. Like I said before, there are two parts to the problem: the benefit of enforcement, and the cost of enforcement. Benefit here can be thought of as the number of birds no longer being disturbed. Cost is simply that of travelling to a given shorebird site and time spent enforcing.

In our case study, the objective was to minimise dog disturbance to migratory shorebirds at roost sites in Moreton Bay, Australia. Several of these species are considered nationally or globally threatened with extinction.

Because we are unsure, without extensive fieldwork, how effective enforcement is (i.e. how many people actually continue putting their dog on a leash after enforcement), we tested two scenarios. One where people are stubborn, and don’t want to put their dog on a leash, and another where people immediately start putting their dog on a leash. The results are surprisingly similar between the two scenarios, many of the same sites appear important in both. What varies is the number of times these sites are visited.

Quite intuitively, if people are reluctant to follow regulations, a site must be visited more often, while if people are willing to follow regulations, money should be invested visiting lots of sites a small number of times. This shows that the methods we develop make sense, but to figure out the exact number of visits to a site, it remains essential to do the maths. No pain, no gain!

low tide
Many shorebird species can only feed during low tide.

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