SHIELD: Protecting Etosha National Park
Our team's entry to the International Mathematical Modelling Challenge, which took an Honourable Mention at the international round. Etosha faces six threats at once across 22,935 square kilometres with 295 staff. We built a protection metric, a deployment plan and a feasibility score, then simulated five years a thousand times.
How do you measure whether a park is protected, when six different things are going wrong at the same time?
The idea the whole entry rests on is that simultaneous threats do not add up. They multiply. A park under poaching and fire and drought at once is worse off than the sum of those three taken separately, because each one degrades the response to the others.
That is bad news for the park. It was the opening for the model, because the same arithmetic runs backwards. Four layers of defence, none of them individually impressive, compound into something strong. Our deployment cut simulated poaching mortality by 86% without any single component being especially good at its job.
We were a team of four. We qualified through the national round and sent the same report on to the international round, where it was awarded an Honourable Mention.
The problem
Etosha National Park in Namibia covers 22,935 square kilometres and is staffed by 295 people from the Ministry. It faces six threats at the same time: rhino poaching, wildfire, endemic anthrax, bush encroachment by Senegalia mellifera, recurring drought, and elephant pressure on mopane woodland. The brief asked how to allocate protection resources, how to measure protection quantitatively, and whether the approach transfers to other reserves.
What we built
SHIELD is the protection metric. It produces a score between zero and one for each species group, in each zone, in each time period, using an exponential survival-decay form borrowed from reliability engineering. It decomposes by threat, so you can see which one is doing the damage rather than only that something is.
The Unified Deployment Model is the allocation. It moves 198 of the existing 295 staff into operational roles and adds 15 thermal drones, vibration and acoustic sensor networks, prescribed burns and specialised ecological units, arranged in four layers where each layer catches what the one before it missed.
The Practicality Index is the check on the other two. It scores a deployment across seven components including night safety, training burden, budget, redundancy and shift continuity, because a plan that is mathematically optimal and cannot be staffed is worth nothing. The two scores combine through a weighted harmonic mean, which forces both above a threshold instead of letting a strong protection score cover for an unworkable plan.
What the simulation said
We ran 1,000 Monte Carlo simulations over a five-year horizon. All seven animal species groups grew in expectation. Black rhino went from 350 to 375, with a 95% confidence interval of 352 to 402 and extinction risk under 0.3%. Poaching mortality fell 86% against the no-deployment baseline. Plant habitat recovered to between 92% and 97% of carrying capacity. The deployment costs $4.7 million a year against Etosha’s estimated $7.5 to $9.4 million of available funding, and most of that is salaries already being paid.
The sensitivity analysis interested me more than the headline numbers. Across eight scenarios and 4,500 further runs, doubling poaching pressure did not reverse population growth. Removing the entire drone fleet raised poaching kills by 60% and the ground layers held. Under simultaneous degraded operations, meaning 75% of personnel with no drones and no sensors, poaching mortality was still 76% below baseline.
The assumptions
We wrote down six, and for each one we said what would break it and which way the error would run. Three are worth repeating here.
Zone independence is the weakest. SHIELD scores each of six zones on its own, and only fire spillover crosses between them. Anthrax spreading through the waterhole network and elephants migrating north in the wet season are both real and both unmodelled, so we underestimate risk in zones next to an outbreak. Doing it properly needs partial differential equations over a waterhole adjacency graph, which is a research programme rather than a competition entry.
Carrying capacity is the most sensitive. Population outcomes depend on K more than on anything else we picked. We set it at three to five times the current population, using the lower bound of published density ranges. If the true value is nearer 1.5 times, rhino growth slows to almost nothing, although no extinction events occurred even then across 500 runs.
Poisson threat arrivals assumes poaching attempts turn up independently, like rain. A syndicate sending three teams to three waterholes on one night is a deliberate tactic that a Poisson process treats as close to impossible, so the model understates how bad the worst nights get, and our anti-poaching figures flatter us on exactly those nights.
Adapting it elsewhere
The brief asked whether the framework transfers, so we recalibrated it for Yellowstone and the Sundarbans, chosen because they are about as different from Etosha and from each other as two reserves can be. The metric structure survived. The inputs did not. In Yellowstone, projected warming ranks above poaching as the top threat and grizzlies replace rhinos at the top of the species weighting. The Sundarbans is a roadless delta, so boat patrols replace road patrols entirely and the disease vector shifts from waterhole-transmitted anthrax to mosquitoes.
Leading the team
I was the orchestrator and the writer, and I built SHIELD, the protection metric.
One of the four disengaged early over disputes inside the team. That was a personal matter on her side and I have no interest in relitigating it now. She still found major flaws in what we had built, and those catches went into the final report.
The more interesting problem was between the other two. Each had designed a way to protect the park, each wanted their own version submitted, and so they kept refining their models to beat the other by a slightly better protection score. It was a rivalry, and it was making both models better by the day.
I did not step in, and that is the decision I would defend hardest. An escalating contest over one number produces a better number, so I let it run.
What I did instead was change what they were competing on. The Practicality Index exists because two people were optimising purely for protection score, and a deployment that scores well on protection but cannot be staffed, funded or sustained is worth nothing. Adding a second axis meant whichever model won had to be good at both. The argument I chose not to settle is a large part of why the final model is as strong as it is, and the thing I built to contain it became one of the three components the whole entry rests on.
What I would do differently
I do not have a clean answer here. We gave it everything, including several nights where nobody slept, and I thought the entry was worth an Outstanding.
The one concrete thing I would change is the research. Our literature work was the weakest part of what we submitted and it should have gone deeper. Whether that is what separated us from a higher award, I have no way of knowing.
Both of those things are true at the same time and I have not reconciled them. I am proud of what the four of us built.
- Modelling
- Monte Carlo
- Teamwork