The mathematics of poaching and gamekeeping

How do we stop poaching? You may think the answer lies in finding a way of giving gamekeepers an advantage over poachers. Oxford Mathematician Tamsin Lee and David Roberts from the University of Kent decided to look at the interaction between rhino poachers and a gamekeeper to predict the outcome of the battle. Their conclusions suggest alternative ways of tackling the problem.

Currently there are many methods used or under consideration for deterring the ever increasing number of poachers. These methods include dehorning, dyes, poisons, and inserting GPS tracking. All these methods devalue the horn considerably, but none of them remove the total value of the horn. Tamsin and David devised a simple model to test the effectiveness of each strategy.

The game has two players, who each have two strategies: the rhino manager may devalue horns or not, and poachers may only target rhinos with full horns, or behave indiscriminately. The game has two equilibriums, that is, either the manager wins or poachers win. The manager wins when devaluing deters poachers, and poachers move to another ranch; poachers win when the value of a damaged horn is still worth the kill, so the manager may as well conserve his/her resources and not devalue horns. A key feature is that poachers can choose their strategy instantaneously.

The model suggests that when devaluing the last few rhinos is expensive, due to sparsity of rhinos, it may not be worth devaluing all rhinos. However, for a poacher, as long as there are a few intact horns, a particular ranch is worth visiting. This is because the value of a rhino horn is so great - greater per unit weight than gold, diamonds or cocaine - that the risk for the poacher has little influence. The game can be tilted, unrealistically, to be in favour of the manager by increasing the risk to the poacher, or lowering the value of a partial horn. However, a poacher is still more likely to make a gain, or minimise loss, by killing rhinos indiscriminately.

In conclusion, the game appears to be challenging for the rhino manager to win. Therefore anti - poaching measures should not seem to tilt the game in the manager's favour, but instead change the game, for example, by legalising trade, or launching campaigns aimed at changing behaviour, although of course the latter may take some time to impact on rhino populations.

The team's research is presented in the Journal of Ecological Modelling and video outlining the paper is also available.