How should you invest $20 million to save the most species from extinction? That was the challenge we put to visitors to The University of Melbourne Open Day. You can take the challenge too!

It is a difficult problem; programs to conserve different species will cost different amounts of money and will have different levels of success.

We used the paper by Liana Joseph and her colleagues as a case study; we had 32 different species, and the total funding required for all of them cost over $100 million. With only $20 million to spend, we need to find more money to invest in species conservation. But while waiting for Treasury to provide more funds, how do we decide which species to save?

Before reading about the optimal solution, you can try for yourself; please download the Excel spreadsheet here. (The expected success of each program differs, as does the cost. Enter the proportion of each program that you want to fund. Unfortunately, you can’t fund them all – you will have to prioritize. Can you save the most species?)

Here is how to construct this as an environmental decision problem; we then use some basic maths to maximize the number of species saved.

Let’s look at the data for the first two species on the spreadsheet we used:

Species | Benefit (Reduction in extinction risk) |
Probability of success | Cost |

Long-tailed bat | 0.95 | 0.21 | $6,210,151 |

North Island brown kiwi | 0.95 | 1.00 | $7,910,292 |

For North Island brown kiwi, the risk of extinction will be reduced by 0.95 if its conservation program is successful. And that particular conservation program is certain to succeed – the probability of success is 1.00. So if it is funded, we’ll improve the expected number of species saved by 0.95.

For the long-tailed bat, the benefit of the conservation program is also 0.95, but the probability of success is only 0.21. So if that is funded, the expected improvement in the number of saved species is only 0.95×0.21 = 0.1995.

The expected benefit of funding the kiwi program is greater, but the long-tailed bat program is cheaper. So which would we prefer to fund?

Well, we simply ask “Which species gives us the best bang for our buck?” That is, we select the option where the expected number of species saved per dollar spent is the greatest.

By multiplying the benefit by the probability of success, and then dividing by the cost, we can rank the options by their relative efficiencies. We fund the species where the relative efficiencies are greatest until we run out of money.

In the example in the Excel spreadsheet, the optimal solution saves just under an extra 7.84 species. You can download that optimal solution here.

This approach to efficient allocation of funding is now being used in New Zealand, and is being adopted in some Australian states. You can read more about it in Liana Joseph’s paper.

Some species might be valued more than others – they might influence the ecology of an area more than others, they might be economically important (e.g., think of the tourism value of koalas), or they might be more evolutionarily distinct. These different factors can be incorporated by modifying the benefit derived from conserving each species.

The benefit of a conservation program might change non-linearly with the level of funding, while this example assumes linear changes. The maths required to solve the non-linear case is more complicated – it requires calculus, but it is not much more complicated than the calculus taught in high schools (email Mick if you want a copy of the paper – this will generate an email, and the automatic response will send you a copy of the paper).

While it is relatively straight-forward to determine the budget for a conservation program, determining the values of saving species and estimating the probability of success can be difficult. If those values are hard to calculate, you might wonder whether this approach is useful. In fact, this approach is particularly useful because it focuses one’s mind on the parameters that need to be determined so that a good decision can be made. We don’t end up worrying about factors that are irrelevant to the decision at hand.

Some might worry that this approach sanitizes the extinction of species – in fact, I think it does the opposite, by making clear that current levels of funding are insufficient. It forces us to calculate how much money is actually required to save species from extinction.

To those who used the spreadsheet at Open Day, thanks for participating. I hope you enjoyed the challenge, and learned a little about some of the things we study at The University of Melbourne. Congratulations to Tim and Sam who figured out the approach to optimizing this particular problem. And thanks to Natasha for organizing everything!

To learn more about using maths to help manage the environment, check out our research centre’s (free) monthly magazine Decision Point.