Your number is up: Species doomed by mathematics

It seems rather grim: a mathematical formula to calculate the probability of animals becoming extinct.

But its Australian creators say that it will aid any decisions on where to target resources – as well as helping to recognise species so close to the brink that they are beyond help.

The Red List of Threatened Species, produced by the International Union for Conservation of Nature (IUCN), already ranks plants and animals in categories ranging from safe to critically endangered.

But it does not distinguish between species at the top and bottom of a category, which is where the new index – called Safe (Species Ability to Forestall Extinction) – comes in.

Devised by researchers from the University of Adelaide and James Cook University, in northern Queensland, Safe can determine how close a population is to its minimum viable size. Professor Cory Bradshaw, director of ecological modelling at Adelaide's Environment Institute, called it "the best predictor yet of the vulnerability of mammal species to extinction".

The issue is particularly sensitive in Australia, which has the world's worst record for mammal conservation. Of all the mammals that have disappeared in the past 200 years, nearly half were Australian.

The Safe index, detailed in a paper published in the journal Frontiers in Ecology and Environment, builds on previous studies into minimum population sizes required to survive in the wild. According to Professor Bradshaw, the tipping-point is 5,000; below that, the risk of extinction from extreme events such as bushfires or cyclones is much higher. Among the animals close to the tipping-point are the tiger and the African wild dog.

Professor Bradshaw acknowledged that, based on the index, some species – such as the Javan rhinoceros and the New Zealand kakapo, the world's largest parrot – might not be worth trying to save. There are just 40 to 60 rhinos left, and 120 or so kakapos.

"If an animal is so rare, and it's going to take a lot of money and resources and could be impossible to restore because the habitat is not there... it might not be worth saving," Professor Bradshaw told The Australian newspaper.

"It's controversial, but when you have a finite amount of resources, one species might be more likely to be brought back from the brink."

The index would assist "practitioners of conservation triage", he said, explaining that: "During wartime, medicos have to go out and say: 'Well, this guy's too far gone, we're not going to waste our time because there's too few of us.' So we have to say: 'These ones are probably too far gone.'"

The Safe index exposes subtleties within the Red List. Both the Javan rhino and Sumatran rhino are critically endangered, but while it may be too late to save the former, the latter – with a population of 220 to 275 – may still be capable of being rescued.

So it therefore makes no sense, argues Professor Bradshaw, to spend more on the Javan species, as is currently the case. "Not all critically endangered species are equal," he said.

To test their formula, designed to be used in conjunction with the Red List, researchers applied it to 95 mammal species. They found that nearly one-fifth were close to extinction, and more than half of those had populations that had already fallen to unsustainable levels.

The Australian animal species that may have to be "cut loose", based on the Safe index, include the hairy-nosed wombat, which is now a critically endangered mammal. The high extinction rate in Australia is believed to be mainly due to the introduction of feral cats and foxes.