For decades people thought it was extinct. It’s one of the most curious animals on earth – a mammal, but highly unusually, a venomous one. The strange and shrew-like Cuban solenodon resembles mammal species that lived almost as long ago as the dinosaurs.

Between 1890 and 1970 there hadn’t been a single specimen found. Then, unexpectedly three were caught a few years later. Subsequent sightings were extremely rare but one, captured in 2003, was positively identified and nicknamed “Alejandrito” – only the 37th Cuban solenodon in history ever to be caught and recorded. The “extinct” species lived on.

Sometimes we hear about animals going extinct in the news. But who does the work to determine that a species has actually died out? What methods, exactly, do scientists use for the job? And can we ever be sure that the animal in question isn’t still around, like the Cuban solenodon, hiding in the bush?

There is a popular myth that conservationists use a very simple rule to declare an animal extinct: if it hasn’t been sighted for 50 years or more, it’s gone forever. “It’s a thing that keeps getting perpetuated that there’s a 50 year rule,” says Craig Hilton-Taylor, head of the Red List unit at the International Union for Conservation of Nature (IUCN).

In truth, biologists go to much greater lengths to determine that a species is extinct – and the process begins with careful monitoring of the species while it still exists.

The IUCN’s Red List unit that Hilton-Taylor heads plays a pivotal role in the process. For more than 50 years it has recorded information on the conservation status of species. The IUCN gathers data from a huge range of sources – biologists, conservationists, statisticians – about many different species to try and build a picture of how each is faring. A thriving species might have a Red List status of “least concern” while struggling creatures might be listed as “vulnerable” or “threatened”.

To work out which Red List category a species falls into, it’s useful to know how large its population is, and how large it was in the past. For example, if a population reduction of 70% or more was observed in the last ten years, the species is considered “endangered”. If the reduction was 90% or more over the same period it becomes “critically endangered”.

It’s crucial, then, to be able to establish the population size of the species you are interested in tracking. Only with that information will you know if and when it becomes so rare that is threatened with extinction.

Biologists use all sorts of techniques to work out that figure. They may look for signs of animal activity – tracks and droppings, for example – which is a particularly useful approach if the animal in question is hard to spot. With some evidence that the species is present in a given area, it might then be a good idea to do some kind of more comprehensive survey, perhaps by walking through the habitat in transects. These are fixed paths dividing up a territory along which the observer may note down sightings of the species itself. But sometimes even this isn’t enough.

Nocturnal animals which live in densely forested areas, for example, might evade even the most eagle-eyed biologist. Camera traps can help in these circumstances. They take pictures when something moves in front of a motion sensor attached to the device. Such traps have been used to successfully record images of endangered pygmy hippos in the middle of the night.

Aerial drones with cameras are useful too. They have been used to monitor marine species from the air – including dugongs around Australia and the United Arab Emirates.

Information on a species doesn’t always come from biologists using bespoke equipment, though, says Hilton-Taylor. The Yangtze River dolphin – listed as critically endangered – is rumoured to still survive in the waters of the huge Yangtze river in China. While there is no hard evidence for this, occasionally possible sightings do come through.

“We keep getting odd reports from different people. Fuzzy photographs, Loch Ness [monster] type photographs that come through,” says Hilton-Taylor. All of these reports must be carefully considered.

And data can also come from industry. Those who catch or hunt animals for people to eat may also provide information about how well the populations of certain species are doing. A good example of this can be found with fish such as Atlantic cod, whose numbers are closely monitored.

In other words, it often takes an extensive network of researchers, professionals and even amateurs to work out the conservation status. UK birds, for example, are monitored by scientists, conservation reserve employees and trained enthusiasts, all of who contribute to annual surveys by the nationwide Royal Society for the Protection of Birds (RSPB). The RSPB then reports to the global organisation Bird Life International which in turn provides data to the IUCN.

“We liaise with all these different specialist groups around the world, we train them how to apply the methodology, help them to run workshops, guide them through the process, and then they gather the data and feed it through to us,” explains Hilton-Taylor. “That’s what goes into the IUCN Red List.”

So much for establishing that a species has become vulnerable: how do we decide it has actually gone extinct? The 50 years with no sighting rule might be a myth, but some of the ways scientists define extinction are actually broadly similar. For example, the RSPB updates its own red list of bird species. It declares a species extinct in the UK if it no longer breeds there. Last year, three species were declared extinct in the UK: the wryneck, the European serin and Temminck’s stint.

“They were all considered breeding birds when we last did the [assessment] six years ago but they haven’t bred in the last five years so they join our list,” says Richard Gregory, head of species monitoring and research at the RSPB.

But all three of these birds do have populations in other European countries and may from time to time come and go in Britain. They are only locally extinct. It is more of a challenge to declare something globally extinct, particularly since individuals of a critically threatened species will be incredibly rare and might be difficult to find.

In fact, even when the last individual of a species is right in front of you, you might not always be able to guarantee an accurate record of its extinction. In the case of the blue-feathered Spix’s macaw, a parrot native to Brazil, the very last wild specimen (a male) was paired with a female from another species. But in the year 2000 both birds disappeared and were never seen again. It’s been 15 years and no sightings of the creature have been made in the wild – but the IUCN hasn’t officially declared it extinct just yet because we don’t know for sure what happened to it.

Surveying alone, then, isn’t enough. Biologists must turn to clever data analysis to help them estimate how really rare species are doing. Ben Collen at University College London has been working on a method for doing exactly that – and it’s one which is changing our understanding of endangered animals around the world.

He and his team at UCL have been developing calculations which, given a certain species and the number of times it has been sighted in the wild, can output a probability of whether it has or hasn’t died out. The formulae may take into account the certainty of past sightings as well as other knowledge about the animal’s habitat – how that has changed over time, for example.

What researchers get when they compute the numbers is a good estimate of whether that specific animal is likely to still be present in the wild.

A good example of how this was used recently is in the evaluation of several uncertain sightings of the ivory-billed woodpecker – which is considered critically endangered. The last confirmed sighting was in 1944, but since then there have been 29 sightings which weren’t definite.

Collen’s model considered the time since the last certain sighting and weighed up the probability that the subsequent, uncertain sightings were reliable. In the end the results supported the hypothesis that the ivory-billed woodpecker is, in fact, extinct.

Such models can never provide conclusive evidence of extinction. Even so, analyses like this – only possible in recent years thanks to the power of modern computers – are now impacting the decision-making of those who are tasked with officially declaring whether or not a species is gone.

For instance, University of Oxford zoologist Tim Coulson has been developing statistical techniques to judge how reliable techniques like camera traps might be for assessing the health of, say, a population of big cats.

Because conservationists are very sure about how many lions are believed to be living in Africa’s Serengeti, Coulson and his team were able to study how well a system of 200 camera traps across the region were able to represent the health of the population. Essentially, they were testing the camera traps to find out just how good they were at their job. In this case, the researchers found that the camera traps were more accurate when they were used at times such as overnight, when the movements of lions were more random.

“That information can obviously be of interest to people trying to assess whether a population or a species has gone extinct because they tell us about how good the methods are that people use in the field to answer the extinction question,” he explains.

Earlier last year, a team of researchers at the University of Oxford published a paper which examined existing methods used by the Indian government to estimate the total number of tigers in the wild based on individual sightings in small study areas.

The results suggested that the current methods were overly optimistic about tiger numbers and that even small amounts of uncertainty in detection rates could have a big impact on what scientists should infer about the population at large.

What Collen’s and Coulson’s studies show is that the very techniques for surveying endangered species mentioned above are now subject to statistical analysis, in order to find out just how reliable they are at estimating population size – and how confident we can be if they suggest that a species is extinct.

Why all of this nit-picking? Well, the consequences of declaring something extinct are not trivial. As Collen points out, saying that something is gone would mean giving up on protecting it.

“Scientists are very understandably reticent to declare a species extinct if there’s still some chance that it might be out there,” he says. “If you declare a species extinct, no-one’s going to put funding towards its conservation.”

Perhaps that’s why the Yangtze River dolphin is still listed as critically endangered even though the best evidence we have that it is still alive comes in the form of the odd fuzzy photograph. “We’re just reluctant to say yes, it is now extinct,” says Hilton-Taylor.

And errors in judgement are far from uncommon. Every few years a species like the Cuban solenodon, thought to be extinct or even officially declared as such, turns up unexpectedly in the wild. This makes it a so-called “Lazarus” species – and there are many examples of this.

These pleasant surprises aside, though, Hilton-Taylor at the IUCN says his group’s overall view of the situation is not rosy. Globally, more species are moving towards extinction than away from it.

That’s why all of this work, although complicated and often infuriatingly inconclusive is nonetheless so important. Discovering that a species has gone extinct – to the extent that one can truly know for sure – is always unfortunate.

But making the effort to find out either way often offers a glimmer of hope. Hope that the animal in question, however rare, however vulnerable, is still out there. If we know that, then we also know that we, as the only species on the planet with the ability and the resources to do so, have a chance of saving it.