Counting the unseen

A maths trick known as capture-recapture allows researchers to estimate the extent of unobservable phenomena, which can help save endangered species, protect abused children and even chase spies.

A tigress and her 12-week-old cubs lounge in Nepal, where parks officials have used a maths formula to show that the country's tiger population was increasing.

How many tigers has no one ever seen ? It sounds like a riddle from Alice in Wonderland, but this was the question that recently faced conservation experts in Nepal. They needed to know how many tigers were left in their country, and whether their conservation efforts had succeeded. No easy task, given estimates of fewer than 200 in a mountainous nation half as big again as the UAE. Fortunately, Jhamak Bahadur Karki and his colleagues at the Department of National Parks and Wildlife Conservation were able to call on a neat mathematical trick to estimate the seemingly unknowable. Over the years, it has been used by everyone from health officials to criminologists and even spymasters to wring big insights from little data.

It is known as the capture-recapture technique, and it turns random sightings of the target of interest into estimates of the total number in existence - even if most are never seen. In its simplest form, it works like this. A survey detects and records a certain number of animals. Then, after a suitable interval to allow the recorded animals to mix among the others again, the survey is repeated, and the number of animals that turn up in the second survey as well as the first is noted. Clearly, the bigger the total population, the smaller the chances of seeing the same animals twice. The maths of capture-recapture gives a formula that turns the number of repeat appearances into an estimate of the likely size of the total population.

In the case of the Nepal tiger survey, the team set up more than 300 cameras spaced about two kilometres apart in Chitwan National Park - a large but reasonably enclosed area, which is important if the technique is to work properly. Over the next 20 days, the cameras captured more than 11,500 images, several hundred of which included a tiger. By analysing the images the team were able to pick out those tigers already captured on camera, and used this to get an estimate of the total population. The results, published last month, were a rare good news story. Nepal has made the protection of tigers a high priority for its conservation programme, and it seems to be working. The survey found that there are around 125 tigers in Chitwan, up from around 90 just a year ago, an increase of almost 40 per cent. And across Nepal as a whole, the team estimates the total population is around 155, a 30 per cent increase on the previous total.