Joan Smith: Everyone, it seems, has a theory about Madeleine

Fifteen months after the disappearance of Madeleine McCann from her parents' holiday apartment in Portugal, the mystery of her whereabouts is as compelling as ever. At least two new theories have emerged this week, one involving a paedophile ring in Belgium and the other a possible sighting in Amsterdam.

The less sinister of the two is based on an incident not long after the disappearance, when a little girl answering Madeleine's description apparently told a shop assistant in Amsterdam that she had been taken from her mother. The other involves a "spotter" photographing Madeleine in Portugal, sending the images to paedophiles in Belgium and then kidnapping the child to order.

Both theories emerged as the police released files on the case, which were immediately seized on as containing significant pointers to Madeleine's fate. Her parents' decision to launch a massive publicity campaign, which was understandable in terms of their desperate situation, produced thousands of sightings in the weeks after the little girl disappeared; most of them were well-meaning but mistaken and there is no evidence that the Amsterdam lead is any different. When a second woman came forward this week, asserting that she too had spotted Madeleine in Amsterdam, it emerged that the local police had responded promptly to her call and decided it was a case of mistaken identity.

"Maddie" has been spotted all over Europe and indeed in Morocco, where a sighting of a blonde child caused great excitement before turning out to have an innocent explanation. Many of these "leads" are based on nothing more substantial than calls to the police switchboard from members of the public who have been racking their brains in the hope of remembering something that might help; the McCanns' media strategy has worked, insofar as it has made millions of people feel personally involved in their daughter's disappearance, but the truth is that most of us have nothing to offer that might help. With reporters hungry for new angles, tip-offs and cases of mistaken identity have been elevated into sensational developments that will supposedly crack the case, producing unbearable feelings of disappointment when they go nowhere.

Few criminal investigations have produced such an intense craving to become involved, but there are parallels. From the beginning, the McCann case has had echoes of the kidnapping in 1932 of the Lindbergh baby, the 20-month-old son of the celebrated aviator Charles Lindbergh, which attracted the intense interest of everyone from the US President to prominent members of the mafia. (It also changed US law, leading to kidnapping becoming a federal offence.)

One of the ransom notes was leaked to a newspaper, prompting a rash of false claims and letters, and all sorts of theories were floated to establish the toddler's whereabouts. But the case ended tragically when his body was found in woods two miles from his parents' house in New Jersey. A German carpenter, Bruno Hauptmann, was convicted and sent to the electric chair four years later.

The reason that a minority of cases catch the public imagination is not just to do with the family's relationship with the media, although the McCanns have become as well known as the Lindberghs in the months since their daughter was spirited from Praia da Luz. As well as incarnating parents' deepest fears, the disappearance (and reappearance) of children is a regular feature of myths and fairy stories, a fact which has clearly, if unconsciously, influenced the theories floated by newspapers.

A persistent theme in coverage of the McCann case is the sighting of a flustered woman, dragging a reluctant toddler in her wake, who has taken Madeleine to fulfil her craving for a child; in this narrative, Madeleine functions as a changeling who might one day be reunited with her real family.

Then there are the strangers with evil intent, who prey on children and steal them for their own wicked purposes; two decades ago, they would have been on the look-out for children to use in Satanic rites, but now they come in the more up-to-date guise of paedophiles.

This is not to argue that such explanations for Madeleine's disappearance could not possibly be true, but it does sound a warning note about placing too much credence in new "leads" unsupported by hard evidence. For more than a year now, the McCanns have been searching for their daughter amid headlines which have repeatedly presented speculation as fact. Tragically for them, the huge publicity surrounding the case has thus far been much more effective in producing fantasies than the breakthrough which might lead to her recovery.