Keeping an open mind on the disappearance of Madeleine McCann amid the surrounding plethora of facts and supposition is almost impossible — for the officers investigating the case, for the media reporting it and for anyone who has read about it.

It appears that the Portuguese police may have fallen into the trap of having first formed a view of who the guilty party is, then seeking out the evidence to support it.

It is rare for people untrained in science deliberately to attempt to refute their own hypotheses: instead we tend to reinterpret anything that happens to fit in with the notion to which we have become increasingly committed.

The only way out of this psychological trap is to have a clear picture of what the possibilities are and to work steadily, safeguarding and collecting all the information that may be relevant to every possibility then systematically excluding the options as the relevant information becomes available.

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In a case such as Madeleine’s disappearance, we should expect professional investigators to pull together systematic accounts of the circumstances of a variety of child abductions and see what they can learn from them.

It does not seem to me that the Portuguese police have done this. If they had, they might have come to the conclusion that the most plausible reason for Madeleine’s disappearance remains our original conclusion — her abduction by a stranger.

At the Centre for Investigative Psychology at the University of Liverpool we routinely build up accounts of the characteristics of particular types of crimes and the criminals who commit them. Most recently one of my graduate students has collected together all the information she can on those child abductions that were obviously not part of some family custody struggle.

Her reviews shows that of the 800 or so abductions that occur in Britain each year about half are carried out by strangers to the family, but the great majority were quickly brought to an end by the abductor being caught in the act or soon after. It is thus extremely rare for people who do not know the children to be able to steal them away. There are about 50 of these cases a year in Britain.

When a child is reported missing the police must start from the strong possibility that someone who knows the child is responsible. Subtle and exotic stories seem to have been developed about the McCanns. But for these stories to have any credence, they require the couple to be disturbed and incompetent medics who have a cohort of professional friends willing to hide the truth under intense scrutiny.

This does not accord with what I call the first law of criminality: people who are criminal in one situation tend to be criminal in other situations. It is remarkably unlikely that parents who committed a crime so heinous would have no previous background that pointed to their evolving evil.

Once we move away from the possibility of the disappearance having roots in the family then the options require us to think carefully about the nature of the victim.

It is not unknown for depressed or disturbed women to steal young children, although their preference is usually for babies.

Many paedophiles seek out opportunities for contact with children. Climbing into a locked apartment with parents visiting to check from time to time is not the sort of impromptu opportunity that a disturbed individual would choose.

Where there is a strong sexual element in the abduction, the child will tend to be older, pubescent or in early adolescence. The horror is the tendency for younger children, of Madeleine’s age, to be abducted in a more planned way, to be trafficked.

The options in Eastern Europe for such trafficking are so great that the question has to be asked why Praia da Luz would be regarded as an appropriate location to find victims.

One of the most challenging aspects of Madeleine’s disappearance is the alacrity with which the McCanns embraced the media. Possibly they should have been advised that had the publicity not been so great an opportunistic abductor would probably have eventually let Madeleine go.

Abductors who had planned to take Madeleine, possibly even as part of an intended ransom demand, would have been disturbed by the feeling that the world’s media were waiting for them to act and would be driven even farther underground.

The McCanns may not realise the irony of calling the fund they have set up to find their daughter Leaving No Stone Unturned Limited. Carrying out a search by turning over every stone is a sure recipe for creating chaos. Habits of the creatures you are looking for need to be studied and understood. Then you can turn over the appropriate stones before your quarry has moved on or killed its prey.

— David Canter is Professor of Psychology at the University of Liverpool. The second edition of his book, Mapping Murder, will be published by Virgin Books in October.

Where does the investigation into Kate and Gerry McCann go now?

Portuguese detectives are awaiting the return of tests on samples taken from apartments in the holiday complex where Madeleine disappeared and cars used by her parents and other people. But without firm evidence of the couple’s involvement, they appear to be relying on inconsistencies in witness accounts and the response of a “cadaver” sniffer dog to the couple’s hire car and Mrs McCann’s clothing.

Why did police make the McCanns official suspects?

Under Portuguese law detectives had to make the couple official suspects, arguidos, when they refused to answer some questions on September 6 and 7. Carlos Anjos, president of the Employees of Criminal Investigation Association, said yesterday that “a difficult and complex case [was] made worse by Madeleine’s parents . . . who do not facilitate nor help the investigation”.

Is there any other evidence?

It seems unlikely as the couple were released on the weakest form of bail, which allowed them to return to Britain. A judge ruled this week that the police had failed to collect any new evidence so could not question the couple again. Mr Anjos said: “There’s no sense in having other interrogations. They are arguidos, a status which allows them to remain silent. They have already said that they would make no more statements. To reinterrogate them is not justifiable.”

Why is the timeline crucial?

Detectives need to know what happened before Madeleine was reported missing by Mrs McCann at 10pm. It was reported yesterday that the girl had not been seen by anyone outside the family since 2.29pm, when the “last” photograph of the missing girl was taken. This unconfirmed report would leave a gap of seven hours.

So what happens next?

Senior Portuguese officers sincerely believe the McCanns are responsible for Madeleine’s death and were involved in disposing of her body. This view appears to pervade the inquiry. If the McCanns are innocent until proven guilty, as is presumed under Portuguese law, then police are effectively back at square one. The McCanns hope that they will refocus the investigation on searching for an abductor.

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