DNA and probability

DR BOB ARDREY, Senior Research Fellow in the Huddersfield University School of Applied Sciences, looks at. the chance of your DNA being unique...

DNA is the genetic material which we all possess, and which makes us what we are.

What makes it so important from a forensic perspective is that around 0.1 per cent of our DNA is unique to each of us.

Thus, if we are able to examine these differences we have the ability to differentiate between individuals and even to identify the person from whom a DNA sample has originated.

This is the basis of forensic DNA (or deoxyribonucleic acid) profiling, first reported by Dr Alex Jeffreys at the University of Leicester in 1984.

To facilitate the use of DNA profiling, the National DNA Database (NDNAD) was set up in 1995 since when it has grown to contain, as of March 31, 2009, the DNA profiles of 4,859,934 individuals.

DNA profiles obtained in criminal investigations can then be rapidly compared with this database and a match of a DNA profile associated with a crime with one, or more, on the database will identify anyone who may be able to assist the police with their inquiries.

There are a number of examples where this has led both to convictions many years after the original offence and also the quashing of convictions.

Notable among these being the conviction of Ronald Castree in 2007 for the murder of Lesley Molseed in Rochdale in 1975, a crime for which Stephan Kiszko spent 16 years in jail.

Despite its value, the use of the NDNAD has raised a number of concerns, not least the way information derived from it is presented in court and is understood by the jury who are using it to decide upon the innocence or guilt of a defendant.

The prosecutor’s fallacy is an important issue when any form of complex evidence is presented in court.

It is an error which arises when the interpretation of a single piece of circumstantial evidence — one from which an inference is made — is erroneously equated directly with innocence or guilt with no consideration of the circumstances of the case. This is best illustrated by means of an example.

A woman presents herself at a police station and alleges she has been raped by an individual she names.

During her subsequent medical examination, a semen sample is obtained and from this a DNA profile is obtained.

From that profile it is possible to calculate its likelihood of occurrence, let us say in this case it is one in 6,000,000 — very small.

A DNA sample is obtained from the individual she has named and a profile obtained.

This profile matches exactly that obtained from the sample taken from the alleged rape victim.

The DNA evidence thus allows us to say that it is 6,000,000 times more likely that the sample taken from the victim came from the named individual than from someone else.

It is very unlikely to have originated from someone else but, importantly, the possibility cannot be totally excluded. The prosecutor’s fallacy is then to extend this argument to state that it therefore follows directly that the probability that the named individual is guilty of rape is also 6,000,000 to one — very high.

This error arises from a misunderstanding of what is known as conditional probability and a failure to consider the circumstances of the case and any other evidence that may be available.

In the example considered, as in many allegations of rape, the accused may admit intercourse took place, but allege that it was consensual and the DNA statistic presented above then becomes irrelevant and other evidence must be considered before guilt or innocence can be established.

The defence are equally able to misuse the same DNA statistics.

If we take the population of the UK to be around 60,000,000 the probability of occurrence of a DNA profile of 6,000,000 to one means that there are likely to be 10 individuals in the UK with that profile.

In the example above, therefore, it might be argued that the likelihood that the named individual is innocent is 9:1 or 90 per cent.

This simplification, again, is equally erroneous as it again fails to consider the circumstances of the case.

This is known as the defender’s fallacy.

The NDNAD can undoubtedly be a valuable tool in criminal investigation but only if its limitations are recognised and safeguards are in place to ensure that information obtained from it is presented properly in court.