The prosecution
Application of the procedures described in the previous sessions typically end with the estimation of the frequency of a certain DNA profile in a population. However, courts are only interested in the probability of guilt or innocence of a defendant. Translation of a frequency into a probability of guilt or innocence can often result in misstatements by both the prosecution and the defense.

Let's assume that the frequency of the DNA profile is 1 in a million and that there is a match of the defendants profile and the profile of DNA taken from the forensic sample. A correct statement to the court could be, "the chance of obtaining this DNA profile if the DNA in the forensic sample came from an individual other than the defendant is 1 in a million." Unfortunately all too often the prosecution will say something like, "there is only a 1 in a million chance the defendant is innocent." This is known as "The Prosecutor's Fallacy."

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	Learn more about the life of Reverend Thomas Bayes.

To the untrained reader, these statements may sound deceptively similar, but in fact to make the second statement incorporates a hidden assumption about guilt or innocence of the defendant. In the first example we are making a statement about the frequency of the DNA profile in the population, while in the second statement, we are making a statement about the guilt or innocence of the defendant conditional on the frequency of the DNA profile of the forensic sample.

Now there is a statistical approach based on a famous theorem known as Bayes' theorem that does allow us to make a statement of probability of guilt or innocence taking into account a prior assumption of innocence as well as the frequency of the DNA profile. Let's look at some calculations using Bayes' theorem incorporating prior assumptions that the defendant is guilty.

We see that the probability that a defendant is guilty, given a 50 percent prior assumption of guilt, is virtually identical to the frequency of the DNA profile in the population. In other words, if we fall into the prosecutor's fallacy and interpret the frequency of the DNA profile as the probability of guilt, we are assuming that the defendant is 50 percent likely to be guilty even before looking at the DNA evidence. A savvy defense attorney may say, "ladies and gentlemen of the jury, whatever happened to that cornerstone on which our law rests--the presumption of innocence?"

The defense
Just as the prosecution may make errors, so may the defense. The defense attorney when faced with the frequency of a DNA profile of 1 in a million may say that this implies that in the US, (which has a population approaching 300 million), 300 individuals possess the same DNA profile, all of which could have committed the crime. He may fall further into the defense attorney's fallacy by saying "any one of those 300 individuals could have committed this crime, so why is the prosecution singling out my client?"

The fallacy in this argument is of course that all 300 individuals with the same DNA profile are not equally likely to have committed the crime. Approximately 150 may be expected to be women, who must obviously be ruled out if the forensic sample from which the DNA was obtained was semen. Still others will be infants or octogenarians, or will have cast-iron alibis by virtue of their geographic location. If the murder was committed in New York City, then it is unlikely that the mailman in a rural community in Nevada is the perpetrator.

So what recourse does the defense attorney have when faced with frequencies of a DNA profile approaching that 1 in several trillion? Apart from questioning some of the assumptions made to obtain such a number, one strategy that has been sometimes used is to invoke the possibility of a laboratory error. In one simple scenario, a laboratory technician mistakenly takes DNA twice from the test tube containing the defendant's DNA, and places it on the electrophoretic gel, both where the defendant's DNA should be but also where DNA from the forensic sample should be. A prefect match will result. Today, the possibility that such an error will occur is low, as stringent quality control guidelines have been developed by the Technical Working Group on DNA Analysis Methods (TWGDAM)—these are a group of forensic DNA analysts from government and private laboratories. These guidelines provide the standards for accreditation of laboratories, including documentation of laboratory procedures and operations, proficiency testing as well as internal and external audits.

What about relatives?
The extraordinary power of DNA profiling to distinguish between individuals has one very important limitation; the procedure is far less powerful in distinguishing between relatives. We receive half our genes from our mother and half our genes from our father, so DNA profiles are much less powerful in distinguishing between parent and child or between siblings. They will be more powerful in distinguishing between more distant relatives such as cousins, but still the calculations and equations presented earlier can be misleading in predicting the chances that relatives will have different DNA profiles. In one criminal trial in Flint, Michigan in the early 1990s, a lack of appreciation of the similarity between relatives had serious consequences for the defendant.

Laury (not her real name), a girl of 14, became pregnant and subsequently underwent an abortion. Since she was below the age of consent, a case file was opened by the police, who questioned her on the identity of the individual who impregnated her. Laury first named a fellow student in high school, but the individual could not be identified as his name did not appear on the school's rolls. She then accused her own father of impregnating her. He was then charged with incest and statutory rape. He claimed innocence and requested a DNA test to prove his innocence. Results from only three loci were obtained, but the court was told that the probability of finding the DNA profile if someone other than the defendant was the father was 1 in approximately 14,000. On the basis of this evidence, the defendant was found guilty and given a life sentence.

	Thinking Point
	What are the rules in your own state or country regarding use of DNA test results in court? What groups, if any, act to lobby for legislative change in your area on this issue?

However the court transcripts showed that the defendant was estranged from his common-law wife and had lived apart from the family for a number of months during which time his daughter became pregnant. Furthermore, Laury shared a bedroom with her brother who was only a year apart in age. Thus, we must also entertain the possibility that Laury's brother impregnated her. In the subsequent appeal, the court was presented with new calculations that showed that the defendant was only 8 times more likely to be the father than the brother. The paternity of the brother could have been excluded by testing, but the mother refused to allow her son--still a minor--to be tested. Although the first appeal was unsuccessful the defendant was finally released, but only after having served several years in jail.