POPULATION GENETICS
In Chapter 10 on serology, remember that the distribution of ABO blood types is about
Type A = 42%
Type O = 43%
Type B = 10%
Type AB = 5%
These population statistics are very important in the interpretation of serologic evidence. They add significance to conclusions about the association between biologic evidence between people. As we will see, the population statistics that can be derived from modern DNA typing have been determined accurately and thus, reliable, scientific associations between DNA evidence and a suspect, for example, can be made. Determination of the frequencies with which particular genetic markers occur in a given population is called population genetics. This branch of statistics can shed light on crucial questions that arise during the admission of biological evidence such as “If the DNA type of the evidence and the accused are the same, what are the chances (probabilities) that this is a coincidence—that someone else could have the same DNA type?” The answers to such questions permit the jury or judge to make meaningful conclusions about the role of this type of evidence in reaching decisions of guilt or innocence. In forensic DNA analysis multiple loci are evaluated, giving rise to many degrees of association. Consider the situation where there are several alleles at a particular locus.
In DNA analysis today, the frequency of occurrence in the population can be determined for each allele. Now consider this situation at several loci. By determining which allele is present at each locus, the frequency of occurrence of all of these alleles can be determined by simply multiplying the frequency of occurrence of each one. This can be illustrated with the familiar coin toss routine. If a coin is tossed once, the probability (frequency of occurrence) for it coming up head is ½ since there are only two equally probable outcomes from one coin toss: head (H) or tail (T). If the coin is tossed twice, the probability of it coming up heads both times is ¼. This is because there are four possible outcomes from tossing a coin twice: H–H, T–T, H–T, and T–H. Only one of these outcomes results in heads coming up twice in a row (H–H). This probability can be determined by multiplying the probability of each toss: ½ × ½ = ¼. Likewise the prob ability of getting three heads in a row is 1/8 (½ × ½ × ½). The technique of multiplying probabilities together is known as the product rule. The product rule for calculating the probabilities of multiple events can only be used when each event or condition is inde pendent of all of the others. An honest coin has no tendency toward head or tail and has no memory of whether head or tail came up the last time it was tossed. Thus, each toss of the coin is independent of all others and the product rule can be used to determine the probability of each possible outcome of multiple tosses. As we will see later in this chap ter, multiple pieces of data about a DNA type are determined during an analysis and the population statistics for each allele of each data point have been determined. In order to arrive at an overall DNA type by invoking the product rule, each data point (each allele present at each locus being studied) is independent of the other data points. The loci used in today’s DNA typing methods have been extensively tested to check for independence. Using the product rule in such cases yields DNA types that are so rare that the chances of finding more than one person at random within a population who has the same DNA type is extremely small. This means that if DNA derived from biological evidence is of the same type as a suspect in the case, the probability of the evidentiary DNA arising from a different individual (other than an identical twin) is extremely remote.
