Forensic Biology
Forensic Biology deals with the crimes where the biological evidence is involved, and the DNA typing technology can be used effectively. The incredible power of DNA technology has been used as an identification tool that brought substantial reformations in criminal justice system and greatly benefited the law enforcement community. DNA analysis has been effective in securing convictions in hundreds of violent crimes, from homicides to assaults. It has also helped to eliminate suspects and has led to the exoneration and release of previously wrongfully convicted individuals \cite{convictions}. During the last century, the criminal justice system has seen a major advancement due to the development and application of forensic techniques to solve the crime.
Over the past 40 years, the forensic biology field has made great strides. The multilocus probe analysis by restriction fragment length polymorphism (RFLP) analysis developed by Alec Jeffreys \cite{Jeffreys_1985} explained genetic differences among individuals \cite{Jeffreys_1985a}. DNA typing quickly progressed to the use of single locus variable number of tandem repeat (VNTR) loci by RFLP analysis \cite{ROYLE_1988}. Single locus analysis offered greater sensitivity, increased species specificity, and standard statistical interpretations compared with the multilocus approach. VNTR typing was adopted by many crime laboratories in some countries and was the mainstream system of the late 1980's through most of the 1990's.
Human STRs were first reported in 1989 \cite{Weber1989}. These STRs were discovered to occur within or between genes along human chromosomes. The STR analysis of the human autosomal DNA provides unique information on the genetic diversity of the populations \cite{Thangaraj_2006}. STR markers were first described as an effective tool for human identity in the early 1990s \cite{Jeffreys1991}. The STR markers used in human identity testing are primarily tetranucleotide repeats \cite{Collins2003}. STR typing is more tolerant to the use of degraded DNA templates than other methods of individual identification.
Forensic statistics
The applicability of STR markers in a certain population depends on "How much informative these markers are for that population". To check this, there are some statistical parameters which describe the efficiency of the chosen STR marker multiplex to be used as a human identification tool.
Allele frequency distribution
It is the frequency distribution of alleles on a certain marker. It describes the variability of the chosen marker to produce maximum number of alleles on a certain locus so that the locus has low match probability.
\(AlleleFreq\ =\ \frac{2Nxx+Nxy}{2N}\)
Where \(Nxx\) is the number of homozygotes for allele X (XX), and \(Nxy\) is the number of heterozygotes containing the allele X and Y. \(N\) is the number of samples in the population. Allele frequency can also be calculated by simple count of the proportion of different alleles.
Observed heterozygosity
Observed heterozygosity is a simple measure of the proportion of heterozygotes in the population at a given locus.
\(H_o\ =\ \frac{Hets}{N}\)
Expected Heterozygosity
It is the proportion of heterozygotes expected under random mating population (Hardy-Weinberg Equilibrium) at a given locus.
\(H_e\ =\ 1-\Sigma pi^2\)
where \(p_i\) is the allele frequency of the allele \(i\).
The difference will be larger for samples that differ from Hardy–Weinberg proportions markedly.
Profile probability
It is the probability that any two selected persons have the same DNA profile.
\(pM\ =\ \Sigma_{i=1}^n\ Px_i^2\)
Where \(i\) is the allele at a locus and \(Px_i\) is the frequency of \(i\)th allele.
The combined match probability is the product of all match probabilities at each locus, assuming the Hardy-Weinberg Equilibrium.
Power of discrimination
It is simply the inverse of the match probability \(pM\). And can be determined by this formula;
\(PD\ =\ 1-pM\)
While the combined power of discrimination is the product of all power of discriminations at each locus.
Power of exclusion
It is the fraction of individuals having a DNA profile that is different from that of a randomly selected individual in a given population. It can be determined by this formula;
\(PE\ =\ h^2\left(1-2hH^2\right)\)
While the combined power of exclusion is the product of all power of exclusions at each locus.
Paternity Index
It is the probability that the person being tested is the biological father, rather than a randomly selected individual in a given population. It can be obtained by using this formula;
\(PI\ =\ \frac{1}{\left(2\Sigma_{i=1}^n\ _{pi^2}\right)}\)