The PI stands for Paternity Index and is independently calculated for  each system analyzed.  There are 19 possible patterns for each system analyzed that supports paternity...the first 14 patterns are possible when the mother of the child participates.  The bottom 5 patterns are used for motherless calculations.

The single letter designation indicates that the individual is homozygous (has two copies of the same marker) in the system.    For line "1" the Trio might look like (14,14) (14,14) (14,14)--the child would have inherited one 14 from their mother and one 14 from the father.

The double letter designation indicates that the individual is heterozygous in that system.  Using line 3 for an example the markers could be (14,14) (14,15) (14,15)--the child has inherited the 14 from the mother and the 15 from the father.  Each subsequent pattern can be interpreted in the same manner.

The pattern determines the formula to be used in each system.  The lower case letter in the formula indicates the frequency of the marker observed in the pattern.  The frequency of each marker (allele) is derived from applicable population database.   

To best demonstrate how this works a table is constructed.  The first column indicates the DNA system analyzed and the subsequent columns list the alleles for the mother, Child, and Father.  For this example when a zero is indicated  in a column it denotes a homozygous system.

Using the same table, patterns are assigned (noted in the yellow rows).

Once the patterns are recognized the proper formula can be applied.  The frequency of the allele designated by the lower case letter is accessed from the applicable population database.  The system designated as FGA in this example lists the frequency of the allele designated 20 as .1625. 

That frequency is used in the formula dictated by the pattern and the result indicates the PI for that system.

That process is repeated for each subsequent system:

The individual PI's are multiplied together to calculate a Combined Paternity Index.

The Combined Paternity Index is the strength of the evidence supporting the hypothesis that the tested man is the biological father as compared to an untested, unrelated man.

The above example produces a CPI of 3,231.