Henry Templeman - Relevant Fingerprint Population

T-Model VERSION 8.2

Fingerprint Identification Based on Match Probability and Relevant Population

Last Update: August 13, 2010

Henry Templeman
henry@henrytempleman.com

Relevant Fingerprint Population

Fingerprint match probability (FMP) and the number of close matches or look-alikes in a given amount of corresponding fingerprint ridge features present in two impressions depends on fingerprint population. The higher the fingerprint population considered for a given amount of shared features the more look-alikes will exist. Vice versa, the smaller the fingerprint population for a given amount the fewer look-alikes are predicted.

The term "relevant population" may be defined as the number of people who could have realistically committed a crime. The location of the crime and time of occurrence fundamentally defines the relative geographic perimeter containing the number of persons who could have plausibly committed the crime at hand.

For example, based on a flight speed of 70 miles per hour, the person who commits a residential burglary that occurs in the city of San Jose, California and is discovered 2 hours later [when it is contained and fingerprints are recovered] establishes a geographic perimeter around the crime location with a radius of 140 miles. The number of 18-65 year olds living within a radius of 140 miles of the crime scene multiplied by 10 defines the relevant fingerprint population. The 18-65 years population for the greater San Francisco Bay Area is 7.7 million. As a result the conservative upper-bound relevant fingerprint population for this particular crime may be defined as approximately 77 million. A fingerprint population of 77 million means that fewer look-alikes are likely to be found compared to a world fingerprint population of 66 billion. Subsequently, it means a smaller amount of corresponding ridge formations are needed in two impressions in order to establish valid basis for sufficiency to individualize.

Example

Based on a conservative upper bound world fingerprint population of 66 billion, the excellent agreement of 9 excellent non-diminishing area bifurcations in sequence, the estimated number of look-alikes is approximately .088 (less than 1). As a result, there is valid basis to infer positive identification. However based on a fingerprint population of 77 million, only 7 excellent bifurcations in excellent agreement will have approximately .09 look-alikes (also less than 1) and consequently there is valid basis to infer positive identification.

For crimes in which a suspect is apprehended within minutes the geographic perimeter may involve only a radius of only 1-2 miles and a subsequent conservative upper bound relevant fingerprint population of only, for example, 100,000. As a result , only 5 bifurcations would be needed to establish an estimated number of look-alikes to be less than 1, i.e. .12, and therefore valid basis for sufficiency to individualize.

Note: Apply the formulae to verify the above figures for yourself!

It is significant to emphasize that many crimes, especially for crimes against persons in which a suspect is apprehended in a timely manner, there is a relatively small relevant fingerprint population which subsequently requires less amounts of corresponding fingerprint ridge formations in order to establish valid basis for sufficiency to individualize. As a result, numbers of criminal identifications made in law enforcement will increase since fingerprint examiners would require lower minimum thresholds of corresponding ridge formations in two impressions in order to establish positive identification.

Relevant population depends on a variety of circumstances, i.e. location and time the crime occurred, population density for the area, suspect flight mode and speed, and so on. For purposes of conservativeness, relevant population should be based on upper-bound estimates of the relevant group that could have committed the crime. For purposes of refinement of the T-Value threshold of 66 billion (based on the FBI standard to match DNA profiles using a total United States population of 300 million people) relevant population may be more precisely defined based on local, state, national and world fingerprint populations for the particular case at hand (Table 6). For purposes of conservativeness each relevant fingerprint population in Table 6 is rounded up to the nearest 1 million.

Table 6

Suggested criteria to define relevant fingerprint population.

It is significant to note that the concept of “relevant population” was initially introduced by Coleman and Walls (1974) who defined it as the group of people who could have committed the crime; however, in the context of a criminal investigation, a relevant population may be considered to be what Lampert (1993) called the “suspect population” which was defined as the group of people who plausibly may be suspected of having committed the crime. [81]
Whatever term is used, for purposes of conservativeness, upper bound numbers for a population should be applied based on the case at hand.

Additionally the idea that background information may be used to assist in the determination of the relevant population from which the criminal may be supposed to have come is supported by Colin Aitken and Franco Taroni [82]. For example, based on reliable witness testimony the sex, age, race, and even clothing description of a suspect may be used to refine the relevant fingerprint population and subsequently allow for a reduced amount of corresponding ridge formations to be used to effect identification.

The following example illustrates how the T Model can be used to establish identification based on reduced population for a case at hand, which otherwise would likely not be made:

Example

A bank robbery occurs in the city of San Jose, CA. Multiple witnesses describe the suspect is a white male, age 18-24, wearing blue jeans and a black hooded sweatshirt. 5 minutes after witnesses report seeing the subject flee the scene, a police officer spots a person matching the description walking on a sidewalk 4 blocks away. The officer detains the subject for questioning. Witnesses are unable to positively identify the subject as the person who committed the crime. The officer fills out a field investigation card, obtaining the suspects descriptor information and elimination fingerprints. The officer releases the subject due to lack of evidence.

At the robbery scene a partial latent fingerprint is recovered from the inside of the bank teller’s cash drawer (the suspect was seen removing cash from the drawer). The partial fingerprint displays 3 strong ending ridges and 1 strong bifurcation in a funnel which are found to be in excellent agreement with the right index fingerprint belonging to the subject’s elimination of the subject’s   The total weight for this amount is defined as 10^3 x 26.75, or 26,750.

What is the conservative upper bound relevant fingerprint population for this case?

The partial print came from inside the cash drawer. The cash drawer is located in a restricted area where only bank employees have access. There are currently 7 bank tellers and 2 supervisors who work at the bank who either routinely access or could have accessed the drawer in the past.   Previous bank employees who could have handled the cash drawer in the past is 3.

The cash drawer is 3 years old and was produced by a local company. The number of people who could have handled the cash drawer during production, transport and installation is conservatively defined as follows:

Company X produced the drawer and has a total of 7 employees all who could have handle the drawer.

Company Y transported and installed the drawer. Records show that 2 employee could have handled the drawer.

There are a total of 21 people who could have reasonably handled the bank teller’s cash drawer from the time it was produced up until the time the crime was committed.

Based on demographic data, the population density for the city of San Jose is 5118 people per square mile, 31.34% are white, 9.9% are 18-24 and approximately 51% are male.

The conservative upper bound flight speed is 60 miles per hour by car.

The number of people wearing both blues jeans and a black hooded sweatshirt at any given time is based on a visual survey of 100 random individuals in the area (which includes the subject) is 2%.

The number of people who could have committed the crime may be defined as follows:

The area containing the total human population is defined by the equation Area = π r ^ 2, where r is the distance from crime location to suspect flight boundary which is determined by flight speed multiplied by time.

In this case the suspects maximum flight boundary is 60mph x .0833h or 5 miles.

As a result the area containing the total human population is determined as follows:

Area = (3.14) (5) ^ 2
Area =   (3.14) (25)
Area = 15.7 square miles

Based on a population density of 5118 people per square mile, the total number of people (P) within this area is determined as follows:

P = 5118 x 15.7
P = 80,353

Based on demographic data of 31.34% for white, 9.9% for age 18-24, and 51% for male, and 2% wearing blues jeans and a black hooded sweatshirt, the number of people who could have committed the crime is determined as follows:

80,353 x .3134 x .099 x .51 x .02 = 25.42

For purposes of conservativeness, this number is rounded up to 26.

The total number of people who could have reasonably handled the bank teller’s cash drawer is defined as 21 + 26, or 47.

The relevant fingerprint population for this case is subsequently defined as 47 x 10, or 470.

Based on an aggregate value of 26,750 (for the 3 excellent ending ridges and 1 excellent bifurcation in excellent agreement) and the relevant fingerprint population of 470, the or number of look-alikes (L) likely to occur within this group, is defined as follows:

T ^ P = 120
26,750 ^ P = 120
P = 27.1

L = (F)(P)/T
L = (470) (27.1) / 26,750
L = 0.47

where,

T = Total quantitative-qualitative weight of arrangement of ridge formations found n two impressions.

P = Number of Parts

L = Number of Look-alikes

F = Relevant Fingerprint Population

A number of look-alikes defined as 0.47 is less than 1 which signifies the amount of corresponding ridge formations in the two impressions is sufficient to infer positive identification. It is significant to note that the value of 0.47 represents a conservative upper bound number of look-alikes likely to occur compared to actual values determined by validation study. Based on a 15%% error rate (see Validation Study) the true number of look-alikes (with a 99% confidence level) is likely to occur is estimated to be not less than 0.39 (still a slightly more incriminating value).

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The above map displays the average number of people per square mile living in the State of California by county in the year 2000 (urban areas are shown in red).

Crimes that occur in low population density areas will have much smaller relevant fingerprint populations compared to crimes that occur in high population density areas. As a result, smaller amounts of corresponding ridge formations are needed in two impressions in order to establish numbers of look-alikes to be less than (or equal to) 1 and are subsequently needed to establish valid basis for sufficiency to infer positive identification.

The value for Relevant Population (RP) depends on the special circumstances for each case, e.g., the number of people on a boat where the crime occurred, the size of an AFIS database which resulted in a “hit”, the number of 18-65 year olds living in the area where the crime occurred, and so on.

Unless the case at hand defines a particular population group, the T-Model sets the default value for “RP” at 66 billion, or the rough fingerprint-part equivalent to 300 million people (multiplied by 10 multiplied by 22) which reflects the same default relevant human population group used by the FBI to analyze DNA profiles.

The T-Model © 2008 (Attribution Non-commercial Share Alike 3.0 United States License) is presented by the author alone and not his employer. This license allows the reader to download, redistribute, translate, refine, change, and build upon this work non-commercially, as long as any license for new creations are under these identical terms. All new work based on the author’s will carry the same license, so any derivatives will also be non-commercial in nature.

Henry Templeman
henry@henrytempleman.com