## Table of contents

Kinship and kinship links
El Salvador orphan simulations
Forensic mathematics home page.

# Kinship Simulations

• Can a kinship problem be solved by DNA testing?
• What are the chances?
• Which relatives should be tested?
• Is it worth asking for an exhumation?
Sibling test with Identifiler
Expected LR distribution
These are questions that are occasionally of great importance, and which it has been nearly impossible to answer before the introduction of the Kinship Simulation feature of the Automatic Symbolic Kinship Program.
 LR distributions for identifying a body using various ancestor combinations. (Identifiler, Caucasian. DNA•VIEW Kinship Simulation program)

To explain the concept of the simulation progam, we begin by reviewing the use of the Kinship program in the context of a particular example.
Available genotypes Assessing H1 vs. H0 H1 – Half-sibling scenario``` S : M + Dad H : N + Dad``` H0 – Unrelated scenario``` S : M + Dad H : N + ?``` Composite of scenarios ``` S : M + Dad H : N + ?``` ``` D3 VWA FGA D18 ... M 15 16 14 17 19 22 15 18 N 17 18 15 19 22 25 16 17 S 15 16 17 19 22 24 14 15 H 17 17 15 19 24 25 16 23``` ```D3S1358 0.5 1 / 2 VWA 3.04 (1+q+s)/(2q+2s) q=0.0848 s=0.112 FGA 4.21 (1+r)/2r r=0.135 D18S51 0.5 1 / 2 ... overall LR 1.08```

## Symbolic Kinship Program

• evaluates the strength of the genetic evidence in all relationship problems.
• paternity, inheritance, immigration, missing bodies, sibship and other uses
Are S and H half-siblings? Two family trees depict two hypothetical explanations for the genetic data. To use Kinship, each tree is transcribed using : and + notation to define all child-parent relationships. These two explanations are merged, using / wherever alternative people occupy a role, and the composite is typed into the program. Genetic types are supplied for some or all of the people involved. Kinship then derives and evaluates the algebraic expressions.

## Predictions and planning

### Kinship Simulation

A completely inconclusive likelihood ratio, as in this example, seems like very bad luck. Could it have been predicted? What to do next? Kinship Simulation answers such questions.

### Testing additional relatives

Would T help? ```S : M + Dad T : M + Dad H : M + Dad/?```
A Monte-Carlo genotype for T ``` D3 VWA FGA D18 ... T 17 17 15 19 24 25 16 23```
Short of exhuming Dad (which would doubtless solve the case but is undesirable), it may be possible to obtain DNA from T, a full sibling of S. Assuming H1 of the definition shown at the left and given the known types of M, N, S, and H, Kinship Simulation randomly assigns alleles to T, then invokes Kinship to determine a representative likelihood ratio, such as 12370. Repeated simulations produce a range of expectable results:
"Typical" LR=270 from 10 Monte-Carlo simulations
LR=0.53
LR=4
LR=10.9
LR=22.9
LR=63.8
LR=135
LR=2430
LR=4250
LR=12370
LR=14460
Assuming H is an heir, testing T in the CODIS loci will usually provide sufficient proof

### Testing additional systems

 efficacy of a 36-SNP panel in establishing half-siblingship "Typical" LR=23. 95% confident=0.18 - 2900 10 Monte-Carlo simulations: LR=0.14LR=1.7 LR=4.7LR=12 LR=34LR=70 LR=108LR=137 LR=237LR=313
Kinship simulation can also predict the benefit of additional tests. What would happen if a panel of SNP's were applied to M, N, S, and H? The incremental performance that can be expected is shown by the set of simulations at right.

### Evaluating DNA batteries

The same idea can be applied to any scenario, even before any DNA typing has been done. Therefore, Kinship simulation is a research tool that can be used to predict how well a given DNA panel will perform on any specified relationship problem.
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