In classic forensic DNA treatments cells are lysed while they are still mixed. This treatment, therefore, carries a significant shortcoming; knowledge about what alleles associate with what cell, and hence cell-type, is lost. 
Single-cell strategies overcome this challenge. Here, each cell is sequestered before lysis, and PCR reagents are added directly to the vessel in which the cell lies. Amplification and fragment analysis results in a set of single-cell electropherograms (epgs) that are interpreted by clustering them into groups by virtue of their (dis-)similarity to one another. Once clustering is complete, we assert the probability we observe the data in a cluster under same and different source propositions. 

With previous work showing our single-cell predictor faithfully clustered epithelial and blood cells according to their contributors, we extend it to consider sperm (haploid) cells that carry only half of the donor’s genetic information. Unlike diploid cells, sperm do not carry the same alleles across cells, and it is for this reason we query the performance of our haploid aware model. To do this, we place common measures of forensic validity within data analytics formulations that categorize a novelty’s viability to meet forensic aims. The categories of interest are Salience, Legitimacy and Credibility (SLC).

With Salience referring to applicability, we begin by discussing what forensic actor would consider 'how many' and 'who' donated 'what number' of sperm relevant questions.

Regarding Legitimacy, which speaks to trustworthiness across a broad factor space, we determined that of 33 sperm mixtures (2-5 sperm donors), all single-sperm epgs were correctly clustered, giving perfect estimates about how many sperm donors there were. When considering the question of contribution, we observed that: i) the relative frequencies of LR values for the H1 and H2 test classes were consistent with calibration; and so ii) P(LR ≥x│H2 )≤1/x for all x >1 and P(LR≤ x│H1 )≤ x for all x< 1.

Regarding Credibility, which speaks to the method’s technical capabilities, we found: i) the largest difference between estimated numbers of epgs belonging to a donor and true values was one; ii) for clusters carrying as few as two sperm, H1-logLRs were 5 to 18; iii) for clusters carrying as few as ten sperm, H1-logLRs were ca. 1/RMP of the donor; iv) H2-logLRs were, at most, -15; and v) logLRs were, generally, unaffected by the number of donors or whether the mixture carried a minor donor, demonstrating single-cell data give robust logLRs.

Authors

• Catherine M. Grgicak (Rutgers University Camden, United States of America)
• Qhawe A. Bhembe (Rutgers University Camden, United States of America)
• Klaas Slooten (Netherlands Forensic Institute, Netherlands)
• Ken R. Duffy (Northeastern University, United States of America)
• Desmond S. Lun (Rutgers University Camden, United States of America)