As expected, the ltLR for both phase 1 and phase 2 enhancement exceeds that for standard 28 PCR cycles at all numbers of replicates, and phase 2 enhancement ltLR typically gives a small improvement over phase 1 enhancement. For

30 PCR cycles, the ltLR exceeds the mixLR for a single replicate but dips slightly below it at six replicates. For the other conditions, the mixLR is always exceeded from four replicates. All three curves in Fig. 3 (middle) show an increasing trend with number of replicates, with the median ltLR being in the expected order throughout (decreasing ltLR with increasing dropout for Q). The median ltLR exceeds the mixLR after one replicate (low dropout), after two replicates (medium dropout) and after four replicates (high dropout). The range is often wide, reflecting a strong dependence of the ltLR on the details of the simulation (in particular the number check details of alleles shared across contributors). The ltLR returned when only standard or only sensitive replicates are used shows a similar trend, but nearly five bans lower for the standard replicates

(Fig. 3, right). For three or more replicates, using mixed types of replicates is superior this website even to only using sensitive replicates, coming to within two bans of the IMP. This partly reflects the limited pool of replicates used in the actual crime case, but suggests that using different sensitivities in the profiling replicates may convey an advantage due to different contributors being better distinguished. We have shown that ltLR computed by likeLTD is bounded above by the IMP in every condition considered, as predicted by theory (Eq. (3)). That the bound is often tight when

Q is the major contributor (Fig. 1 and Fig. 2 (top)) supports the validity of the underlying mathematical model, and its correct implementation in the likeLTD software. Our results should help counter any misconception that FAD combining multiple noisy profiling replicates only compounds the noise: in fact, multiple noisy replicates can fully recover the genotype of a contributor [14]. A novel feature of likeLTD, is that it can accommodate uncertain allele designations, which diminishes the problem of an all-or-nothing allele call, therefore mitigating the problem highlighted by [15] of choosing a detection threshold. We have shown (Fig. 1 (right)) that introducing many uncertain allele calls leads to ltLRs that satisfy the bound, which is reasonably tight with as few as three replicates even when 80% of true alleles are designated as uncertain and there are also multiple uncertain non-alleles. We have further shown that mixLR, the LR computed from knowing every allele that is represented in the profile of at least one contributor to the CSP, is often surpassed after only a handful of replicates.