Correlation of DNA fragment sizes within loci in the presence of non-detectable alleles

At present most forensic databases of DNA profiling of individuals consist of DNA fragment sizes measured from Southern blot restriction fragment length polymorphism (RFLP) analysis. Statistical studies of these databases have revealed that, when fragment sizes are measured from RFLP analysis, some of the single-band patterns of individuals may actually be due to heterozygosity of alleles in which fragment size resulting from one allele remains undetected. In this work, we evaluate the effect of such allelic non-detectability on correlation of fragment sizes within individuals at a locus, and its impact on the inference of independence of fragment sizes within loci. We show that when non-detectable alleles are present in a population at a locus, positive correlations of fragment sizes are expected, which increase with the proportion of non-detectable alleles at the locus. Therefore, a non-zero positive correlation is not a proof of allelic dependence within individuals. Applications of this theory to the current forensic RFLP databases within the US show that there is virtually no evidence of significant allelic dependence within any of the loci. Therefore, the assumption that DNA fragment sizes within loci are independent is valid, and hence, the population genetic principles of computing DNA profile frequencies by multiplying binned frequencies of fragment sizes are most likely to be appropriate for forensic applications of DNA typing data.