Of ongoing interest in the forensic community is the ability to evaluate Y-chromosome STR profiles. Numerous statistical methods have been proposed to calculate a haplotype probability, a match probability or a likelihood ratio. A major hurdle to overcome in most methods is that multi-locus haplotypes are typically rare, requiring huge surveys of the population in order to obtain stable estimates of frequencies. One method that has gained popularity relies on modelling the population as a number of clades, each of which is clustered around a central haplotype. This method was pioneered for YSTR analysis by Andersen and extended by Kruijver to handle complex YSTR loci and alleles (i.e. such as duplicated regions or partial repeats). 

When individuals within a population database are separated into clades for evaluation using the discrete Lapalce model, the Partitioning Around Medoids algorithm is employed. This is typically iterative and settles on medians and dispersion parameters for each clade that describe parameters in the discrete Laplace distributions. Whilst not required, a favoured interpretation in forensic biology is to think of the clades as groups of individuals who could all be traced back to a single common ancestor. With this thinking, any differences in the haplotypes of individuals within the clade will have come from mutations, during meioses, away from the ancient central haplotype for that clade. 

In this work the performance and behaviour of the discrete Laplace model is explored through simulation of a population over many generations, that starts with a single founder. The pedigree of the entire population is recorded to allow questions of clade formation and founding to be investigated. These findings are then compared to the common interpretation of clades arising from an ancient central haplotype. In particular, clade formation age occurring purely from genetic drift (i.e. without any introduction of population substructure) is investigated.  

Also considered is how the concept of genetic drift can lead to a situation where the ancient central haplotype does not correspond to the mode of the discrete Laplace distribution in the extant members of a clade, but that this does not affect performance (or practical interpretation of the model). 

Author

• Duncan Taylor (Forensic Science SA and Flinders University, Australia)