The distribution of males with identical Y-chromosomal DNA profiles

In this article we study the distribution of males with the same Y-profile determined on a set of loci; for example, on a set of Y-STR loci such as done by forensic laboratories. We review several methods that aim to quantify the evidential value of corresponding profiles, or to yield a probabilistic assessment of the meiotic distances between two males whose profiles turn out to be the same. For all of these methods, it is relevant to have an understanding of the pedigrees of males with the same Y-chromosomal DNA profile on the considered loci. If the mutation rate of these loci is large enough compared to the population growth rate, all profiles die out exponentially fast. From this observation, we devise a simulation scheme to investigate the Y-profile persistence and prevalence dynamics based only on the simulation of profile pedigrees, avoiding the simulation of a whole population. In particular this allows to study fast growing populations in combination with rapidly mutating markers. For parameters amenable to direct simulation we compare results with Andersen and Balding (2017) and find good agreement. Our results for other choices of population growth rates illustrate that, when corresponding Y-profiles are observed without further information on the individuals they are obtained from, they may be very distantly related and cluster sizes of identical profiles may be very large, except when the mutation rate of the profile is very high such as obtained with multiplexes with rapidly mutating loci. On the other extreme, for sets of loci who do not mutate fast enough compared to the population growth rate, there is no limit on how prolific a profile on those loci can become.