The paper presents models and methods for analysing forensic DNA profiles which evidently contain DNA from more than one individual, as can arise for example in cases of rape or violent murder.

The innovation is to allow for family relationships among the contributors to such DNA mixtures; for a simple example, this means that we can evaluate the strength of evidence that perpetrators in a gang rape are cousins. Central to this being possible is a novel compact but precise quantitative representation of relatedness among individuals, that can be efficiently computed from a pedigree, or family tree. Did you know in what sense you are differently related to your mother and your sister, although in both cases you share half of your genes?

This representation is relevant to any genetic analysis in the presence of close relationships, not just forensics; as an illustration we compute exactly how inbred the Roman emperors Caligula and Nero were! The forensic methods are implemented  in freely available software; this uses Bayesian networks and allows analysis of even complex cases in a few seconds.