Violations of the ceiling principle: exact conditions and statistical evidence

The National Research Council recommended the use of the ceiling principle in forensic applications of DNA testing on the grounds that the ceiling principle was believed to be "conservative," giving estimates greater than or equal to the actual genotype frequencies in the appropriate reference population. We show here that the ceiling principle can fail to be conservative in a population with two subpopulations and two loci, each with two alleles at Hardy-Weinberg equilibrium, if there is some linkage disequilibrium between loci. We also show that the ceiling principle can fail in a population with two subpopulations and a single locus with two alleles if Hardy-Weinberg equilibrium does not hold. We give explicit analytical formulas to describe when the ceiling principle fails. By showing that the ceiling principle is not always mathematically reliable, this analysis gives users of the ceiling principle the responsibility of demonstrating that it is conservative for the particular data with which it is used. Our reanalysis of VNTR data bases of the FBI provides compelling evidence of two-locus associations within three major ethnic groups (Caucasian, black, and Hispanic) in the United States, even though the loci tested are located on different chromosomes. Before the ceiling principle is implemented, more research should be done to determine whether it may be violated in practice.