The properties of human DNA fingerprints detected by multilocus minisatellite probes 33.6 and 33.15 have been investigated in 36 large sibships and in 1,702 Caucasian paternity cases involving the analysis of over 180,000 DNA fingerprint bands. The degree of overlap of minisatellite loci detected by these two probes is shown to be negligible (approximately 1%), and the resulting DNA fingerprints are therefore derived from independent sets of hypervariable loci. The level of allelism and linkage between different hypervariable DNA fragments scored with these probes is also low, implying substantial statistical independence of DNA fragments. Variation between the DNA fingerprints of different individuals indicates that the probability of chance identity is very low (much less than 10(-7) per probe). Empirical observations and theoretical considerations both indicate that genetic heterogeneity between subpopulations is unlikely to affect substantially the statistical evaluation of DNA fingerprints, at least among Caucasians. In paternity analysis, the proportion of nonmaternal DNA fragments in a child which cannot be attributed to the alleged father is shown to be an efficient statistic for distinguishing fathers from nonfathers, even in the presence of minisatellite mutation. Band-sharing estimates between a claimed parent and a child can also distinguish paternity from nonpaternity, though with less efficiency than comparison of a trio of mother, child, and alleged father.