We have examined DNA replication in three mammalian cell lines (L, muntjac and MDBK) by statistical analyses of light microscopic DNA fiber autoradiograms in order to determine whether the sites where replication is initiated are spatially random or organized. A quantitative model was developed to predict the properties of a random spatial arrangement of initiation sites and was tested against experimental data. A description of the actual spatial organization of activated initiation sites is proposed. The number of sites per strand and the mean distance between sites depend heavily on the length of the strands measured, according to both observation and theory. However, in all three cell lines, the observed relationship between those variables and strand length differed from the relationship predicted by the random model. The modal inter-initiation distance was nearly the same in all three cell lines (5 to 15μm). Three methods were used to provide estimates of, or lower bounds on, the mean inter-initiation distances on the unbroken DNA fiber. The ranges of estimates were 8 to 23 μm for muntjac cells, 22 to 45 μm for MDBK cells, and 14 to 63 μm for L cells. Because inter-initiation distance depends on strand length and strands break with excess probability near hot-labeled regions, alternatives to the testing of pooled samples were developed. Statistical tests of the randomness of interinitiation distances were applied to individual strands containing at least nine initiation distances. A test of exponentiality against alternative Weibull distributions demonstrated that the probability of the distribution of inter-initiation distances being random was less than one in 10,000. The Kolmogorov-Smirnov and Keiding tests indicated differences in organization between the three cell lines. Long exposure to 5-fluoro-2′-deoxyuridine (5 × 10-7 m) shifted the organization of initiation sites in MDBK cell DNA toward randomness. Neither the mean nor the modal inter-initiation distance detected these changes in organization. The tests for exponentiality employed here provide more sensitive tools for studying the organization of DNA replication. © 1979.