Recent studies of eukaryotic DNA replication timing profiles suggest that the time-dependent rate of origin firing, I(t), has a universal shape, which ensures a reproducible replication completion time. However, measurements of I(t) are based on population averages, which may bias the shape of the I(t) because of imperfect cell synchrony and cell-to-cell variability. Here, we measure the population-averaged I(t) profile from synchronized Saccharomyces cerevisiae cells using DNA combing and we extract the single-cell I(t) profile using numerical deconvolution. The single cell I(t) and the population-averaged I(t) extracted from DNA combing and replication timing profiles are similar, indicating a genome scale invariance of the replication process, and excluding cell-to-cell variability in replication time as an explanation for the shape of I(t). The single cell I(t) correlates with fork density in wild-type cells, which is specifically loosened in late S phase in the clb5Δ mutant. A previously proposed numerical model that reproduces the wild-type I(t) profile, could also describe the clb5Δ mutant I(t) once modified to incorporate the decline in CDK activity and the looser dependency of initiation on fork density in the absence of Clb5p. Overall, these results suggest that the replication forks emanating from early fired origins facilitate origin firing in later-replicating regions.