Eukaryotic cells seem unable to monitor replication completion during normal S phase, yet must ensure a reliable replication completion time. This is an acute problem in early Xenopus embryos since DNA replication origins are located and activated stochastically, leading to the random completion problem. DNA combing, kinetic modelling and other studies using Xenopus egg extracts have suggested that potential origins are much more abundant than actual initiation events and that the time-dependent rate of initiation, I(t), markedly increases through S phase to ensure the rapid completion of unreplicated gaps and a narrow distribution of completion times. However, the molecular mechanism that underlies this increase has remained obscure.Using both previous and novel DNA combing data we have confirmed that I(t) increases through S phase but have also established that it progressively decreases before the end of S phase. To explore plausible biochemical scenarios that might explain these features, we have performed comparisons between numerical simulations and DNA combing data. Several simple models were tested: i) recycling of a limiting replication fork component from completed replicons; ii) time-dependent increase in origin efficiency; iii) time-dependent increase in availability of an initially limiting factor, e.g. by nuclear import. None of these potential mechanisms could on its own account for the data. We propose a model that combines time-dependent changes in availability of a replication factor and a fork-density dependent affinity of this factor for potential origins. This novel model quantitatively and robustly accounted for the observed changes in initiation rate and fork density.This work provides a refined temporal profile of replication initiation rates and a robust, dynamic model that quantitatively explains replication origin usage during early embryonic S phase. These results have significant implications for the organisation of replication origins in higher eukaryotes.