doi: bioRxiv preprint modifications. However, whether the replication timing is a cause, a consequence, or an independent correlate of chromatin structure is a matter of debate (Rhind and Gilbert, 2013).In budding yeast, where replication origin locations are well defined, origin firing is stochastic, with each origin firing with a specific probability, independent of neighboring origins (Czajkowsky et al., 2008;Yang et al., 2010; de Moura et al., 2010). Such stochastic firing leads to reproducible replication profiles at the population level, because more efficient origins are more likely to fire early and therefore, on average, have early replication times; by contrast, inefficient origins usually fire late or are passively replicated (Rhind et al., 2010). The heterogeneous and inefficient nature of metazoan replication initiation is also consistent with stochastic initiation. Simulations with a stochastic firing model, in which initiation is regulated only by a local-firing-probability function, faithfully reproduce experimental genome-wide replication timing profiles, suggesting that no deterministic timing program is required (Gindin et al., 2014b). Furthermore, if the local initiation rate is predicted by DNase I hypersensitivity, the simulation closely matches experimental results, consistent with the observed correlation between promoters and enhancers, which are DNase I hypersensitive, and initiation frequency (Gindin et al., 2014b). On the other hand, the reproducible replication timing of individual replication domains measured in single cells has led to the suggestion that replication within those domains initiates at defined times in most cells in the population (Dileep and Gilbert, 2018). Furthermore, neighboring initiation sites have been proposed to show both cooperative firing and lateral inhibition (Cayrou et al., 2011;Guilbaud et al., 2011;Löb et al., 2016), neither of which are consistent with strictly stochastic models. Therefore, whether metazoan initiation timing is stochastic or deterministic, or some combination of the two, is still very much an open question (Bechhoefer and Rhind, 2012).A powerful solution to the problems of heterogeneity and low signal-to-noise ratios is single-molecule analysis, which allows the identification of sites of replication initiation on individual DNA fibers (Técher et al., 2013). Traditional single-molecule approaches-such as fiber autoradiography (