How Xenopus laevis replicates DNA reliably even though its origins of replication are located and initiated stochastically

DNA replication in Xenopus laevis is extremely reliable, failing to complete before cell division no more than once in 10,000 times; yet replication origins sites are located and initiated stochastically. Using a model based on 1d theories of nucleation and growth and using concepts from extreme-value statistics, we derive the distribution of replication times given a particular initiation function. We show that the experimentally observed initiation strategy for Xenopus laevis meets the reliability constraint and is close to the one that requires the fewest resources of a cell.