The duration of the embryonic cell cycle depends on temperature. For this paper, we take the cell cycle time to be $25\min$ at $23°\mathrm{C}$ [61]. A typical duration of $S$ phase used is $\approx 20\min$ [16, 18]. Longer times ($25\min$ for $S$ phase and $30\min$ for the cell cycle) have been observed at $20°\mathrm{C}$ [61].

It is known that when DNA polymerases introduce copying errors in the process of synthesizing nucleotides, replication forks stall to repair the mispairing [63]. These fork stalls occur stochastically in time. Thus, in our model, a constant fork velocity is a mean-field approximation of the time-varying fork velocities and the fork-to-fork variation in progression speed.

The original inference of the in vitro data was fitted using a bilinear function [11]. Using the transformation in Sec. III to transpose the bi-linear $I_{\mathit{vitro}}$, we obtained a scaled bilinear $I_{\mathit{\text{vivo}}}$. For ease of calculation, in parts of the paper, we approximate both bilinear functions with power-law functions. Both initiation functions are approximately quadratic ($I_{\mathit{vitro}}\sim t^{2.62}$ and $I_{\mathit{\text{vivo}}}\sim t^{2.45}$).

$I_{\mathit{vitro}}$ is approximately quadratic except for a decrease $[I\left(t\right)\to 0]$ toward the end of $S$ phase [11]. Since the errors on the decreasing part of the data are large, we neglected the decrease in our previous work [13, 15]. However, a recent repeat of the original experiment has shown that the decrease is not an artifact of poor statistics but represents a real feature of the replication process [61]. Thus, we examined how the decrease in $I\left(t\right)$ affects the end-time distribution. We found that with the decrease the mode of the distribution was delayed by $\approx 3\%$ and the width increased by 15%. These quantities approximately translate into an $S$ phase that is prolonged by $\approx 0.5\min$. This difference is small compared to the overall duration of $S$ phase $\left(20\min \right)$.

In [15], we estimated a failure rate $F\approx {10}^{-4}$ using a simple model that neglected the complications due to the branching process. Since $t^{**}$ depends on the logarithm of $F$ from Eq. (12), the factor of 30 between the two estimates of $F$ results only in a roughly $1-\min$ shift in the $t^{**}$ of the end-time distribution and does not alter the qualitative conclusion of the previous work.

Using the in vitro fork velocity $(v=0.6\mathrm{kb}∕\min )$, we find $P_g=O\left({10}^{-9}\right)$. Thus, whether our assumption that $v_{\mathit{\text{vivo}}}>v_{\mathit{vitro}}$ is true or not, we always expect $P_g⪡F$.