Fig. 7.

Plots showing the time evolution of probability distribution function of the birth rate as obtained from simulation of the full stochastic multi-scale model. We show three snapshots (time increasing from left to right) for the region behind the interface (upper row) and ahead of the interface (lower row). These results show that behind the interface the distribution of the empirical birth rate, calculated using Eq. (38), is centred around the equilibrium birth rate, Eq. (40), vertical red line. By contrast, ahead of the interface the birth rate distribution is much broader. Therefore, whereas behind the interface the equilibrium birth rate is a good approximation, this is not the case ahead of the interface. See also supplementary movies A.11 and A.12. Θ = 2000. For other parameter values see Section 5. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)