For growing Nm, in equilibrium model there will be again only two coalescence phases, namely the scattering and collecting, with the latter having a lower rate of coalescence than the former independently of the simulated parameters. This is why we observed always a strong bottleneck consistent with the distribution of the IICR statistics in any equilibrium model (Chikhi et al., 2018; Mazet et al., 2015; Rodríguez et al., 2018). In non-equilibrium model, there will be two different situations: a) TCOL (in generations) is of the same order of the deme size NDEME. In this setting, going backward in time few lineages would have escaped the sampled demes before TCOL. This corresponds to a shift in the coalescence rate directly from the scattering to the ancestral phase, resulting in a bottleneck of lower intensity compared to an equilibrium model (Figures 4, 5, S1 and S2), for the same reasons as above; b) TCOL (in generations) is larger than NDEME. In this setting, some coalescence events may occur during the collecting phase, at a rate much slower than the two other phases. This determines the hump observed in the stairwayplot (Figures 4, 5, S1 and S2) and explains why in this window of parameters it is also possible to correctly estimate TCOL using our ABC framework. Further simulations under the FIM model confirmed those patterns even though the ancestral expansion could be detected for lower long-term Nm than the corresponding SST scenario (Figure S4). This is probably due to a higher apparent connectivity underlined the by FIM, where lineages can move more freely during the collecting phase in comparison to SST where migrants only come from the closest neighbours. If many coalescence events occur during the collecting phase, the change in coalescence rate will affect the resulting gene genealogy and it will be detected by the stairwayplot (or any other unstructured method based on coalescent theory).