Using coalescence arguments, we clarified why simple meta-population models with constant connectivity generate a gene genealogy harbouring a signature of a recent decline for any parameters’ combination. The signature of bottleneck detected by the stairwayplot in the three shark species best described by SST can be therefore interpreted as a consequence of the underlying structure. However, connectivity likely changes through time. For instance, human activities have likely impacted the evolutionary history of a large number of species either by decreasing their effective population size and/or by fragmenting their habitat (i.e., reducing migration rates between demes). This intuitively should exacerbate the signature of population decline in the resulting gene genealogy. However, it remains to be shown whether this signature is qualitatively and quantitatively distinguishable from models with constant connectivity. This is a question of fundamental importance to understand whether it is possible to detect recent bottleneck in structured populations. To this end, we further investigated by coalescent simulations the expected gene genealogy in SST-CH (and FIM-CH) models with a change in connectivity 10 or 50 generations B.P., which matches the beginning of extensive anthropogenic influence on biodiversity considering our species’ generation time (Ceballos et al., 2015). The resulting gene genealogies were poorly affected by the recent drop in connectivity, with both the normalized SFS and the inferred Ne dynamic following the same trajectory of the corresponding scenario with the same long-term Nm and TCOL (Figures 6, S7, S8, S9, S10, S11, S12 and S13). We noticed the drop in NDEME (Figures 6, S9, S12 and S13) had stronger influence than the drop in (Figures S7, S8, S10 and S11), consistent with previous finding showing that the distribution of coalescence events depends not only by the Nm compound parameter but also by their individuals values (Mona, 2017). This can be explained once again in the light of the length of the coalescence phases (Figure 7). Reducing NDEME will increase exponentially the number of coalescence events, drastically shortening the scattering phase and the number of surviving lineages. Reducing m will only linearly reduce the probability of migrations outside the deme, marginally affecting the length of the scattering phase and the number of surviving lineages compared to constant Nm scenarios. This is why a 100-fold reduction in NDEME significantly reduces the number of lineages entering in the collecting phase, almost hiding the ancestral expansion in high long-term Nm scenarios (Figures 6, S9, S12 and S13), while a 100-fold reduction in m is barely detectable (Figures S7, S8, S10 and S11). Similarly, the recent reduction in either NDEME or m cannot be detected for lower long-term Nm scenarios, where the collecting phase is already missing. This explains why the general pattern is strikingly similar between SST-CH and SST simulations, which implies that the simulated change in connectivity is too recent to significantly alter the pattern of coalescence events and that a recent drop can be hardly detected on the basis of the SFS only. Our empirical data are consistent with these findings: when we compared SST vs. SST-CH models in the three shark species using the ABC framework, we failed to clearly distinguish the two models (Tables S9 and S10, Figure S6). This seems to be a paradox: we observed a recent bottleneck in species of conservation concern using unstructured model, but we cannot exclude that this is just the consequence of population structure.