While it may seem counterintuitive to apply unstructured models to demes belonging to a meta-population, we further investigated the demographic history of the four species by means of the stairwayplot. When enough data is available, non-parametric unstructured models (such as the PSMC (Li & Durbin, 2011), the extended Bayesian skyline plot (Heled & Drummond, 2008) and the stairwayplot among others) provide a careful description of the distribution of coalescence times of the gene genealogy, which ultimately depends from the “true” demographic history (whether it is known or not) of the sampled lineages. If panmixia is the most likely scenario, the distribution of coalescence times is directly related to the variation of Ne through time and can therefore have a direct biological interpretation. This is the case for G. cuvier (Table 1), whose reconstructed stairwayplot suggests that this species experienced a mild ancestral expansion and a recent ~4-fold bottleneck around 2,000 years B.P. (consistent with the results of Pirog et al. (2019), Figure 3). Conversely, signals detected by the stairwayplot in the remaining three species, better described by the SST model (Table 1), cannot be directly interpreted as changes in Ne over time. In this light, we ran coalescence simulations to provide helpful and general insights into the understanding of the relation between the inferences performed under unstructured and structured models.