Simulation study
We ran coalescent simulations under FIM, SST and their modified version FIM-CH and SST-CH, where the Nmparameter is changed at TCH generations B.P. (Figure 1), to first inspect the shape of the SFS and to further uncover the variation of Ne over time assuming a panmictic population by means of the stairwayplot. We investigated in total 288 demographic scenarios under the four meta-population models (Tables 2, S2, S3, S4, S5 and S6). Similarly to the analyses performed on the real data, all scenarios were represented by d=100 demes exchanging migrants. We sampled 10 diploid individuals either from a randomly selected deme in the case of FIM/FIM-CH (since all demes have the same coalescencehistory) or from the central deme of the array in the case of SST/SST-CH (to avoid border effects). Deme size was fixed to NDEME =5000 with m varying accordingly to obtain a long-term Nm of 1, 5, 10, and 15 in order to encompass the range of the estimated values (see results). TCOL was fixed to 5,000, 15,000 and 50,000 generations B.P. or to ∞ (i.e., equilibrium model), and the ancestral effective size was fixed to NANC = 50,000. Change of connectivity occurred at TCH=10 or 50 generations B.P., to mimic human induced effects due to overfishing and/or habitat modifications (i.e., climate changes). Looking forward in time, we modelled the change in connectivity by instantaneously decreasing m or NDEMEby a factor 10 or 100 with respect to the long-term Nm (Tables S3, S4, S5 and S6). For each combination of parameters, we performed 100 coalescent simulations of 50,000 Rad-like loci of 115 bp. Mutation rate per site per generations was set to 1.93×10-8 and the generation time to 10 years. We computed for each scenario (averaged over the 100 replicates): a) summary statistics (θπ, θw, and TD); b) the normalised SFS as in (Lapierre, Lambert, & Achaz, 2017); c) the stairwayplot, to reconstruct the apparent variation of Ne through time. We note that the number of diploid individuals and simulated loci were chosen to be consistent with our data (preliminary analyses conducted on a subsample of 5,000 loci produced consistent results).