Spectacular long-term cycles (around 110 years), independent of human exploitation, have been seen in historical catches of Atlantic bluefin tuna (Thunnus thynnus). Previous studies indicated that such variations could have been generated by contrasting but equally plausible dynamic processes, i.e., changes in carrying capacity or migration. A simulation framework was therefore used to test whether the International Commission for the Conservation of Atlantic Tuna stock assessment model, i.e., a virtual population analysis (VPA), can capture such dynamics. The main outcome is that knowledge of the underlying process is crucial, because distinct hypotheses lead to different population dynamics and contrasting performances of the stock assessment model. The VPA is indeed able to reconstruct accurately the historical stock parameters under the carrying-capacity hypothesis, but not under the migratory hypothesis, for which there is often strong bias (up to 500%) in absolute values and in trends of spawning stock biomass and F. Furthermore, it was shown that (i) different phases between exploitation and long-term cycle can induce contrasting terminal F for a same effort and (ii) that there was considerable confounding between the dynamics and increasing effort (as currently seen). We conclude that it is difficult to infer the actual dynamics on the basis of commercial catch data and that novel fishery-independent observation is needed.