Most scenarios for the world’s human population predict continued growth into the 22nd century, while some indicate that it could stabilize or begin to fall before 2100. Almost always, decline is seen as not being faster than the preceding growth. Different scenarios are obtained if we consider the human population as a complex system, subject to the general rules that govern complex systems, in particular their tendency to show rapid changes which – in the case of populations – may take the shape of true collapses (defined here as “Seneca Collapses”). The present survey examines a small number of examples of rapid population collapses in the human and in the animal domains. While not pretending to be exhaustive, the data presented here show that biological populations do show rapid “Seneca-style” collapses. So, it is possible that the same phenomenon could occur for the world’s human population.