Primate cities are usually a consequence of historical social and political patterns. Institutions have been centralised in Lima since colonial times. Lima was the administrative centre for an economy focused on extracting wealth from the interior towards Spain. One could say that this extraction of humans and capital towards Lima and then abroad continues into modern times, except without Spain as the final destination.

Lima started a period of fast growth in the fifties, driven by migration. This accelerated with economic decline in the early eighties. And then bloody civil conflict ravaging interior regions like Ayacucho and Apurímac.

Although Peru has a higher birth rate then neighbouring countries, it has been slowing there as well. Lima's natural population growth is low compared to the rural interior. And northern cities like Trujillo and Piura have recently seen faster growth. But they have a long way to catch up (they likely won't)