The paradox of Vito Volterra’s predator-prey model

The aim of this article is to propose on the one hand a brief history of modelling starting from the works of Fibonacci, Robert Malthus, Pierre Francis Verhulst and then Vito Volterra and, on the other hand, to present the main hypotheses of the very famous but very little known predator-prey model elaborated in the 1920s by Volterra in order to solve a problem posed by his son-in-law, Umberto D’Ancona. It is thus shown that, contrary to a widely-held notion, Volterra’s model is realistic and his seminal work laid the groundwork for modern population dynamics and mathematical ecology, including seasonality, migration, pollution and more.