Abstract

The birth of modern biomathematics took place in the 1920s and was characterized by two significant new facts: the systematic use of mathematics in biology not as a technical aid but as a conceptual tool, and the attempt to apply a determinist or a mechanist conception to biology. In this paper we deal with the developments of population dynamics and with the main contributions to this trend, i.e. the works of Vito Volterra and Alfred J. Lotka. The purpose is to show that these contributions are representative — in different and sometimes contrasting ways — of the new developments of biomathematics. The analysis of the priority question concerning the discovery of the 'Volterra-Lotka' equations and the analysis of the Volterra-Lotka correspondence show that Volterra's approach was strictly adherent to the classical physico-mathematical paradigm, while Lotka's point of view was more eclectic and open-minded as regards the new developments of physics, and somewhat skeptical about formal statements. We could say that while Volterra followed the 'mechanical analogy' Lotka had an inclination for the 'thermodynamic analogy' and had a great interest for the energetic problems in population dynamics