### Fish in the Formula. Population Dynamics and the Mathematization of Biology 1920-1940

How is it possible that an Italian physicist and mathematician in Rome (Vito Volterra, 1860-1940) and an Austrian-Hungarian chemist and actuary in New York (Alfred James Lotka, 1880-1949) proposed independently of each other and simultaneously laws of population dynamics? These laws can predict in a simple predator-prey model the quantitative fluctuations of the two competing species. While Volterra mathematically modeled the shifting populations based on the sales figures of Italian fish markets, the same differential equations build one part of Lotka’s all-embracing idea of global distribution of resources in a biological as well as economic way. Both claim that these laws can illuminate the theory of evolution.

The dissertation, by means of a micro historical investigation of the practice of the two researchers, questions their claim to develop an instrument for mathematical predictability and for causal explanation of natural processes. How can we describe the relationship between experience and theory in their works? What kind of data did they have at hand? What did they know about biological processes and animals? How can we explain the simultaneous and independent ‚discovery’ of the same laws at different places?

Since 1900 scientists of biological disciplines have been attempting to establish a theoretical basis. While quantification and its statistical interpretation were already quite common, the mathematical applications in biology (population genetics) were intensified through the re-discovery of the Mendelian laws. How can the Lotka-Volterra-laws be interpreted against the background of the attempt of interdisciplinary demarcation and legimitation in the discipline of biology? What is the added gain of a mathematical description of population dynamical processes? Lotka’s and Volterra’s formulas incorporate the abstraction from any environmental influence and interactions. This fact could explain why the laws were received predominantly in the fields of economics, demography, and system theory and not in biological sciences.

key words: population dynamics – mathematization – evolutionary theory – history of biology – Alfred James Lotka – Vito Volterra