Modeling causal structures: Volterra's struggle and Darwin's success

Abstract

The Lotka-Volterra predator-prey-model is a widely known example of model-based science. Here we reexamine Vito Volterra's and Umberto D'Ancona's original publications on the model, and in particular their methodological reflections. On this basis we develop several ideas pertaining to the philosophical debate on the scientific practice of modeling. First, we show that Volterra and D'Ancona chose modeling because the problem in hand could not be approached by more direct methods such as causal inference. This suggests a philosophically insightful motivation for choosing the strategy of modeling. Second, we show that the development of the model follows a trajectory from a "how possibly" to a "how actually" model. We discuss how and to what extent Volterra and D'Ancona were able to advance their model along that trajectory. It turns out they were unable to establish that their model was fully applicable to any system. Third, we consider another instance of model-based science: Darwin's model of the origin and distribution of coral atolls in the Pacific Ocean. Darwin argued more successfully that his model faithfully represents the causal structure of the target system, and hence that it is a "how actually" model. © 2012 Springer Science + Business Media B.V.