Modeling causal structures
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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.
KeywordsModeling Causal inference Volterra Predator-prey-model Darwin Coral atolls
We are indebted to Kärin Nickelsen, Tilman Sauer and Adrian Wüthrich for helpful comments on an early draft of the paper. We have also benefitted from the discussion of the paper at the European Philosophy of Science Association Conference in Athens, Greece, in October 2011. Tim Räz was supported by a grant from the Swiss National Science Foundation (100011_124462/1).
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