The Robust Volterra Principle*

Abstract

Theorizing in ecology and evolution often proceeds via the construction of multiple idealized models. To determine whether a theoretical result actually depends on core features of the models and is not an artifact of simplifying assumptions, theorists have developed the technique of robustness analysis, the examination of multiple models looking for common predictions. A striking example of robustness analysis in ecology is the discovery of the Volterra Principle, which describes the effect of general biocides in predator-prey systems. This paper details the discovery of the Volterra Principle and the demonstration of its robustness. It considers the classical ecology literature on robustness and introduces two individual-based models of predation, which are used to further analyze the Volterra Principle. The paper also introduces a distinction between parameter robustness, structural robustness, and representational robustness, and demonstrates that the Volterra Principle exhibits all three kinds of robustness. Disciplines PhilosophyThis journal article is available at ScholarlyCommons: http://repository.upenn.edu/philosophy_papers/5 106The Robust Volterra Principle* Michael Weisberg and Kenneth Reisman † ‡ Theorizing in ecology and evolution often proceeds via the construction of multiple idealized models. To determine whether a theoretical result actually depends on core features of the models and is not an artifact of simplifying assumptions, theorists have developed the technique of robustness analysis, the examination of multiple models looking for common predictions. A striking example of robustness analysis in ecology is the discovery of the Volterra Principle, which describes the effect of general biocides in predator-prey systems. This paper details the discovery of the Volterra Principle and the demonstration of its robustness. It considers the classical ecology literature on robustness and introduces two individual-based models of predation, which are used to further analyze the Volterra Principle. The paper also introduces a distinction between parameter robustness, structural robustness, and representational robustness, and demonstrates that the Volterra Principle exhibits all three kinds of robustness.

The Volterra Principle Generalized

“…The identification of the common structure concludes step 2 of robustness analysis. Weisberg and Reisman (2008) push robustness analysis further, and they refine the results regarding the Volterra Principle. First, they distinguish three kinds of robustness.…”

“…Weisberg and Reisman analyze further models with respect to the Volterra Principle. In Weisberg (2006b), robustness analysis was restricted to parameter and structural robustness-the models are all formulated in the framework of coupled ordinary differential equations-while Weisberg and Reisman (2008) also includes an analysis of individual-based models (IBMs). These are finite models with discrete space and time, which can be taken to represent individual animals.…”

“…Does this mean that the Volterra Principle is questionable as well? Weisberg (2006b), and Weisberg and Reisman (2008) argue that this is not the case. They propose that the Volterra Principle can also be established from other predator-prey models.…”

“…5 Does this mean that the Volterra Principle is also doomed to fail? This question has been brought to philosophers' attention in two papers (Weisberg 2006b;Weisberg and Reisman 2008). Weisberg and Reisman argue that the Volterra Principle does not de-5.…”

Computer models and the evidence of anthropogenic climate change: An epistemology of variety-of-evidence inferences and robustness analysis

“…The literature on this subject distinguishes several notions of robust reasoning pertaining to theorems, phenomena, modes of detection (Calcott, 2011;Levins, 1966Levins, , 1993Orzack and Sober, 1993;Wimsatt, 2001), inferences, measurements, derivations, causal relationships (Woodward, 2006), parameter values, mathematical structures, representation frameworks (Weisberg & Reisman, 2008), computer models and simulations (Houkes & Vaesen, 2012;Lloyd, 2015;Muldoon, 2007;Parker, 2011). Although distinctions among these ideas are philosophically interesting, for the purposes of this paper I will focus on a general sense of robust evidential reasoning, which 1 Also see Staley (2011Staley ( , 2012.…”