Abstract
The aim of this paper is to develop ideas about robustness analyses. I introduce a form of robustness analysis that I call sufficient parameter robustness, which has been neglected in the literature. I claim that sufficient parameter robustness is different from derivational robustness, the focus of previous research. My purpose is not only to suggest a new taxonomy of robustness, but also to argue that previous authors have concentrated on a narrow sense of robustness analysis, which they have inadequately distinguished from other investigations of models such as sensitivity analysis.
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Notes
Sensitivity analysis is a term with different meanings. My definition is not intended to correspond to the activity in which the modeler investigates how the uncertainty in the input of a model could affect the uncertainty of its output, despite the fact that the latter is sometimes referred to as sensitivity analysis. Moreover, by sensitivity analysis I do not refer to perturbation analysis, which is a method to solve equations.
According to the latitudinal diversity gradient, the number of species within a taxonomic group tends to increase with decreasing latitudes, i.e., diversity increases towards the tropics and decreases towards the poles.
Broken up or violated is meant in the sense that there will be exceptions to the model’s predictions and/or the model exhibits different dynamic behavior(s) over some range of parameter values.
The population growth of certain biological systems is discrete rather than continuous over time, and hence the reason we use a discrete model to model their population growth is adopted for substantial reasons rather than tractability reasons. One and the same assumption or “mathematical structure” can thus be used either as a substantial or tractability assumption, and its status as either depends on the contextual and pragmatic aspects of modeling. In other words, the status of a modeling assumption cannot be evaluated in isolation. At the same time, when the contextual and pragmatic aspects of modeling are fixed, the status of modeling assumptions can be compared as to whether they introduced mainly to “facilitate modeling” or whether they represent the “core aspects” of a model or a set of similar models.
I do not claim that the presented taxonomy of modeling assumptions is exhaustive. In fact, with a more detailed taxonomy of modeling assumptions (Musgrave 1981; Mäki 2000) we could arrive at a more detailed taxonomy of robustness analyses of models. Moreover, Kuorikoski et al. (2010) distinguish a third type of modeling assumption, namely, Galilean assumptions. Galilean assumptions serve to isolate certain entities, factors, and so on from the involvement of everything else (Mäki 1992, 1994). Rather than thinking of Galilean assumptions as an independent kind of modeling assumption, we should understand these as stating that the aim of scientific theorizing and modeling is isolation, whereas tractability and substantial assumptions are devices for accomplishing isolations.
Lotka–Volterra models have been criticized as being poorly tested, giving inaccurate predictions, and lacking explanatory power (Smith 1952; Pielou 1981; Hall 1988; Shrader-Frechette 1990). Even if we neglect the fact that models have functions other than furnishing explanations and giving predictions (Pielou 1981; Odenbaugh 2005), the above is not damaging to my position. The criticism is typically directed at the Lotka–Volterra predation model. The Lotka–Volterra competition model, which I use as an example, is on firmer ground with regard to the above. The Lotka–Volterra competition model’s representational accuracy and its ability to save the phenomena are not at issue here, however. It suffices to show that the equations in the Lotka–Volterra competition model represent a modular system of invariant equations; the fact is that the Lotka–Volterra competition model remains invariant during variations in the values of its “independent” variables (N 1 or N 2), at least for certain parameter values. This shows that the model gives us at least potentially valid causal or mechanistic explanations, that is, the Lotka–Volterra competition model is an explanatory model rather than a phenomenological model devoid of any explanatory power.
In fact, Koch (1974a) demonstrated that the co-existence of two competitors with one resource in a seasonally varying environment is a robust result of competition models, which included substantial modeling assumptions different from the classical competition model.
Some of the assumptions mentioned are Galilean assumptions. However, the point is that these assumptions were incorporated into the model to make it more tractable.
The only recent paper I know of that discusses sufficient parameters in detail is Winther (2006). His ideas have developed from a different angle than mine.
The above is, in crude terms, the explanation that Hutchinson (1961) gave to his paradox of the plankton referred to above.
Nothing in the above presupposes that for genuine or true explanations the identification of the actual cause or mechanism has become redundant, owing to sufficient parameter robustness of the results of models. Abstract causal surrogates—sufficient parameters—should not be mistaken for the actual causes and mechanisms of phenomena. To do otherwise is to commit oneself to a reification fallacy. What has just been said is one of the main motivations behind mechanistic or resource-based competition models as well (Tilman 1980; Pacala and Tilman 1994; Leibold 1995).
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Acknowledgments
A version of this paper was presented at the Philosophy of Science Group seminar 17 November 2008 at the University of Helsinki. This research was supported financially by the Finnish Cultural Foundation and the Academy of Finland as a part of the project Modeling Mechanisms (project number 112 2818). I am grateful to the members of the Philosophy of Science Group in Helsinki, especially Aki Lehtinen and Petri Ylikoski, and an anonymous referee for this journal who provided helpful comments on earlier drafts of this paper.
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Raerinne, J. Robustness and sensitivity of biological models. Philos Stud 166, 285–303 (2013). https://doi.org/10.1007/s11098-012-0040-3
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DOI: https://doi.org/10.1007/s11098-012-0040-3