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The Robust Volterra Principle*

Published online by Cambridge University Press:  01 January 2022

Michael Weisberg  and
Kenneth Reisman
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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.

Type
Research Article
Information
Philosophy of Science , Volume 75 , Issue 1 , January 2008 , pp. 106 - 131
Copyright
Copyright © The Philosophy of Science Association

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Footnotes

‡

Earlier versions of this paper were presented at the Australasian Association of Philosophy, the London School of Economics, and the University of Bristol. The authors wish to thank those audiences as well as Patrick Forber, Ken Waters, Deena Skolnick Weisberg, Uri Wilensky, and Bill Wimsatt for many helpful comments. Special thanks to Giacomo Sillari for his assistance in translating Volterra's original paper and his insightful thoughts about Volterra's aims and methods. Some of the research in this paper was supported by NSF grant SES-0620887 to MW.

References

Bartell, S. M., Breck, J. M., Gardner, R. H., and Brenkert, A. L. (1986), “Individual Parameter Perturbation and Error Analysis of Fish Bioenergetics Models”, Individual Parameter Perturbation and Error Analysis of Fish Bioenergetics Models 5:160–168.Google Scholar
Berryman, A. A. (1992), “The Origins and Evolution of Predator-Prey Theory”, The Origins and Evolution of Predator-Prey Theory 73:1530–1535.Google Scholar
Briggs, C. J., and Hoopes, M. F. (2004), “Stabilizing Effects in Spatial Parasitoid-Host and Predator-Prey Models: A Review”, Stabilizing Effects in Spatial Parasitoid-Host and Predator-Prey Models: A Review 65:299–315.Google ScholarPubMed
Catagirone, L. E., and Doutt, R. L. (1989), “The History of the Vedalia Beetle Importation to California and Its Impact on the Development of Biological Control”, The History of the Vedalia Beetle Importation to California and Its Impact on the Development of Biological Control 34:1–16.Google Scholar
DeAngelis, D. L., and Mooij, W. M. (2005), “Individual-Based Modeling of Ecological and Evolutionary Processes”, Individual-Based Modeling of Ecological and Evolutionary Processes 36:147–168.Google Scholar
Donalson, D. D., and Nisbet, R. M. (1999), “Population Dynamics and Spatial Scale: Effects of System Size on Population Persistence”, Population Dynamics and Spatial Scale: Effects of System Size on Population Persistence 80:2492–2507.Google Scholar
Dreschler, M. (1998), “Sensitivity Analysis of Complex Models”, Sensitivity Analysis of Complex Models 86:401–412.Google Scholar
Elton, C. S. (1958), The Ecology of Invasions by Animals and Plants. New York: Wiley.CrossRefGoogle Scholar
Forber, P. (2007), “On Biological Possibility and Confirmation”, manuscript. Medford, MA: Tufts University.Google Scholar
Grimm, V., and Railsback, S. F. (2005), Individual-Based Modeling and Ecology. Princeton, NJ: Princeton University Press.CrossRefGoogle Scholar
Hanski, I., Henttonen, H., Korpimaki, E., Oksanen, L., and Turchin, P. (2001), “Small-Rodent Dynamics and Predation”, Small-Rodent Dynamics and Predation 82:1505–1520.Google Scholar
Holling, C. S. (1959), “The Components of Predation as Revealed by a Study of Small Mammal Predation of the European Pine Sawfly”, The Components of Predation as Revealed by a Study of Small Mammal Predation of the European Pine Sawfly 91:293–320.Google Scholar
Korpimäki, E., and Norrdahl, K. (1991), “Numerical and Functional Responses of Kestrels, Short-Eared Owls, and Long-Eared Owls to Vole Densities”, Numerical and Functional Responses of Kestrels, Short-Eared Owls, and Long-Eared Owls to Vole Densities 72:814–826.Google Scholar
Leslie, P. H. (1948), “Some Further Notes on the Use of Matrices in Population Analysis”, Some Further Notes on the Use of Matrices in Population Analysis 35:213–245.Google Scholar
Levins, R. (1966), “The Strategy of Model Building in Population Biology”, in Sober, E. (ed.), Conceptual Issues in Evolutionary Biology. Cambridge, MA: MIT Press, 18–27.Google Scholar
Lewontin, R. C. (1963), “Models, Mathematics, and Metaphors”, Models, Mathematics, and Metaphors 15:274–296.Google Scholar
Lotka, A. J. (1956), Elements of Mathematical Biology. New York: Dover.Google Scholar
MacArthur, R. H., and Connell, J. H. (1966), The Biology of Populations. New York: Wiley.Google Scholar
May, R. M. (2001), Stability and Complexity in Model Ecosystems. Princeton Landmarks in Biology. Princeton, NJ: Princeton University Press.CrossRefGoogle Scholar
Maynard Smith, J. (1974), Models in Ecology. Cambridge: Cambridge University Press.Google Scholar
Odenbaugh, J. (2007), “True Lies: Robustness and Idealizations in Ecological Explanations”, manuscript. Portland, OR: Lewis and Clark College.Google Scholar
Orzack, S. H., and Sober, E. (1993), “A Critical Assessment of Levins's The Strategy of Model Building in Population Biology (1966)”, A Critical Assessment of Levins's The Strategy of Model Building in Population Biology (1966) 68:533–546.Google Scholar
Papaj, D., and Lewis, A. (1993), Insect Learning. New York: Chapman & Hall.CrossRefGoogle Scholar
Ricklefs, R. E., and Miller, G. L. (2000), Ecology. New York: Freeman.Google Scholar
Rose, K. A. (1989), “Sensitivity Analysis in Ecological Simulation Models”, in Singh, M. G. (ed.), Systems and Control Encyclopedia. New York: Pergamon, 4230–4235.Google Scholar
Roughgarden, J. (1979), Theory of Population Genetics and Evolutionary Ecology: An Introduction. New York: Macmillan.Google Scholar
Roughgarden, J. (1997), Primer of Ecological Theory. Upper Saddle River, NJ: Prentice-Hall.Google Scholar
Royama, T. (1971), “A Comparative Study of Models for Predation and Parasitism”, Researches on Population Ecology, Supplement 1:1–91.CrossRefGoogle Scholar
Saltelli, A. F., Tarantola, F., Campolongo, F., and Ratto, M. (2004), Sensitivity Analysis in Practice: A Guide to Assessing Scientific Models. New York: Wiley.Google Scholar
Tinbergen, L. (1960), “The Natural Control of Insects in Pinewoods: I. Factors Influencing the Intensity of Predation by Songbirds”, The Natural Control of Insects in Pinewoods: I. Factors Influencing the Intensity of Predation by Songbirds 13:266–336.Google Scholar
Volterra, V. (1926a), “Fluctuations in the Abundance of a Species Considered Mathematically”, Fluctuations in the Abundance of a Species Considered Mathematically 118:558–560.Google Scholar
Volterra, V. (1926b), “Variazioni e fluttuazioni del numero d’individui in specie animali conviventi”, Variazioni e fluttuazioni del numero d’individui in specie animali conviventi 2:5–112.Google Scholar
Vose, D. (2000), Risk Analysis: A Quantitative Guide. Chichester: Wiley.Google Scholar
Weisberg, M. (2006), “Robustness Analysis”, Robustness Analysis 73:730–742.Google Scholar
Wilensky, U. (1998), “Netlogo Wolf Sheep Predation Model”. Evanston, IL: Center for Connected Learning and Computer-Based Modeling, Northwestern University, http://ccl.northwestern.edu/netlogo/models/WolfSheepPredation.Google Scholar
Wilensky, U. (1999), Netlogo. Evanston, IL: Center for Connected Learning and Computer-Based Modeling, Northwestern University.Google Scholar
Wilensky, U., and Reisman, K. (2006), “Thinking Like a Wolf, a Sheep or a Firefly: Learning Biology through Constructing and Testing Computational Theories—an Embodied Modeling Approach”, Thinking Like a Wolf, a Sheep or a Firefly: Learning Biology through Constructing and Testing Computational Theories—an Embodied Modeling Approach 24:171–209.Google Scholar
Wimsatt, W. C. (1981), “Robustness, Reliability, and Overdetermination”, in Brewer, M. and Collins, B. (eds.), Scientific Inquiry and the Social Sciences. San Francisco: Jossey-Bass, 124–163.Google Scholar