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Allometries and scaling laws interpreted as laws: a reply to Elgin

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Abstract

I analyze here biological regression equations known in the literature as allometries and scaling laws. My focus is on the alleged lawlike status of these equations. In particular I argue against recent views that regard allometries and scaling laws as representing universal, non-continent, and/or strict biological laws. Although allometries and scaling laws appear to be generalizations applying to many taxa, they are neither universal nor exceptionless. In fact there appear to be exceptions to all of them. Nor are the constants in allometries and scaling laws truly constant, stable, or universal in character, but vary in value across different taxa and background conditions. Moreover, these equations represent evolutionary, strongly contingent generalizations, which threatens their lawlike status. Lastly, allometries and scaling laws do not offer stable probabilities to which they hold in different backgrounds. I further suggest that many allometries and scaling laws function to elucidate explananda rather than explanantia or covering laws.

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Notes

  1. Lawlikeness is not only the distinctive property of laws; it is also the property that gives laws their support in counterfactuals or subjunctives. Counterfactual support of laws tells how laws govern not just what actually happens, but what would have happened under certain background conditions had they happened. In other words, laws do not just describe what happens in the world, but they also dictate what must happen and what would happen had the conditions been such-and-such or this-and-that. That laws support counterfactuals is what gives laws explanatory and predictive power, modal force, and necessity—or least it illuminates how they get these qualities. Given the points just outlined, it is natural to suppose that laws would be something over and above things that elucidate data from phenomena, namely, that they function as explanantia of phenomena.

  2. According to Bergmann’s rule, the members of a species of (endothermic) animals are larger in their body size in colder regions or at higher latitudes than members of the same species in warmer regions or at lower latitudes. According to Cope’s rule, there is a general evolutionary trend toward larger body size in many taxa.

  3. There is a distinction between allometries and scaling laws in the literature that is irrelevant to the present discussion: “‘[A]llometry’ is used to denote changes internal to the organisms that occur with size change (e.g., anatomical, metabolism, physiology). For changes external to the individual, such as in population density, predator or prey size, that occur with body-size increase, I use… [the] term’scaling’… This should help distinguish between two qualitatively different kinds of change that occur as an organism increases in size, dichotomising the changes that occur within the individual and those that reflect changes in interactions with its abiotic and biotic external environment” (McKinney 1990: 78).

  4. I have omitted error terms that represent variation in the dependent variable due to other possible independent variables and measurement errors in the independent variable.

  5. The evolutionary contingency thesis, along with many responses to it and its implications, for the existence of biological laws are discussed and analyzed in more detail by me elsewhere (see Raerinne forthcoming: Chapters 2 and 5). Although many think of weak contingency or “exceptions” as the central problem in the context of biological generalizations’ lawlikeness, this is probably a misapprehension, since there are accounts of laws that tolerate exceptions to them, such as the ceteris paribus account and the account that views biological generalizations as probabilistic laws. In other words, the central problem for the lawlikeness of biological generalizations is their strong contingency rather than weak contingency.

  6. The Hardy–Weinberg rule describes what will happen to gene and genotype frequencies in a population unaffected by evolutionary forces according to which both gene frequencies and genotype frequencies will remain constant in successive generations.

  7. Its probabilistic formulation would not affect the point I made here.

  8. I have discussed and criticized the ceteris paribus account of laws elsewhere (see Raerinne 2003), where I argue that the account raises several empirical, epistemological, and semantic problems that are unresolved, at least given the proposal of ceteris paribus laws in the literature (see also Schiffer 1991; Mott 1992; Wallis 1994; Earman and Roberts 1999; Schurz 2001, 2002; Earman et al. 2002; Mitchell 2002; Woodward 2002). In other words, it has proven to be difficult to define exactly what ceteris paribus clauses mean. If a more precise meaning or semantics is not given, then we have generalizations that are empirically, epistemologically, and semantically vague.

  9. Mitchell (1997, 2000), Lange (1993, 2005), and many others have suggested redefining laws—at least in part to respond to Beatty’s evolutionary contingency thesis—to redeem the lawlike status of biological generalizations. I have criticized such re-definitions of laws elsewhere (see Raerinne forthcoming: Chapters 3 and 5).

  10. In developing the above argument, I had ecological and paleobiological generalizations in mind. Some authors have suggested that generalizations from evolutionary biology, such as what Brandon (2006) have dubbed as “the principle of drift,” could be probabilistic laws. Although I think that the argument just presented applies to biological generalizations in general, I shall not argue for this here.

  11. According to the latitudinal diversity gradient, there exist a geographical or latitudinal gradient in species richness or diversity according to which 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.

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Acknowledgments

The work was supported financially by the Academy of Finland as a part of the project Modelling Mechanisms: A New Approach to Scientific Understanding and Inter-Disciplinary Integration (project number 112 2818). I am grateful to Markus Eronen and two anonymous referees for this journal that provided helpful comments and suggestions on a previous draft of this paper.

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  1. Department of Philosophy, History, Culture, and Art Studies, University of Helsinki, P.O. Box 24 (Unioninkatu 40 A), SF-00014, Helsinki, Finland

    Jani Raerinne

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Raerinne, J. Allometries and scaling laws interpreted as laws: a reply to Elgin. Biol Philos 26, 99–111 (2011). https://doi.org/10.1007/s10539-010-9203-9

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