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Diversifying the picture of explanations in biological sciences: ways of combining topology with mechanisms

  • S.I.: Mechanistic & Topological
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Abstract

Besides mechanistic explanations of phenomena, which have been seriously investigated in the last decade, biology and ecology also include explanations that pinpoint specific mathematical properties as explanatory of the explanandum under focus. Among these structural explanations, one finds topological explanations, and recent science pervasively relies on them. This reliance is especially due to the necessity to model large sets of data with no practical possibility to track the proper activities of all the numerous entities. The paper first defines topological explanations and then explains why topological explanations and mechanisms are different in principle. Then it shows that they are pervasive both in the study of networks—whose importance has been increasingly acknowledged at each level of the biological hierarchy—and in contexts where the notion of selective neutrality is crucial; this allows me to capture the difference between mechanisms and topological explanations in terms of practical modelling practices. The rest of the paper investigates how in practice mechanisms and topologies are combined. They may be articulated in theoretical structures and explanatory strategies, first through a relation of constraint, second in interlevel theories (Sect. 3), or they may condition each other (Sect. 4). Finally, I explore how a particular model can integrate mechanistic informations, by focusing on the recent practice of merging networks in ecology and its consequences upon multiscale modelling (Sect. 5).

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Notes

  1. See Potochnik (2009) and Rose and Lauder (1996) on optimisation in behavioural ecology.

  2. One is however entitled to say that these properties are secondarily properties of the system itself. Think of properties of a food web of an ecological community, for instance: such a property can legitimately be seen as a property of the community itself.

  3. In this context one can of course recall that historically the same problem was at the source of topology and of graph theory—i.e. the “bridges of Königsberg” problem, namely, the problem of knowing whether there exists one pathway through which a traveller can cross all the seven bridges of Königsberg just once. Euler solved it, laying the bases of topology and later graph theory. The answer is negative. All the graphs with seven “bridges” (i.e. “edges” in graph theory) that are such that no such pathway exists are therefore equivalent regarding any permutation of vertices—and the same thing holds for all networks that allow one pathway with exactly one double crossing, etc.

  4. The homonymy is damageable but it is present in the literature, therefore I keep the same word, and prefer not to use artificial typographical tools (indices etc.) to indicate the difference; it should be clear enough according to the contexts.

  5. In what follows, “mechanistic model” refers to the scientists’ common use of distinguishing mechanistic and phenomenological models; “mechanistic explanations” refer to the explanations in which mathematics have a merely representational use, which is taken by the “new mechanicists” as a property of any explanation in neuroscience (at least until examples of the contrary are given).

  6. “Mathematical description, while not essential to all mechanistic explanations, is certainly a useful tool for characterizing the complex interactions among components in even moderately complicated mechanisms” (p. 606).

  7. In the former example of the keys, the “organization”, in the sense of the link between two states (correspondence/no correspondence) and the motion of the lock, plays a heavy role.

  8. More precisely the isomorphism holds between “data model” and “theoretical model”. One could argue that this is one kind of relation between pattern models (a form of data model) and mechanistic model but it is left out of this paper.

  9. Or, according to another interpretation, evolution of sets of genotypes in an abstract space—in each case one axis is the fitness, either of the population characterized by a specific repartition of alleles, or of the genotype constituted by the alleles.

  10. “Populations can evolve and diverge along bands of highly-fit genotypes without going across the states with a large number of low-fit genotypes (that is without crossing any adaptive valleys)” (Gavrilets 1999, p. 3).

  11. “Extended (nearly) neutral networks are important in adaptation for they can be “used” by a population to find areas in genotype space with higher fitness value.” (Gavrilets 2003, p. 149).

  12. “Connectivity analysis has already led to a number of new insights about brain organization. For example, segregated brain regions may be identified by their unique patterns of connectivity, structural and functional connectivity may be compared to elucidate how dynamic interactions arise from the anatomical substrate, and the architecture of large-scale networks connecting sets of brain regions may be analyzed in detail” (Behren and Sporns 2011, p. 144). But see Craver (forth.) for a defence that these models are not explanatory.

  13. Notice that the edges in the graph do not represent interactions but relations defined by the result of some interactions.

  14. For example, Craver (2007) writes: “there is a temptation to say that the activation of cyclic GMP phosphodiesterase, which catalyzes the conversion of cyclic GMP to 5c/-GMP, causes rod cells to hyperpolarize, which in turn causes the eye to transduce light into neural activity. But the activation of cyclic GMP phosphodiesterase is part of the activity of depolarization, which is part of the eye’s transduction of light” (p. 15).

  15. This paper is not committed to the validity of any version of the Gaia hypothesis, the example is just chosen for its simplicity.

  16. I’m of course not claiming that frequency-dependence prevent natural selection to lead to equilibria, since such equilibria are pervasive in behavioural ecology. The point is rather that frequency-dependent selection models, when they account for adaptive evolution and extant equilibria, do implicitly assume this clause, which is indeed rather mild.

  17. Note that the status of this clause parallels the condition of heritability, necessary for having evolution by natural selection—if heritability is too low, natural selection may change frequencies of traits and alleles but only for one generation, and thus no evolution (and especially the cumulative selection that gives rise to adaptive evolution) would be possible (Brandon 2008).

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Acknowledgments

The author warmly thanks Isabelle Drouet, Daniel Kostic, Carl Craver, Anya Plutynski, Denis Walsh, and the participants of the Topology and mechanisms conference in Belgrade (2013) for their feedbacks (2012). Many thanks to two anonymous reviewers for their hugely constructive criticisms. This work is supported by the ANR Grant Explabio (#ANR 13-BSH3-0007).

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    Philippe Huneman

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Huneman, P. Diversifying the picture of explanations in biological sciences: ways of combining topology with mechanisms. Synthese 195, 115–146 (2018). https://doi.org/10.1007/s11229-015-0808-z

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