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Explaining the behaviour of random ecological networks: the stability of the microbiome as a case of integrative pluralism

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Abstract

Explaining the behaviour of ecosystems is one of the key challenges for the biological sciences. Since 2000, new-mechanism has been the main model to account for the nature of scientific explanation in biology. The universality of the new-mechanist view in biology has been however put into question due to the existence of explanations that account for some biological phenomena in terms of their mathematical properties (mathematical explanations). Supporters of mathematical explanation have argued that the explanation of the behaviour of ecosystems is usually provided in terms of their mathematical properties, and not in mechanistic terms. They have intensively studied the explanation of the properties of ecosystems that behave following the rules of a non-random network. However, no attention has been devoted to the study of the nature of the explanation in those that form a random network. In this paper, we cover that gap by analysing the explanation of the stability behaviour of the microbiome recently elaborated by Coyte and colleagues, to determine whether it fits with the model of explanation suggested by the new-mechanists or by the defenders of mathematical explanation. Our analysis of this case study supports three theses: (1) that the explanation is not given solely in terms of mechanisms, as the new-mechanists understand the concept; (2) that the mathematical properties that describe the system play an essential explanatory role, but they do not exhaust the explanation; (3) that a non-previously identified appeal to the type of interactions that the entities in the network can exhibit, as well as their abundance, is also necessary for Coyte and colleagues’ account to be fully explanatory. From the combination of these three theses we argue for the necessity of an integrative pluralist view of the nature of behaviour explanation when this is given by appealing to the existence of a random network.

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Fig. 1

(From Sporns et al. 2004: p. 419)

Fig. 2

(From Coyte et al. (2015: Supplementary Figure 1C)

Fig. 3

(From Coyte et al. 2015: Supplementary Figure 1D)

Fig. 4

(From Coyte et al. 2015: SM. Figure S3)

Fig. 5

(From Coyte et al. 2015: Supplementary Figure S4)

Fig. 6

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Notes

  1. To refer to mathematical explanations as “structural explanations” might be confusing, since the later could be interpreted as special cases of the former, as one reviewer has correctly suggested. However, the way in which Huneman (2018a) describes them, as well as the family of explanations that he includes under the umbrella of “structural explanations” makes clear that the two are synonymous. For purposes of clarity, however, we will refer to this family of explanations as “mathematical explanations”.

  2. We take all the aforementioned properties to be different types of mathematical properties.

  3. The exact definition of stability is an agitated topic in ecology, and different diversity-stability hypotheses are formulated accordingly (McCann 2000: p. 230, Table 1; Nikisianis and Stamou 2016: pp. 35–36; Gonze et al. 2018: p. 42, Box 1). In most cases, though, a system is qualified as stable if and only if it is able to return to its initial state after a perturbation (resilience), or also the capacity of a population to resist invasions by external species. We will specify later what “stability” means in our case study.

  4. In ecology, the concept of “stability” can be used to mean both that the number of species of the microbiome remains constant (i.e. that no species gets extinguished, also called persistence), and that the species density in the community recovers quickly after the community has been perturbed (i.e. once the density of one of the species in the community has slightly changed, also called resilience). A community whose species density remains constant is said to be in equilibrium. Obviously, if a community is stable in the second sense, it will also be stable in the first sense, but the opposite is not necessarily the case. In the case study that we present here, “stability” refers to the ability of the microbiome to recover its initial species density after a perturbation, i.e. it is a model to study resilience.

  5. Their research consists in three different mathematical methods. In method 1 (linear stability analysis), they only consider communities that are close to equilibrium, while in methods 2 and 3 (permanence analysis, individual-based model) they investigate the behaviour of communities that are far from their equilibrium. Those two later methods yield the same results as the former (cooperation destabilizes communities). For reasons of space, we only consider method 1 for our analysis of the nature of explanation.

  6. We will use “stable points” to refer to what mathematically are defined as “asymptotically stable points”.

  7. In their model, Coyte et al. do not exactly determine at which point the system will become unstable. It is enough for their explanation to show the general tendency of the community to an increasing value of Pm.

  8. Our argument in this section is inspired by a similar argument presented in Issad and Malaterre (2015: p. 284).

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Acknowledgements

A previous version of this paper was presented at the IX Conference of the Spanish Society for Logic, Methodology and Philosophy of Science (UNED, Madrid, 2018). We acknowledge all the participants for their helpful suggestions. José Díez, Johannes Findl, Christophe Malaterre, Eric Muszynski, and two anonymous reviewers provided insightful comments on a previous version of the paper. APC and JS are especially thankful to Sabina Leonelli, who had the idea of bringing together researchers from the Living Systems Institute and Egenis (University of Exeter), and thanks to whom the authors met and started to think about the issues that gave origin to this paper. The following institutions are formally acknowledged: RD and JS, Spanish Ministry of Economy and Competitiveness (FFI2016-76799-P); RD, Spanish Ministry of Economy and Competitiveness (BES-2013-063239); JS, Spanish Ministry of Education (FFU16/02570). APC, Spanish Ministry of Economy and Competitiveness (MTM2012-31714).

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Authors and Affiliations

  1. Logos – Research Group in Analytic Philosophy, University of Barcelona, Barcelona, Spain

    Roger Deulofeu & Javier Suárez

  2. Egenis – The Centre for the Study of Life Sciences, University of Exeter, Exeter, UK

    Javier Suárez

  3. Department of Mathematics, Universitat Politècnica de Catalunya, Barcelona, Spain

    Alberto Pérez-Cervera

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  1. Roger Deulofeu
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Correspondence to Roger Deulofeu.

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The paper is the result of the discussion among the three authors, who actively collaborated in the development of all the ideas. JS conceived and structured it. RD and APC wrote Section 3. RD and JS wrote the philosophical analysis.

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Deulofeu, R., Suárez, J. & Pérez-Cervera, A. Explaining the behaviour of random ecological networks: the stability of the microbiome as a case of integrative pluralism. Synthese 198, 2003–2025 (2021). https://doi.org/10.1007/s11229-019-02187-9

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