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Robustness in evolutionary explanations: a positive account

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Abstract

Robustness analysis is widespread in science, but philosophers have struggled to justify its confirmatory power. We provide a positive account of robustness by analysing some explicit and implicit uses of within and across-model robustness in evolutionary theory. We argue that appeals to robustness are usually difficult to justify because they aim to increase the likeliness that a phenomenon obtains. However, we show that robust results are necessary (under certain conditions) for explanations of phenomena with specific properties. Across-model robustness is necessary for how-possibly explanations of multiply instantiated phenomena, while within-model robustness is necessary for explanations of phenomena with multiple evolutionary starting points. In such cases, the appeal of robustness is explanatory rather than confirmatory.

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Notes

  1. The how-actually/how-possibly distinction, due to Dray (1957), is taken up by Brandon (1990) in the context of evolutionary theory.

  2. McElreath and Boyd (2007) also mention one of the benefits of modelling approaches as providing ‘existence proofs’ (p. 6).

  3. This idea has been recently defended by Ylikoski and Aydinonat (2014), according to whom ‘the main point of theoretical how-possibly explanations is to refine, systematize, and expand the menu of available explanations’ (31). They particularly develop and emphasise this latter point.

  4. We are grateful to [redacted] for raising this issue.

  5. Bokulich’s account has been attacked for being too liberal; for instance, Saatsi and Pexton (2013) doubt “that capturing a mere abstract structure ‘up to isomorphism’ of counterfactual relations can be explanatory” (223–224), if such counterfactual relations cannot be causally interpreted. This need not concern us, as the explanatory targets of evolutionary models are fundamentally causal—although not necessarily governed by factors on which one could intervene.

  6. Brian Skyrms’ (2010) analysis of signalling systems contains other examples of this kind of reasoning.

  7. As noted by an anonymous referee, this is not to say that basin comparisons cannot be unproblematic in some cases, for instance when we compare basin sizes in two models that accurately represent two different systems.

  8. When the models differ E should not be considered as the same evidence for both, as it stands for “the behaviour of interest was obtained in some runs of the simulation”; strictly speaking we should write E1 and E2. However, this modification would only strengthen our point that the direct comparison between P(E|M1) and P(E|M2) is not necessarily insightful.

  9. One may further object that even if we accept that we can attribute probabilities to models, we could never assess these probabilities precisely. This does not matter here, as our discussion does not hinge on the precise values of the P(Mi) but on their equality.

  10. However, authors such as Sugden (2000) would disagree: he sees models as ‘credible fictions’, where credibility is not to be expressed in terms of a probability of being true – models are credible in the way fictions are.

  11. Two possible objections to the use of Bayesian formalism are that P(E) cannot be determined, as it involves considering an infinite number of models. However, only finitely many models can ever be considered. Moreover, the precise value of P(E) does not impinge on our discussion, provided it is not 0.

  12. We thank [redacted] for recommending the use of this Bayesian perspective.

  13. Specifically, if an equilibrium is a global, asymptotically stable attractor then the population reaches that equilibrium eventually. Alexander (2007) relies on similar robustness claims for spatially structured populations.

  14. This might for instance be true of models in which preferential interaction is not based on conditional strategies but on other sources of correlation such as spatially structured interactions or limited dispersal (not included in Skyrms’ aforementioned models).

  15. Since the model uses simulations to estimate basin sizes we cannot, in this case be sure that such a requirement is met.

  16. In a similar spirit, D’Arms et al.’s (1998) criticism of some earlier work of Skyrms can be read as mitigating conclusions drawn from considerating basins by emphasising the greater prior plausibility of alternative modelling assumptions.

  17. Skyrms at least has claimed that within-model robustness has explanatory value, although for unstated reasons: “The fact that the signalling system equilibrium is a global attractor […] and remains so if the replicator dynamics is replaced by any qualitatively adaptive dynamics, strikes me as explanatorily powerful.” (2000, 110).

  18. It corresponds to Woodward’s (2006) ‘causal robustness’ and to Calcott’s (2011) ‘robust phenomena’.

  19. Note that in the case of physical robustness, basin comparison approaches could be defended; our criticisms of “The basin comparison problem” section only bear on such approaches in the context of within-model robustness.

  20. Odenbaugh and Alexandrova (2011) also highlight a heuristic (rather than confirmatory) role of robustness analysis: it helps us identify acceptable candidate hypotheses. For Forber (2010), this role has indirect confirmatory consequences, as it affects the list of competing hypotheses later to be confirmed or disconfirmed.

  21. Again, this is not to say that models always need to represent the robustness of properties, if only because phenomena of interest may be robust with respect to myriad of parameters not represented in the model.

  22. Note that although Sugden (Ibid., 21–23) takes robustness as warranting model-to-model inferences, our defence argues for a model-to-world inference, in which a property of the target system should be similar to the robust model itself.

  23. For relevant examples about experiments on cooperative behaviour in microorganisms see Diggle et al. 2007, Gore et al. 2009, Popat et al. 2012 and Sanchez and Gore 2013.

  24. This is not to say that evolutionary theory is never mentioned in literature on robustness. For instance, Levins’ (1966) seminal paper deals with population biology, and Weisberg’s (2006) analysis focuses on Lotka–Volterra predator–prey models.

  25. Although the mechanisms of social learning and of natural selection differ, they share similar principles: a trait’s fixation respectively depends on its effect on fitness or its consequences for rewards (see Benaim et al. 2004). Moreover, models and their basins have similar importance for both, as Skyrms’ analysis renders manifest. Accordingly, we consider our focus on evolutionary models to include social learning.

  26. However, they do refer to general mechanisms and conditions not limited to signalling behaviour, such as imitative learning or freedom of interaction. These may constitute necessary conditions for a signalling model, but not its common core, because following Weisberg’s condition (2), the presence of such a common core would have to entail the evolution of signalling (to lead to a robust theorem), rather than being able to produce it. Imitative learning and freedom interaction are too general and high level to constitute a common core.

  27. Still, this is not impossible, as pointed out by [redacted].

  28. Note that if the phenomenon really is multiply instantiated, then we should only be satisfied with how-possibly explanations that are different enough, that is, that do not only aim to represent different causal scenarios but different causal mechanisms—a distinction found in Ylikoski and Aydinonat (2014). Where two causal scenarios are just alternative causal histories, which may disagree regarding only one fact, causal mechanisms are more general and involve types of causal links (and so may constitute ‘skeletons of causal processes’ (27) upon which detailed causal scenarios can be built).

  29. Also note that it does not draw on Bokulich’s account of explanation.

  30. Our positive take applies to robustness within one model and with respect to very different models, but probably not to robustness with respect to tractability or modelling assumptions, which have no clear real-world counterparts.

  31. If robustness analysis à la Weisberg aims to identify the common causal core responsible for a target phenomenon that occurs in several (possibly similar) contexts, then the absence of homogenous across-model robustness would actually provide reasons to look for heterogeneous across-model robustness.

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Acknowledgments

We thank Conor Mayo-Wilson, Seamus Bradley, Catherine Herfeld and Aidan Lyon for comments on previous versions of this paper, as well as the audiences of the Philosophy of Biology in the UK (2012) and of the BSPS 2013 conferences. The remarks of several anonymous referees also proved extremely valuable. Cédric Paternotte was supported by the Alexander von Humboldt Foundation.

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  1. Départment de Philosophie, Université Paris-Sorbonne, 1 rue Victor Cousin, 75006, Paris, France

    Cédric Paternotte

  2. Department of Philosophy, University of Bristol, Cotham House, Cotham Hill, BS6 6JL, Bristol, United Kingdom

    Jonathan Grose

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Correspondence to Cédric Paternotte.

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Paternotte, C., Grose, J. Robustness in evolutionary explanations: a positive account. Biol Philos 32, 73–96 (2017). https://doi.org/10.1007/s10539-016-9539-x

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