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Locating uncertainty in stochastic evolutionary models: divergence time estimation

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Abstract

Philosophers of biology have worked extensively on how we ought best to interpret the probabilities which arise throughout evolutionary theory. In spite of this substantial work, however, much of the debate has remained persistently intractable. I offer the example of Bayesian models of divergence time estimation (the determination of when two evolutionary lineages split) as a case study in how we might bring further resources from the biological literature to bear on these debates. These models offer us an example in which a number of different sources of uncertainty are combined to produce an estimate for a complex, unobservable quantity. These models have been carefully analyzed in recent biological work, which has determined the relationship between these sources of uncertainty (their relative importance and their disappearance in the limit of increasing data), both quantitatively and qualitatively. I suggest here that this case shows us the limitations of univocal analyses of probability in evolution, as well as the simple dichotomy between “subjective” and “objective” probabilities, and I conclude by gesturing toward ways in which we might introduce more sophisticated interpretive taxonomies of probability (modeled on some recent work in the philosophy of physics) as a path toward advancing debates on probability in the life sciences.

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Notes

  1. I thank a reviewer for noting that the mere use of the term ‘uncertainty’ here, which I have imported from the biological literature in an effort to avoid confusion with these sources, carries a strong philosophical implication that these probabilities are merely subjective; I will argue against this interpretation in what follows.

  2. For a host of further details, as well as worked-out examples for a number of clades, the interested reader can consult Benton et al. (2009).

  3. The constant factor of two, here, indicates that both lineages have continued to diverge since the original branching event.

  4. And, as already discussed, its traces in the fossil record, though we are not considering those at the moment. We will return to the question of combining fossil and molecular data shortly.

  5. Their model uses a per-locus-varying molecular clock, though, as they note, a relaxed-clock model is only likely to add further uncertainty.

  6. A reviewer has urged the point.

  7. Which one will often depend on the kind of analysis and the theory being considered. For instance, analyses of quantum mechanics tend to focus on (4), as QM offers us strict limits on what can be observed in principle (Earman 2007). In evolutionary biology, the focus of philosophers of biology on practical considerations tends to shift the analysis to (2), though some work (such as that on the empirical methods of measuring natural selection found in Endler 1986) focuses on instances of (1).

  8. To be clear, this is not a criticism of Werndl, for whom measure-theoretic models of particle location are the central example, and hence limits on accuracy are precisely the relevant focus of her work.

  9. Symmetry would argue for the introduction of (6\(^\star\)) uncertainty which enters into our measurements of a quantity as a feature of the models for estimating that quantity, which would be eliminable in principle (i.e., would disappear given the use of more sophisticated models). No (6\(^\star\))-type uncertainty seems to me to be present in the case study here, as it seems impossible to construct an identifiable model for divergence time.

  10. And not just biologists, either—see, for example, the robust literature on the tracking and management of uncertainty in climate science (e.g., Foley 2010).

  11. The already much-mentioned work of authors like Strevens and Abrams on the role of mechanistic probability provides one excellent example of this (Strevens 2011, 2013, 2016; Abrams 2012a, b, 2015).

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Acknowledgements

My sincere thanks to two anonymous reviewers for this journal, who very dramatically improved this paper (and caught a few serious errors!). For comments on a very early version of this project, thanks to an audience at the Models and Simulations 6 conference, at the University of Notre Dame. Many thanks also to Mario dos Reis for the initial inspiration behind the project, which was born at NESCent—still inspiring interdisciplinary work years after its unfortunate closure.

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  1. Institut supérieur de philosophie, Université catholique de Louvain, 1348, Louvain-la-Neuve, Belgium

    Charles H. Pence

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Pence, C.H. Locating uncertainty in stochastic evolutionary models: divergence time estimation. Biol Philos 34, 21 (2019). https://doi.org/10.1007/s10539-019-9683-1

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