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Explaining Drift from a Deterministic Setting

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Abstract

Drift is often characterized in statistical terms. Yet such a purely statistical characterization is ambiguous for it can accept multiple physical interpretations. Because of this ambiguity it is important to distinguish what sorts of processes can lead to this statistical phenomenon. After presenting a physical interpretation of drift originating from the most popular interpretation of fitness, namely the propensity interpretation, I propose a different one starting from an analysis of the concept of drift made by Godfrey-Smith. Further on, I show how my interpretation relates to previous attempts to make sense of the notion of expected value in deterministic setups. The upshot of my analysis is a physical conception of drift that is compatible with both a deterministic and indeterministic world.

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Notes

  1. Note that this way of characterizing drift might not capture all the different meanings of drift used in the biological literature, but it captures some important meanings of it and is grounded in influential theoretical work (e.g., Grafen 2000; Rice 2004, 2008). For thorough reviews of the notion of drift see Plutynski (2007) and Millstein (2016).

  2. Note that strictly speaking expected reproductive outputs are just one way to characterize propensities. In simple models propensities can be reasonably approximated with expected value (e.g., Mills and Beatty 1979). But doing so leads to a number of problems (see, for instance, Beatty and Finsen 1989). A number of authors have proposed new propensity interpretations of fitness (e.g., Brandon 1990; Ramsey 2006; Pence and Ramsey 2013) or some other interpretation (e.g., Abrams 2009) that attempt to solve these problems.

  3. By “entity” I will mean any object of a population able to undergo evolution by natural selection (e.g., organism, gene, cell, group).

  4. Note that some could consider that small differences in the environment affecting reproductive outputs are in some sense the “brute indeterministic facts about reality” even though the setup is deterministic. This will not be the interpretation given here since by definition indeterministic facts cannot occur in a deterministic setup. I recognize that epistemically one might want to take some facts as indeterministic even though the setup is deterministic, but the epistemic and the ontological questions should not be confused.

  5. I am appealing here to the same kind of distinction made by Rosenberg (2001, pp. 537–538) between a statistical or indeterministic theory and an indeterministic world. Having a theory that is indeterministic does not imply that the world is and vice versa. Here the relevant distinction is that although a system might be deterministic, its input might not, and vice versa.

  6. Although, as Godfrey-Smith recognizes, the terms “intrinsic” and “extrinsic” are controversial in philosophy, I will follow him in his view that the main idea behind the distinction can be useful. For more on this distinction see Weatherson (2014).

  7. This consequence relies on the assumption that no asymmetric extrinsic properties (e.g., “being less tall than”) are involved in differences in reproductive outputs, in which case it would be impossible to have the same extrinsic property for all the members of a population. This assumption is of course far from any real biological case, but I use it merely to make a conceptual distinction.

  8. I use here Brandon’s (1990) notion of selective environment as all the factors surrounding an organism (or more generally an entity) that differentially affect its reproductive output when compared to another organism.

  9. This way of representing the environment in the context of evolutionary change is compatible with Abrams’s (2014) framework on environmental variation.

  10. Suppose, for instance, a case with ten possible microstates present in equal proportions. It would imply that entities encounter each microstate with equal probability (0.1).

  11. This explanation is to put in perspective the account proposed by Ramsey (2013), for whom drift results from the heterogeneity in the possible causes one entity can experience, leading to different reproductive outputs.

  12. Thanks to Kim Sterelny for bringing this case to my attention.

  13. According to Godfrey-Smith (2009, p. 63), this list of five parameters is incomplete and could include other features.

  14. For our purposes in this article this is equivalent to realized reproductive output.

  15. Specifically, the Breeder’s equation tells us that the response to selection R is equal to a selection differential S multiplied by heritability h 2 so that R = S × h 2.

  16. I write “usually” because some plants need fire for their seeds to germinate, for instance.

  17. This example is mistakenly attributed to Scriven (1959), who was rather talking of individuals sitting where a bomb or a tree falls.

  18. Note here that this problem is not encountered in Godfrey-Smith’s initial account. This is because in his account of drift, the parameter C introduces an element of randomness.

  19. Note that the contrapositive is not true: something unpredictable might not necessarily be random.

  20. Note however that some might want to define drift more broadly than it is classically done and include cases of correlated responses as cases of drift.

  21. Note that by “unpredictable” I am referring here to a single outcome. In the case of drift this would amount to the evolutionary success of a single allele. At the population level it is quite predictable that a population will exhibit drift.

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Acknowledgments

I am thankful to Mark Colyvan, Paul Griffiths, Aidan Lyon, Maureen O’Malley, Charles Pence, Arnaud Pocheville, and Kim Sterelny for their comments on a previous version of the manuscript. This research was supported under the Australian Research Council’s Discovery Projects funding scheme (Project Number DP150102875).

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  1. Department of Philosophy, History and Philosophy of Science Unit & Charles Perkins Centre, University of Sydney, Sydney, NSW, Australia

    Pierrick Bourrat

  2. Department of Philosophy, Macquarie University, Sydney, NSW, Australia

    Pierrick Bourrat

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Bourrat, P. Explaining Drift from a Deterministic Setting. Biol Theory 12, 27–38 (2017). https://doi.org/10.1007/s13752-016-0254-2

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