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Selection in a Complex World: Deriving Causality from Stable Equilibrium

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Abstract

It is an ongoing controversy whether natural selection is a cause of population change, or a mere statistical description of how individual births and deaths accumulate. In this paper I restate the problem in terms of the reference class problem, and propose how the structure of stable equilibrium can provide a solution in continuity with biological practice. Insofar natural selection can be understood as a tendency towards equilibrium, key statisticalist criticisms are avoided. Further, in a modification of the Newtonian-force analogy, it can be suggested that a better metaphor for natural selection is that of an emergent force, similar in nature to entropic forces: with magnitude and direction, but lacking a spatiotemporal origin or point of application.

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Notes

  1. There is no consensus as to what precisely are the defining conditions (e.g. additivity) of Newtonian forces. A detailed discussion of this would bring us too far from the main argument of this paper, but see Wilson (2007) or Stephens (2010).

  2. Verlinde (2011) describes an entropic force as an “effective macroscopic force that originates in a system with many degrees of freedom by the statistical tendency to increase its entropy.”

  3. To emphasize: complexity is here taken to refer to the number of degrees of freedom, not functional complexity, or number of part-types (see Strevens 2003; McShea 2000).

  4. There are more accurate and sophisticated measures of fitness available (such as Pence and Ramsey 2013b): see the discussion of fitness models later on.

  5. Note that in this way I do not view what is sometimes termed the ‘metrological’ and ‘conceptual’ roles of fitness (Pence and Ramsey 2013a) as wholly independent. Constructing quantitative fitness measures and estimating fitness values is surely a separate endeavor from investigating whether fitness as a concept allows for some causal interpretation. Nonetheless, the statisticalist argument against the possibility of a privileged estimation of fitness as quantitative measure—i.e., the argument that any quantitative measure of fitness is unavoidably dependent on explanatory interests—casts serious doubt on fitness as causal concept.

  6. This is continuous with Huneman’s (2012) definition of selection pressures as ecological “reliable factors which differentially affect the trait types” (185). The only difference is that reliableness is specifically defined here in reference to an effective directionality.

  7. Determining the response to selection when traits are correlated through nonadditive genetic effects is more complicated, but there are methods using multivariate regression, such as Lande’s equation: \(R = \mathbf {G} \mathbf P ^{-1} \mathbf {s}\), where \(\mathbf {G}\) and \( \mathbf {P}\) are the additive genetic and phenotypic variance-covariance matrices. In its canonical formulation, this equation describes the response within a generation (see Lande and Arnold 1983), so it could be conceivably extended to describe the effective response over multiple generations by means of an effective selection coefficient vector: \(R_{eff} = \mathbf {G} \mathbf P ^{-1} \mathbf {s_{eff}}.\)

  8. See also Abrams (2009) for a discussion of how what Abrams calls the ‘reference environment’ is dependent on the target explanandum.

  9. In this respect, the account presented here is continuous with the suggestion that natural selection is a structuring cause in the space of population life-histories (Ramsey 2015). See also Kaplan (2013) for the suggestion that natural selection is some measure of robustness.

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Acknowledgments

I would wish to thank Michael Strevens, Grant Ramsey, Andreas De Block, Charles Pence, Philippe Huneman and an anonymous referee for helpful comments on previous versions of this paper.

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  1. Higher Institute of Philosophy, KULeuven, Blijde Inkomststraat 108/11, 3000, Leuven, Belgium

    Hugh Desmond

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Correspondence to Hugh Desmond.

Appendix: Instability of H–W Equilibria

Appendix: Instability of H–W Equilibria

First, let us investigate when two distributions (p, q, r) and \((p',q',r')\) will give rise to the same H–W equilibrium. Then the following three identities must hold:

$$\begin{aligned} p+q+r&= {p' + q' + r' =1}\\ p+q/2&= p' + q'/2\\ r+q/2&= r' + q'/2 \end{aligned}$$

These equations are dependent, and taking \(r'\) as a parameter, we get the following set of solutions \(\{(p-r+r', 1-p+r-2r',r')|r' \in [0,1]\}\). This can be simplified with the change of variable \(\delta = r' - r\), and thus we can say that the basin of the H–W equilibrium \(((p+q/2)^2,2(p+q/2)(r+q/2),(r+q/2)^2)\) is

$$\begin{aligned} \{(p+\delta , q-2\delta ,r+\delta )|\delta \in [-r,1-r]\}. \end{aligned}$$

The basin of a single H–W equilibrium point is the line with direction \((1,-2,1)\) in distribution space. As one would expect, by letting \(\delta = (p + q/2)^2 - p\) one can see that the H–W equilibrium itself is part of its own basin.

Hence we may conclude that there is no open neighbourhood \(\mathcal {N}\) around any H–W point (p, q, r) such that N is enclosed by the basin of (p, q, r). H–W equilibria are stable only along one specific line, and hence are unstable equilibria.

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Desmond, H. Selection in a Complex World: Deriving Causality from Stable Equilibrium. Erkenn 83, 265–286 (2018). https://doi.org/10.1007/s10670-017-9889-z

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