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Using causal models to integrate proximate and ultimate causation

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Abstract

Ernst Mayr’s classical work on the nature of causation in biology has had a huge influence on biologists as well as philosophers. Although his distinction between proximate and ultimate causation recently came under criticism from those who emphasize the role of development in evolutionary processes, the formal relationship between these two notions remains elusive. Using causal graph theory, this paper offers a unified framework to systematically translate a given “proximate” causal structure into an “ultimate” evolutionary response, and illustrates evolutionary implications of various kinds of causal mechanisms including epigenetic inheritance, maternal effects, and niche construction. These results not only reveal the essential interplay between proximate and ultimate causation in the study of evolution, but also provide a formal method to evaluate or discover non-standard or yet unknown evolutionary phenomena.

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Notes

  1. For discussions about the (mis)uses of the proximate/approximate distinction in biological literatures, see e.g., Amundson (2005), Laland et al. (2011).

  2. Throughout this paper I use uppercase letters to denote random variables and lowercase letters to denote their values.

  3. For a derivation of the Price equation, see e.g., Okasha (2006).

  4. Equation 2 does not follow if \(W\) and \(Z\) are confounded by some common cause (Otsuka, forthcoming). But in this paper we ignore such cases.

  5. To be precise, such a systematic change in phenotypes may include migration as well as selection acting at lower levels, but in this paper I ignore them.

  6. This is the reason that the Price equation does not give a definitive answer to the question of causal agency in multi-level selection (Okasha 2006).

  7. To be precise, to calculate the mean of a variable one also needs to know its marginal distribution, which is also given through the structural equation and the distribution over its causes.

  8. On the other hand, an effect of litter size can be represented by drawing a causal arrow from parental fitness \(W\) to \(Z'\) (not shown in the graph), since by definition fitness is nothing but litter size. For the sake of simplicity in this paper we limit our attention to the univariate evolution of the maternal care trait alone, but the extension to include the simultaneous evolution of the care trait (e.g., lactation) and its beneficiary (e.g., body size) is straightforward.

  9. Kirkpatrick and Lande (1989) further showed that this term equals \(m \big [ \Delta \overline{Z}_{GP} - {{\mathrm{Var}}}(Z) \beta _{GP} \big ]\), where \(\Delta \overline{Z}_{GP}\) and \(\beta _{GP}\) are the evolutionary response and selection gradient in the previous generation, respectively. To derive this from Eq. 9, note that the mean after selection in the grandparent generation is given by \(\overline{Z}^*_{GP} = \overline{Z}_{GP} - S_{GP}\) where \(S_{GP} := {{\mathrm{Cov}}}(W_{GP}, Z_{GP}) = {{\mathrm{Var}}}(Z_{GP})\beta _{GP}\) is the selection differential. Their result follows from Eq. 9 by noting \(\Delta \overline{Z}_{GP} := \overline{Z} - \overline{Z}_{GP}\) and assuming a constant phenotypic variance between generations, i.e., \({{\mathrm{Var}}}(Z_{GP}) = {{\mathrm{Var}}}(Z)\).

  10. This entails that a nonlinear fitness function is not essential for a niche construction model to produce non-standard evolutionary dynamics.

  11. This point is often made by the distinction between the “functional” or “biochemical” epistasis and “statistical” epistasis (Wade 1992).

  12. The dependence relation may go the other way around, when one considers that organismal structures themselves are products of evolution. The relationship in reality is hence “reciprocal,” as Laland et al. (2011) note.

  13. One such example can be found in the opening remark of Maynard Smith’s Evolution and the Theory of Games, where he claims “One consequence of Weismann’s concept of the separation of germ line and soma was to make it possible to understand genetics, and hence evolution, without understanding development. [\(\ldots\)] We can progress towards understanding the evolution of adaptations without understanding how the relevant structures develop” (Maynard Smith 1982, p. 6).

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Acknowledgments

I thank James Griesemer, Elisabeth Lloyd, Samuel Ketcham, Kim Sterelny, and an anonymous reviewer for providing useful comments. Proofreading by Stephen Friesen is also appreciated. This work was supported by Japan Society for the Promotion of Science.

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  1. Department of Philosophy, University of California, Davis, 1240 Social Science and Humanities, One Shields Avenue, Davis, CA, 95616, USA

    Jun Otsuka

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Correspondence to Jun Otsuka.

Appendix: The trek rule

Appendix: The trek rule

For a linear system the covariance of two variables can be obtained by the method of path coefficients (Wright 1934), also known as the trek rule. A trek is any non-overlapping sequence of edges between two variables that does not contain a collider where two edges on the path collide at one variable (e.g., \(\rightarrow V \leftarrow\)). A trek thus defined is equivalent to a pair of directed paths that share the same source (but note that one of the pair may be empty). For each trek, we can calculate the trek coefficient by multiplying the variance of its source and all the linear coefficients on the edges constituting the trek. The trek rule states that the covariance of two variables equals the sum of trek coefficients over all the treks connecting them. That is, if \({\mathbf {T}}\) is the set of all the treks between \(X\) and \(Y\) and \(\beta _{ti}\) is the linear coefficient of the \(i\)th edge on \(t \in {\mathbf {T}}\),

$$\begin{aligned} {{\mathrm{Cov}}}(X, Y) = \sum _{t \in {\mathbf {T}}} \sigma ^2_t \prod _{i \in t} \beta _{ti} \end{aligned}$$

where \(\sigma ^2_t\) is the variance of the source of trek \(t\).

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Otsuka, J. Using causal models to integrate proximate and ultimate causation. Biol Philos 30, 19–37 (2015). https://doi.org/10.1007/s10539-014-9448-9

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