# John Maynard Smith on reductive vs effective thinking about evolution

“The logic of animal conflict” — a 1973 paper by Maynard Smith and Price — is usually taken as the starting for evolutionary game theory. And as far as I am an evolutionary game theorists, it influences my thinking. Most recently, this thinking has led me to the conclusion that there are two difference conceptions of evolutionary games possible: reductive vs. effective. However, I don’t think that this would have come as much of a surprise to Maynard Smith and Price. In fact, the two men embodied the two different ways of thinking that underlay my two interpretations.

I was recently reminded of this when Aakash Pandey shared a Web of Stories interview with John Maynard Smith. This is a 4 minute snippet of a long interview with Maynard Smith. In the snippet, he starts with a discussion of the Price equation (or Price’s theorem, if you want to have that debate) but quickly digresses to a discussion of the two kinds of mathematical theories that can be made in science. He identifies himself with the reductive view and Price with the effective. I recommend watching the whole video, although I’ll quote relavent passages below.

In this post, I’ll present Maynard Smith’s distinction on the two types of thinking in evolutionary models. But I will do this in my own terminology to stress the connections to my recent work on evolutionary games. However, I don’t think this distinction is limited to evolutionary game theory. As Maynard Smith suggests in the video, it extends to all of evolutionary biology and maybe scientific modelling more generally.

As I’ve stressed before, I think that a distinction of fundamental importance is the philosophical distinction between tokens and types. Maynard Smith echoes this when he looks at “two kinds of mathematical or formal theory that one can make in science.” Turning first to tokens, he talks of a “microscopic theory” where “you try to explain the behavior of something in terms of its components [i.e tokens] and the way they interact”. The physics example of this would be statistical mechanics and describing gases in terms of how individual tokens of molecules bump into each other. Unsurprisingly, I would call this a reductive model.

Maynard Smith contrasts these reductive theories with “what one might call phenomenological theories which describe behaviour of systems in terms of measures made on whole things.” The physics example of this would be the “classical thermodynamics developed by Gibbs in which you ascribe properties like temperature and entropy (and so on) to the system as a whole and you write down relations about how those global properties will change.” Here, by focusing on “whole things”, he is shifting to the language of types. In particular, the “global properties” become attributed to types and are functions of types. More importantly — at least for my recent post on abstraction — these types are realizable or implementable by various assortments and arrangements of tokens. This is an effective model.

I choose the label of ‘effective’ instead of ‘phenomenological’ for a few reasons. The first is pronunciation: I struggle with ‘phenomenological’ (although not as much as I struggle with ‘meteorologist’). The second reason is that I want to allow for the possibility of effective theories that are not experimentally measurable. Or, in the language of Maynard Smith, where only a hypothetical measure exists. Non-experimental measures seem at odds with the term ‘phenomenological’, since such theories are always defined in terms of direct observations. But they seem less at odds with ‘effective’, even though effective theories in physics are still usually defined in terms of observable effects. The third reason is that I want to contrast with reductive theories on the context of scale and causality. Reductive theories always want to be read as causal explanations on the microdynamic scale. Effects, however, are macroscopic properties and do not always make claims to causation or some clear ontological grounding. The final reason is that population genetics already has terms like “effective population size” but not terms like “phenomenological population size”.

However we name them, reductive vs effective provide two different approaches to modelling and theory building. For Maynard Smith, “most scientists think in one of those modes, but not both”. And many phenomena in science can be described from either (or both) perspectives. In this way, I think this has some overlap with Jeremy Fox’s dynamic vs regression dichotomy for thinking about ecology. On the one hand, the two distinctions have some similarities. For example, Aakash Pandey suggests putting them along a spectrum from reductive (dynamic) models to effective models to regression. On the other hand, I think the two distinctions are orthogonal to each other. Although as I described them here, I think that Fox would view both reductive and effective theories as dynamic thinking. But that is a clarification for another post.

In his dichotomy, Maynard Smith viewed himself as a “microscopic man” and felt more at home with reductive models. In contrast, George R. Price was an effective man. In their joint work on the logic of animal conflict — or less charitably, in Maynard Smith grasping Price’s unpublished ‘Antlers, Intraspecific Combat, and Altruism’ — we can see hints of both modes of thought. In particular, the paper has a pay-off matrix, but the entries of that matrix are generated by many runs of simulated conflicts between two combatants that decide many moves one after the other in succession. In this way, we have a simple type-level average of a token-level process. However, the rest of the interpretations are given primarily from the reductive token-level perspective. And of course, effective games are about more than just averaging. Maynard Smith claimed the credit for introducing game theory to biology and he was much more influential in EGT — writing the foundational textbook. As such, his token-level reductive view of EGT dominates the field. However, I think it is fun to imagine how a more type-level friendly theorist like Price might have developed EGT and what he would have thought of effective games.

What about you, dear reader: are you a reductive or effective thinker when it comes to evolution?