On 50 years of the Price equation: looking back vs. looking ahead

50 years ago, George Price published an equation in Nature, applying to any instance of evolution by natural selection. The equation partitioned total directional evolutionary change into components attributable to different evolutionary forces. The paper was so original, it cited nothing. It attracted relatively little notice at the time, and what notice it did attract was strikingly wide-ranging. Bill Hamilton regarded the equation as a deep fundamental insight, while Richard Lewontin dismissed it as trivial (before later changing his mind). Interest in the equation grew over time, as it came to be widely applied to a range of problems both within and outside evolutionary biology.

The new issue of Philosophical Transactions of the Royal Society B, looks back on “50 years of the Price equation“. I read it with interest because I’m a Price equation user myself. Here are a few thoughts.

The issue lives up to its title: it’s almost entirely backward-looking, I presume intentionally so. There are review papers from most of the senior people in evolution theory who’ve written a lot about the Price equation over the last 20+ years–Steven Frank, Samir Okasha, David Queller, Andy Gardner, Sean Rice, Alan Grafen, Richard Michod, Matthijs van Veelen, Troy Day, Sylvain Gandon. Each mostly reviews their own work. There’s also a paper from Price’s biographer Oren Harman. And there are a few other papers, which are also review papers for the most part.

Your mileage may vary whether a backward-looking review is what you’re looking for. It’s certainly convenient one-stop shopping for anyone new to the Price equation, especially those working in social evolution. But given that there are recent reviews by many of these authors that cover this same ground, I’m not sure that convenience adds much value even for newbies. I dunno, not being a newbie to the Price equation myself, I’m not a good judge of what newbies would find useful here. For my own part, having read and admired many previous papers by many of these authors, I didn’t find anything new here. Perhaps I missed a novel nugget or two because I was reading quickly, but even if I did it wouldn’t change my overall impression.

So, selfishly, I found myself wishing for a different, more forward-looking compilation of papers. One that would look ahead to the next 50 years of the Price equation rather than back to the first 50. And one that would do more to connect the Price equation to broader conceptual issues in science and philosophy. Discussion of the Price equation within social evolution theory doesn’t seem to have advanced much lately, as best I can tell as an admitted outsider to that field. Maybe opening the windows and letting in some new ideas from other fields might freshen things up a bit? A forward-looking compilation might’ve asked questions like:

  • How can the Price equation be used outside of evolutionary theory? Do non-evolutionary applications of the Price equation shed any light on debates about the interpretation and value of the Price equation within evolution? And are there insights from discussions of the Price equation within evolutionary theory that ought to inform non-evolutionary applications of the Price equation? In particular, ecologists have been advancing the use of the Price equation as a data analytic tool, as opposed to a theoretical tool. See for instance the outstanding work of Lynn Govaert and her colleagues developing the Price equation as a practical empirical tool for teasing apart eco-evolutionary dynamics.
  • What are the commonalities and differences between the Price equation and other partitions? The Price equation is just one of many “partitions” in science (see here for some examples of ecological partitions). It seems to me that some conceptual debates about the value of partitions “run to type” in many areas of science; they aren’t specific to the Price equation. But other debates about the Price equation are specific to the Price equation. A comparative approach to thinking about the value of partitions might put some debates about the Price equation in a new light. For instance: Steven Frank argues that many key features of the Price equation, and mathematically-related approaches in other fields of science, are ultimately down to the fact that the Price equation describe zero-sum dynamics. For instance, allele frequencies at a given locus have to add up to 1, so any increase in the frequency of one allele has to come at the expense of some other allele(s). But there are many other partitions in science that do not describe zero-sum dynamics, or that describe dynamics that are only partially zero-sum (modern coexistence theory is one example of the latter, and the “additive partition” is another; see Fox 2005). What do partitions of non-zero-sum dynamics gain, and lose, in terms of interpetability from the fact that they lack the zero sum constraint?
  • A meta-question: What would it take to resolve some of the long-standing debates about the Price equation in future? And should we be concerned if the answer is “those long-standing debates are irresolvable, for reasons XYZ”?
  • Other questions I haven’t thought of. I’m sure that, like everyone, I tend to overrate the extent to which other people share my own personal interests. So I’m sure “forward-looking questions about the Price equation that I personally happen to find interesting” doesn’t overlap perfectly with “forward-looking questions about the Price equation that are actually interesting.”

George Price himself was one of the most original, creative scientific minds of the 20th century. We should recall his seminal contributions to evolutionary theory and how they’ve been built upon over the last 50 years. But we should also honor his legacy by continuing to think “outside the box” about his insights.


2 thoughts on “On 50 years of the Price equation: looking back vs. looking ahead

  1. I was hoping you had seen this issue – I am surprised you have pre-emptively answered a question I had about the issue regarding it being very much review-like and backward-looking. I’m not especially familiar with the area, but skimming the issue it did seem like most of it was about what had already been done, and besides the pieces arguing about validity, there wasn’t much in the way of “next steps” or far future research directions (that I saw on skimming at least).

    We’re currently organizing a Phil. Trans. A issue on a similarly-contested but established idea, and sent out invitations asking for opinion pieces/review articles. But what I have in mind is to really try and frame this issue in ways which are useful going forward, rather than just explain what we have done up to this point. Thanks for your data point that this is possibly a valuable approach!

    • I’m reassured that it wasn’t just me who found the Phil Trans issue on the Price equation very backwards-looking.

      Good luck with your Phil Trans A issue. Agree that something forward-looking is the way to go. The point of reviewing what’s been done before is so that we can build on it (or maybe discard it!) in future.

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