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.

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Personal case study on the usefulness of philosophy to biology

At the start of this month, one of my favourite blogs — Dynamic Ecology — pointed me to a great interview with Michela Massimi. She has recently won the Royal Society’s Wilkins-Bernal-Medawar Medal for the philosophy of science, and to celebrate Philip Ball interviewed her for Quanta. I recommend reading the whole interview, but for this post, I will focus on just one aspect.

Ball asked Massimi how she defends philosophy of science against dismissive comments by scientists like Feynman or Hawking. In response, she made the very important point that for the philosophy of science to be useful, it doesn’t need to be useful to science:

Dismissive claims by famous physicists that philosophy is either a useless intellectual exercise, or not on a par with physics because of being incapable of progress, seem to start from the false assumption that philosophy has to be of use for scientists or is of no use at all.

But all that matters is that it be of some use. We would not assess the intellectual value of Roman history in terms of how useful it might be to the Romans themselves. The same for archaeology and anthropology. Why should philosophy of science be any different?

Instead, philosophy is useful for humankind more generally. This is certainly true.

But even for a scientist who is only worrying about getting that next grant, or publishing that next flashy paper. For a scientist who is completely detached from the interests of humanity. Even for this scientist, I don’t think we have to concede the point on the usefulness of philosophy of science. Because philosophy, and philosophy of science in particular, doesn’t need to be useful to science. But it often is.

Here I want to give a personal example that I first shared in the comments on Dynamic Ecology.
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Token vs type fitness and abstraction in evolutionary biology

There are only twenty-six letters in the English alphabet, and yet there are more than twenty-six letters in this sentence. How do we make sense of this?

Ever since I first started collaborating with David Basanta and Jacob Scott back in 2012/13, a certain tension about evolutionary games has been gnawing at me. A feeling that a couple of different concepts are being swept up under the rug of a single name.[1] This feeling became stronger during my time at Moffitt, especially as I pushed for operationalizing evolutionary games. The measured games that I was imagining were simply not the same sort of thing as the games implemented in agent-based models. Finally this past November, as we were actually measuring the games that cancer plays, a way to make the tension clear finally crystallized for me: the difference between reductive and effective games could be linked to two different conceptions of fitness.

This showed a new door for me: philosophers of biology have already done extensive conceptual analysis of different versions of fitness. Unfortunately, due to various time pressures, I could only peak through the keyhole before rushing out my first draft on the two conceptions of evolutionary games. In particular, I didn’t connect directly to the philosophy literature and just named the underlying views of fitness after the names I’ve been giving to the games: reductive fitness and effective fitness.

Now, after a third of a year busy teaching and revising other work, I finally had a chance to open that door and read some of the philosophy literature. This has provided me with a better vocabulary and clearer categorization of fitness concepts. Instead of defining reductive vs effective fitness, the distinction I was looking for is between token fitness and type fitness. And in this post, I want to discuss that distinction. I will synthesize some of the existing work in a way that is relevant to separating reductive vs. effective games. In the process, I will highlight some missing points in the current debates. I suspect this points have been overlooked because most of the philosophers of biology are focused more on macroscopic organisms instead of the microscopic systems that motivated me.[2]

Say what you will of birds and ornithology, but I am finding reading philosophy of biology to be extremely useful for doing ‘actual’ biology. I hope that you will, too.

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Cataloging a sparse year of blogging: IMO workshop and preprints

Happy 2018!

With 2017 finally behind us, TheEGG enters its 8th calendar year. This past year has been a slow one for the blog, with only 10 new articles and two posts cataloguing 2016 (on cancer and on more theoretical aspects of evolution and general modelling). Half the months were barren: I posted nothing in March, April, May, July, August, September; and only October and November saw more than one post. But those two months of activity were good. We saw the list of TheEGG authors joined by David Robert Grimes, Vincent Cannataro, and Matthew Wicker; plus the return of Robert Vander Velde.

If you’re keeping score at home, this means that I only wrote six new articles last year.

As in the past, I want to start the new year by summarizing the old.

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Ontology of player & evolutionary game in reductive vs effective theory

In my views of game theory, I largely follow Ariel Rubinstein: game theory is a set of fables. A collection of heuristic models that helps us structure how we make sense of and communicate about the world. Evolutionary game theory was born of classic game theory theory through a series of analogies. These analogies are either generalizations or restrictions of the theory depending on if you’re thinking about the stories or the mathematics. Given this heuristic genealogy of the field — and my enjoyment of heuristic models — I usually do not worry too much about what exactly certain ontic terms like strategy, player, or game really mean or refer to. I am usually happy to leave these terms ambiguous so that they can motivate different readers to have different interpretations and subsequently push for different models of different experiments. I think it is essential for heuristic theories to foster this diverse creativity. Anything goes.

However, not everyone agrees with Ariel Rubinstein and me; some people think that EGT isn’t “just” heuristics. In fact, more recently, I have also shifted some of my uses of EGT from heuristics to abductions. When this happens, it is no longer acceptable for researchers to be willy-nilly with fundamental objects of the theory: strategies, players, and games.

The biggest culprit is the player. In particular, a lot of confusion stems from saying that “cells are players”. In this post, I’d like to explore two of the possible positions on what constitutes players and evolutionary games.

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Cataloging a year of cancer blogging: double goods, measuring games & resistance

Happy year of the Rooster and 2017,

This month marks the start of the 7th calendar year of updates on TheEGG. Time to celebrate and summarize the posts of the year past. In 2016 there was the same number of posts as 2015, but instead of being clustered in a period of <7 months, they were more uniformly distributed across the calendar. Every month had at least one new post, although not necessarily written by me (in the case of the single post by Abel Molina in October). There were 29 entries, one linkdex cataloging 2015, and two updates on EGT reading group 51 – 55 & 56 – 60.

In September, as part of my relocation from Tampa to Oxford, I attended the 4th Heidelberg Laureate Forum. I wrote two pieces for their blog: Alan Turing and science through the algorithmic lens and a spotlight on Jan Poleszczuk: from HLF2013 to mathematical oncology. You can read those (and more posts coming this year) on their blog. I won’t go into more detail here.

As before, this post is meant to serve as an organizing reference and a way to uncover common themes on TheEGG. A list of TL;DRs from 2016. The year was split up into four major categories: cancer, complexity & evolution, other models, and philosophy. The cancer posts make up almost half the articles from last year, and are further subdivided into three subsections: double goods game, experimental game theory, and therapy resistance. I want to focus on these cancer posts for this linkdex, and the other three categories in the next installment.

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Multiple realizability of replicator dynamics

Abstraction is my favorite part of mathematics. I find a certain beauty in seeing structures without their implementations, or structures that are preserved across various implementations. And although it seems possible to reason through analogy without (explicit) abstraction, I would not enjoy being restricted in such a way. In biology and medicine, however, I often find that one can get caught up in the concrete and particular. This makes it harder to remember that certain macro-dynamical properties can be abstracted and made independent of particular micro-dynamical implementations. In this post, I want to focus on a particular pet-peeve of mine: accounts of the replicator equation.

I will start with a brief philosophical detour through multiple realizability, and discuss the popular analogy of temperature. Then I will move on to the phenomenological definition of the replicator equation, and a few realizations. A particular target will be the statement I’ve been hearing too often recently: replicator dynamics are only true for a very large but fixed-size well-mixed population.

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Choosing units of size for populations of cells

Recently, I have been interacting more and more closely with experiment. This has put me in the fortunate position of balancing the design and analysis of both theoretical and experimental models. It is tempting to think of theorists as people that come up with ideas to explain an existing body of facts, and of mathematical modelers as people that try to explain (or represent) an existing experiment. But in healthy collaboration, theory and experiment should walk hand it hand. If experiments pose our problems and our mathematical models are our tools then my insistence on pairing tools and problems (instead of ‘picking the best tool for the problem’) means that we should be willing to deform both for better communication in the pair.

Evolutionary game theory — and many other mechanistic models in mathematical oncology and elsewhere — typically tracks population dynamics, and thus sets population size (or proportions within a population) as central variables. Most models think of the units of population as individual organisms; in this post, I’ll stick to the petri dish and focus on cells as the individual organisms. We then try to figure out properties of these individual cells and their interactions based on prior experiments or our biological intuitions. Experimentalists also often reason in terms of individual cells, making them seem like a natural communication tool. Unfortunately, experiments and measurements themselves are usually not about cells. They are either of properties that are only meaningful at the population level — like fitness — or indirect proxies for counts of individual cells — like PSA or intensity of fluorescence. This often makes counts of individual cells into an inferred theoretical quantity and not a direct observable. And if we are going to introduce an extra theoretical term then parsimony begs for a justification.

But what is so special about the number of cells? In this post, I want to question the reasons to focus on individual cells (at the expense of other choices) as the basic atoms of our ontology.

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Measuring games in the Petri dish

For the next couple of months, Jeffrey Peacock is visiting Moffitt. He’s a 4th year medical student at the University of Central Florida with a background in microbiology and genetic engineering of bacteria and yeast. Together with Andriy Marusyk and Jacob Scott, he will move to human cells and run some in vitro experiments with non-small cell lung cancer — you can read more about this on Connecting the Dots. Robert Vander Velde is also in the process of designing some experiments of his own. Both Jeff and Robert are interested in evolutionary game theory, so this is great opportunity for me to put my ideas on operationalization of replicator dynamics into practice.

In this post, I want to outline the basic process for measuring a game from in vitro experiments. Games in the Petri-dish. It won’t be as action packed as Agar.io — that’s an actual MMO cells-in-Petri-dish game; play here — but hopefully it will be more grounded in reality. I will introduce the gain function, show how to measure it, and stress the importance of quantifying the error on this measurement. Since this is part of the theoretical preliminaries for my collaborations, we don’t have our own data to share yet, so I will provide an illustrative cartoon with data from Archetti et al. (2015). Finally, I will show what sort of data would rule-out the theoretician’s favourite matrix games and discuss the ego-centric representation of two-strategy matrix games. The hope is that we can use this work to go from heuristic guesses at what sort of games microbes or cancer cells might play to actually measuring those games.
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Abusing numbers and the importance of type checking

What would you say if I told you that I could count to infinity on my hands? Infinity is large, and I have a typical number of fingers. Surely, I must be joking. Well, let me guide you through my process. Since you can’t see me right now, you will have to imagine my hands. When I hold out the thumb on my left hand, that’s one, and when I hold up the thumb and the index finger, that’s two. Actually, we should be more rigorous, since you are imagining my fingers, it actually isn’t one and two, but i and 2i. This is why they call them imaginary numbers.

Let’s continue the process of extending my (imaginary) fingers from the leftmost digits towards the right. When I hold out my whole left hand and the pinky, ring, and middle fingers on my right hand, I have reached 8i.

But this doesn’t look like what I promised. For the final step, we need to remember the geometric interpretation of complex numbers. Multiplying by i is the same thing as rotating counter-clockwise by 90 degrees in the plane. So, let’s rotate our number by 90 degrees and arrive at \infty.

I just counted to infinity on my hands.

Of course, I can’t stop at a joke. I need to overanalyze it. There is something for scientists to learn from the error that makes this joke. The disregard for the type of objects and jumping between two different — and usually incompatible — ways of interpreting the same symbol is something that scientists, both modelers and experimentalists, have to worry about it.

Rigorous proof

If you want an actually funny joke of this type then I recommend the image of a ‘rigorous proof’ above that was tweeted by Moshe Vardi. My writen version was inspired by a variant on this theme mentioned on Reddit by jagr2808.

I will focus this post on the use of types from my experience with stoichiometry in physics. Units in physics allow us to perform sanity checks after long derivations, imagine idealized experiments, and can even suggest refinements of theory. These are all features that evolutionary game theory, and mathematical biology more broadly, could benefit from. And something to keep in mind as clinicians, biologists, and modelers join forces this week during the 5th annual IMO Workshop at the Moffitt Cancer Center.

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