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Evolutionary game theory: a case of too much theory?

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by Alex Szorkovszky and Shyam Ranganathan

Back in the 90s, Paul Krugman presented a talk to his fellow economists about what they can learn from evolutionary biologists. After discussing various similarities and differences between the fields, he suggests: “that economics would be a more productive field if we learned something important from evolutionists: that models are metaphors, and that we should use them, not the other way around." Biologists 1 - Economists 0, is what  evolutionary biologists might conclude. But could it be the case that theoretical models have evolutionists in their grasp too?

We looked into the literature on evolutionary game theory to investigate this question. Our methodology is simple. We build a citation network of journal articles, classifying them as either "theory” papers that generate and work on models, or "data” papers that bring in new observations or analysis of existing data. These two categories account for most scientific journal articles. Review articles, which generally survey theory along with data, are put in a third category.

Krugman's quote suggests that metaphors should not take place of their subject of study. That is, that "modelling" should not be an end in itself in research. Models are an important part of studying evolution and we need people working exclusively on modelling or theory. But the real point of making models is to use them to answer interesting questions in evolutionary biology. So theoreticians would like other researchers to use these models on data. Not only should hypotheses be testable, they need to actively invite testing in the real world.

If biological researchers do not succumb to the metaphor, there will be a significant number of people writing "data" papers citing models developed by others.  On the other hand, if theoreticians are lost in the metaphor then there will be lots of just "theory" papers that do not explicitly apply models on data. If more people are writing "theory" papers than "data" papers, then there is the possibility evolutionary biologists are falling in to a similar trap as economists.

To evaluate the relative density of "theory" and "data" papers over time, we focus on a much smaller universe of papers stemming from John Maynard Smith and George Prices's seminal 1973 Nature paper "The Logic of Animal Conflict". Maynard Smith was the first to apply a game theoretical analysis, previously limited to the social sciences, to animal behaviour with the hawk-dove model. This paper radically extended game theory with the mathematical framework of Evolutionary Stable Strategies. While the analysis was of a simulation, it was very carefully modelled on existing empirical studies, and Maynard Smith’s further work gives clear advice for how to test the theory in the field (Maynard Smith, Evolution and the Theory of Games, ch. 7). “The Logic of Animal Conflict” has been cited around 1200 times in various disciplines, both theoretical and applied. There are any number of biases that are introduced by looking at this small subset of evolutionary biology research but it is an interesting question anyway.

We classify a paper as “data” if its abstract contains at least one of the following words:
observed, empirical* ,subjects, particip*, exhibit*, territor*, taxa, wild, habitat*, conspecific*
and neither of the following:
simulat*, dynam*

For a manually classified set of articles citing “The Logic of Animal Conflict”, we find that these words identify more than half of true data papers, with a false positive rate of around 10%. Note that apart from “subjects” and "particip(ant/s)", these lists are somewhat biased towards biological terminology, but are otherwise quite general.

We classified all articles since 1990 with abstracts on Web of Science that cite Maynard Smith and Price and sorted them according to year of publication.

maynardsmith

The heights of the red and blue areas above are proportional to the number of data and theory papers, respectively, in each year. Overall around one-third of citations involve data, and there are two periods with a significant jump in interest, one which is currently ongoing.

To explore this further, we found the top 10 articles citing "The Logic of Animal Conflict" according to the average number of citations per year, and did a similar analysis for each.

citesvstimeall2

Most explicitly theoretical papers have a fairly low data-to-theory ratio. This includes canonical papers in the field of adaptive dynamics, generally considered the mature offspring of evolutionary game theory, published in solidly biological journals. The recent surge of interest from the physics community, for whom behavioural dynamics provide exciting new mathematical problems, is certainly not helping matters (as has been well noted in the past).

It's not all bad news. Axelrod and Hamilton popularised the idea of the evolution of co-operation for the social sciences, and while these are deluged with game theoretical models (as Krugman laments above), Axelrod's computer tournaments have inspired many to do their own experiments. Johnson and Gaines’ review of the evolution of dispersal provides a good example for evolutionary biology, with their detailed overview of models and empirical work leading to a healthy data-to-theory ratio.

It seems that we can separate evolutionary game theory into communities, some of which are closer to data than others. In a future post we will explore this in much more detail using citation networks.