Modeling for metascientists: some first steps

Minhua Yan

Part 5 of the 6-part series, Modeling for metascientists (and other interesting people).

Hopefully you are now convinced that formal models are useful tools to help scientists understand the world. As an anthropologist with training in evolutionary biology who started her career as a modeler, I chose to do mathematical modeling because models have the following three advantages:

1. Compared to the real world, models are simple and easy to understand.
2. Compared to verbal models (which all researchers use), models are clear and transparent and are more likely to generate precise and valid predictions.
3. Compared to experiments, models can test hypotheses (or at least, their logic) more conveniently.

This last feature is especially relevant for metascience: we often can’t feasibly run experiments on the entire scientific community to modify incentive structures and just see what happens, but with mathematical models, we can easily create a toy world in which we can rapidly explore a wide range of ideas.

When I was first introduced to metascience, I was pleasantly surprised to find that evolutionary biological theories and methods were being actively applied. The ability of evolutionary game theory and evolutionary dynamics to inform scientific reforms is not surprising. After all, scientists are social organisms. Their payoffs depend on their peers’ strategies, and their success determines how likely they are to “survive” or “reproduce”, that is, to stay in academia and pass their scientific practices on to the next generation of scientists. What surprised me was how much researchers in metascience acknowledge the value of formal models. This level of appreciation is, unfortunately, not shown in every field that can benefit from modeling work. It is assuring to know that metascientists, who devote themselves to improving science itself, are using sound methods to achieve this goal.

The question remains: what should an empiricist do, if they do not have the necessary skills in mathematical modeling?

I see three options, with increasing technological difficulty:

1. Ignore mathematical models completely (please don’t choose this)
2. Collaborate with modelers without learning how to solve equations or write codes
3. Learn how to design and implement models oneself.

Now, between options 2 and 3, which one is more desirable?

I think that the decision is not either-or, but rather how much to invest in individual learning. Of course, the answer depends on your research agenda and career stage. If you frequently rely on mathematical models to generate results and can comfortably invest in new skills, I would recommend learning both the principles and technologies in mathematical modeling. It will, however, require some basic mathematical skills. Derivatives and integrals are often used to find the evolutionarily stable strategy and used in games with continuous strategies. Knowledge about matrix operations can help one write more efficient Matlab or R codes. Due to its technological difficulties and consequent time investment, this option is not for everyone.

On the other hand, if you exclusively work with empirical data, or do not have the capacity to learn all these techniques, just learning the principles is a more sensible decision. In this case, a good place to start might be this paper, which provides ten simple rules for tackling your first mathematical model.

You may also want to sit in an undergraduate level class on models in evolutionary biology or read through some classical toy models. In particular, work through the Hawk-Dove game to familiarize yourself with how to read a payoff matrix, how to calculate the expected payoff of a strategy, how to construct the next generation based on different strategies’ payoffs in a game with discrete strategies, and understand the concept of an evolutionarily stable state (a state that can sustain itself against the appearance of rare mutant strategies). For the Hawk-Dove game, you can check out section A in Chapter 2 of Evolution and the Theory of Games by John Maynard Smith. Its Kindle version is available for free for 7 days through Amazon.

I suggested learning the principles for even those who work exclusively with empirical data, because any researcher (or in fact, any individual) who wants to improve their ability to think clearly can benefit from adopting the thinking scheme of a modeler. This means, when making or evaluating an argument, clearly lay out one’s assumptions, check whether these assumptions make sense, and think through to what results such assumptions may lead.

Our brains are imperfect and can easily make mistakes, particularly at that last step of thinking through the logical consequences of assumptions. This is precisely why modelers rely on math and codes. But even with only our computationally challenged human brains, progressing through the above logical steps can be easier once we have a bit more modeling experience, and is sure to yield more reliable insights than if we didn’t use models as scaffolds to help our brains make sense of the world.

Smith, J. M. (1982). Evolution and the Theory of Games. Cambridge university press.