We all knew it, but now it’s official: Tim W. Fawcett and Andrew D. Higginson show in a new PNAS article titled “Heavy use of equations impedes communication among biologists” that
The density of equations in an article [addition: in the field of ecology and evolution] has a significant negative impact on citation rates, with papers receiving 28% fewer citations overall for each additional equation per page in the main text. […] In contrast, equations presented in an accompanying appendix do not lessen a paper’s impact.
I suppose this doesn’t really come as a surprise to most people who observe the impact and citations of papers in ecology and evolution. The conclusion Fawcett and Higginson draw from this is that
- Equations negatively impact the success of a paper.
- Ideally, we would “enhance the technical understanding of biology graduates” so that equations do no longer hinder scientific communication, but because this is difficult to achieve, “a complementary and more immediate solution is for those doing theoretical work to describe their models in a way that can be more easily digested by a diverse audience”.
I think there is definitely some truth in both statements, but I have the feeling that there’s also some things that require a bit more thinking. Let me first reply to the first assertion.
1) Are equations really causal for the observed lower citation rates?
I’m sure equations have an effect, but I wonder how big this effect really is. The authors control for a few potentially confounding factors such as article length, but they leave out other factors that I would consider as strong candidates for confounding effects. Some of them are:
- Article type and target audience – Even in the same journal, I might be writing a review, or a broad paper to give an overview about a topic or some general results, or I might write a more specialized paper in order to communicate to the experts in the field. Depending on that, I will adjust the complexity of the presentation and the number of equations. It might so happen that more specialized papers are less cited, but the reason for this lower citations could well be that they are more specialized, and not that they use more equations.
- Topic – Nearly the same point could be made about the topic: some topics might require the use of more equations, and if it so happens that people are less interested in those topics, those papers get less cited, but the cause for the lower citations is the topic and not the equations
- Journal preferences – When writing for higher impact journals, people tend to use less equations. Most high impact journals such as Nature and Science put nearly all equations in an online appendix – sure, those papers get cited well (this point is controlled to a certain extent by the study though, but not fully).
In conclusion, my gut feeling is also that many equations are not attractive for the average ecological reader, but we still have to ask ourselves:
Would a paper that examines the Lyapunov exponent of a oscillatory predator prey system in 27 spatial dimensions published in Theoretical Population Biology really massively increase in citations if they dropped the maths?
2) If equations are causal, does that imply we should use less equations?
Anyway, let’s assume for the moment that equations are really causal for citations, does that imply we should we use less equations? Again, I think we have to be careful.
I completely agree that, when communicating theory, we should try to maximize the information that is received by the reader. However, even when doing so, there are different classes of readers, and different appropriate levels of complexity associated with this readers. You can write very broad, nearly for a laymen audience, and you can write very dense, for experts. May be that the broad papers get more citations than the expert papers, but would we be really better off if everyone would only write broad papers?
Already now, this is turning into an arms race where everyone is trying to broaden his presentation at the cost of loosing clarity. Often, I have to read so far as the methods until I understand what a paper is exactly testing, because abstract and intro are filled with common places to make the paper appear interesting to the widest possible audience. The authors demonstrate this somewhat involuntarily themselves: in their title, they refer to “impedes communication among biologists”, but in the article, they consider only papers from ecology and evolution. Did they struggle with the title word limit, or did they think that there are simply more biologists to cite this paper than people in ecology and evolution? Words might boost your citation counts, but they may also be deceiving because they can be used to make a study or a model appear broader and more general than it actually is, and this is not a good thing.
Thus, I completely agree that we have to consider the mathematical abilities of our target audience. I’m also happy to conceit that many mathematical presentations are unnecessarily complex. However, what I missed in the paper completely is a bit of praise for equations, saying something like: our goal in science communication is clarity – sometimes equations may be in the way of clarity, and then they should be avoided, but often they are also absolutely essential because words are easily misunderstood. So, drop your unnecessary equations, but don’t think about dropping the essential ones!
Addition 25.7.12: somewhat related, a Nature feature defending the (wise) use of scientific jargon.