Sunday, July 22, 2012

More Equations, Fewer Citations?

Heavy use of equations impedes communication among biologists

Tim Fawcett & Andrew Higginson
Proceedings of the National Academy of Sciences, 17 July 2012, Pages 11735-11739

Abstract: Most research in biology is empirical, yet empirical studies rely fundamentally on theoretical work for generating testable predictions and interpreting observations. Despite this interdependence, many empirical studies build largely on other empirical studies with little direct reference to relevant theory, suggesting a failure of communication that may hinder scientific progress. To investigate the extent of this problem, we analyzed how the use of mathematical equations affects the scientific impact of studies in ecology and evolution. The density of equations in an article 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. Long, equation-dense papers tend to be more frequently cited by other theoretical papers, but this increase is outweighed by a sharp drop in citations from nontheoretical papers (35% fewer citations 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. Our analysis suggests possible strategies for enhancing the presentation of mathematical models to facilitate progress in disciplines that rely on the tight integration of theoretical and empirical work.

Interesting.  I wonder if the same holds for economics and political science.    My five most cited works vary quite a bit. Two are books, with some equations, but mostly text.  The 1986 APSR is almost pure equations, and no emprical work, but we did try to make it accessible with the accompanying text.  And the 1989 and 1994 APSRs are mostly empirical, with some equations as estimations.

Angus's top five (we share the 1994 APSR, of course) is not terribly equation-heavy.  The largest one, the paper with Tullock in 1989, has nearly 1,000 cites (you think that's easy?  try it at home).  And Grier-Tullock 1989 is almost Hemingway-esque in its pared down simplicity and clarity. 

So, a conjecture:  obfuscating meaning with equations may help you get a paper published in the first place, especially at a lesser journal.  So the "survival test" is biased toward junking the paper up. But clarity and careful presentation help published papers have more impact.

What think you, folk?

Nod to Kevin Lewis


Thomas W said...

For an informative comparison, math and physics papers should also be compared. These can vary from primarily text to primarily equations.

Exogenous Combustion said...

But what we should care about for publication (if we only care about citations) is citations at the margin.

This study gives us average citations. A simple equilibrium would say that at the margin, theoretical papers and empirical papers get the same number of quality-adjusted citations per unit effort. It just turns out that empirical papers are "cheaper" on average, not at the margin.

Simon Spero said...

See e.g.

Differences in knowledge production between disciplines based on analysis of paper styles and citation patterns, which seems to indicate that at least biochemists don't like equations...

The Quest for Citations: Drivers of Article Impact, which looked at marketing, finds a very small negative correlation between number of equations and citations; half as strong as making the paper harder to read.

Angus said...

Mungo: we have 4 joint papers each with over 100 cites. Not too shabby my friend!