In the July issue of PNAS, Fawcett and Higginson argue, based on statistical analysis of citation rates, that a high density of equations will increase citation by theoreticians, but reduce citations by nontheoreticians even more. They advocate putting a minimum of equations in the main text, move everything else to the (online) appendix, and insert a maximum of verbal explanations of each equation.
This sounds trivial. Don’t we teach all our students to leave out unnecessary maths in presentations and manuscripts? Apparently this is easier said than done, as we still see very equation-rich papers in journals for the general ecological and evolutionary audience (such as Oikos). The reason may be that “necessity of equations” is subjective. For a thorough understanding, a full mathematical derivation seems indispensable, and hiding it from view by putting it in an appendix may also hide it from peer review. This may be good for the author (higher acceptance probability and more citations), but can be detrimental for science, and in the long run also for the author: there is nothing more terrifying for a theoretician than being confronted with an error in a derivation after publication, please let it be found during peer review!
Hence the theoretician faces a serious dilemma for which I have no full solution, only a couple of recommendations. To minimize errors, find collaborators that can check your derivations (so editors, be suspect of single author theoretical papers). A thorough verbal explanation of a model’s assumptions (and some of the derivation) may not only aid the reader, but may also advance the author’s own understanding of his/her work: when a theoretician has difficulty explaining what he/she is doing, the work is either unrealistic or incorrect. And, something Fawcett & Higginson did not analyse in detail, use simple equations: avoid Greek or curly symbols whenever possible, divide the equation in pieces where each piece has a clear meaning. Finally, when you’re really reluctant to banish your cherished formulas to an appendix, use a box. A box is really an inline appendix, and may represent the best of both worlds. Remember to think out of the box!
Rampal Etienne, SE Oikos