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. impact factor | mathematical formula | mathematical literacy | theoretical biology T he efficient exchange of new findings and insights between empirical and theoretical approaches is critical to a range of scientific disciplines, including nuclear physics (1), physical chemistry (2), neuroscience (3), epidemiology (4), ecology (5), and atmospheric science (6). In evolutionary biology, for example, the integration of empirical and theoretical work is essential for understanding how natural selection shapes organisms and their interactions (7-16). Most biological research is empirical, yet empirical studies rely fundamentally on theory for generating testable predictions and interpreting observations. In return, empirical data provide both tests of established theory and guidance in the development of new models. However, the importance of presenting theory in sufficient technical detail can sometimes conflict with the need to communicate the essence of a model in a clear, accessible manner. Concise and precise description of the structure of a mathematical model demands the use of equations, but such technical details might deter a broad audience of scientists doing largely empirical research. A cursory reading of the biological literature reveals that many empirical studies build largely on other empirical studies, with little direct reference to relevant theory. This observation suggests a breakdown of communication that may impede scientific progress. To explore the extent of this problem, we systematically investigated how the use of mathematical equations affects the scientific impact of studies in ecology and evolution. We examined the use of equations and obtained citation data for all papers (total n = 649; Dataset S1) published in 1998 in the top three journals specializing in ecology and evolution: Evolution, Proceedings of the Royal Society of London B, and The American Naturalist. We find that heavy use of equations reduces citation rates, because papers with a high density of equations per page attract fewer citations from nontheoretical papers. Our results suggest 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. To quantify the technical level of any theory presented in the articles, we counted equations, inequalities, and other mathematical expressions (hereafter referred to simply as "equations") in the main text and any printed appendixes. We divided this count by the number of pages to give a measure of equation density, which ranged from 0 to 7.29 equations per page (mean ± SEM: 0.43 ± 0.04) and was uncorrelated with the length of the article (r 647 = 0.056, P = 0.151).
This result was not supported by other in different disciplines: Fawcett et al. studied the citations of 28,068 papers published in the top three journals specializing in ecology and evolution and found that heavy use of equations has a significant negative impact on citation rates REF .
Heavy use of equations impedes communication among biologists
Proceedings of the National Academy of Sciences of the United States of America
Proceedings of the National Academy of Sciences of the United States of America
Computer Science Medicine