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Growth rates of modern science: A bibliometric analysis based on the number of publications and cited references
Lutz Bornmann, Ruediger Mutz
TL;DR
The paper revisits how science has grown using updated, cross-disciplinary evidence. It analyzes Web of Science publications and cited references with segmented regression, identifying three cited-reference growth phases whose rates rose from below 1% to 2–3% and then 8–9%.
Problem
The study re-examines the question of the growth of science using more current data and analyses across disciplines and scientific fields.
Method
The study analyzes Web of Science publication counts and cited-reference counts with segmented regression across historical and disciplinary series.
Results
Growth rates across cited-reference phases rose from less than 1% before the mid-18th century to 2–3% between phases and 8–9% through 2012.
Takeaways & Limitations
The analysis identifies three successive growth phases in the development of science, each tripling the growth rate relative to the previous phase.
Abstract
from arXiv · showhide
Many studies in information science have looked at the growth of science. In this study, we re-examine the question of the growth of science. To do this we (i) use current data up to publication year 2012 and (ii) analyse it across all disciplines and also separately for the natural sciences and for the medical and health sciences. Furthermore, the data are analysed with an advanced statistical technique - segmented regression analysis - which can identify specific segments with similar growth rates in the history of science. The study is based on two different sets of bibliometric data: (1) The number of publications held as source items in the Web of Science (WoS, Thomson Reuters) per publication year and (2) the number of cited references in the publications of the source items per cited reference year. We have looked at the rate at which science has grown since the mid-1600s. In our analysis of cited references we identified three growth phases in the development of science, which each led to growth rates tripling in comparison with the previous phase: from less than 1% up to the middle of the 18th century, to 2 to 3% up to the period between the two world wars and 8 to 9% to 2012.
1 Corresponding author: Division for Science and Innovation Studies, Administrative
The section lists a telephone contact for the corresponding author.
- The listed telephone number begins with the international dialing prefix +49.
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2 Professorship for Social Psychology and Research on Higher Education, ETH Zurich,
The paper concerns growth of science, bibliometrics, and cited references.
- The study examines the growth of science.
- It uses bibliometric analysis.
- Cited references are part of the analysis.
1 Introduction
The study re-examines the growth of science using current data, disciplinary analyses, segmented regression, and two bibliometric data sources. Cited references extend analysis into the early period of modern science but omit uncited literature and infer early publishing from later citing.
- 1 Introduction: The study re-examines the established question of how science grows.Earlier work, including Price’s research, characterized scientific growth as exponential during certain periods.
- 1 Introduction: The analysis uses data through publication year 2012 across all disciplines and separately for natural, medical, and health sciences.
- 1 Introduction: Segmented regression identifies historical segments with similar growth rates.
- 1 Introduction: The study counts Web of Science source publications by publication year and cited references by cited reference year.
- 1 Introduction: Cited references provide insight into early modern science because no database covers source publications from that period.Their disadvantage is that uncited literature is excluded and early publishing is inferred from later citing, here from 1980 onward.
2 Methods
The methods assemble publication and cited-reference time series and fit exponential and segmented regressions. The segmented model explains 99% of reference-count variance and divides 1650–2012 into four segments.
- 2 Methods: The study uses publications and cited references as data for investigating scientific growth.An increase in cited references indicates more citing and/or cited publications.
- 2 Methods: The dataset contains 38,508,986 publications from 1980–2012 and 755,607,107 cited references dated 1650–2012.
- 2 Methods: Annual publication counts are fitted with a nonlinear exponential-growth model, with 96% of their total variance explained.
- 2 Methods: Segmented regression models logarithmised annual cited-reference counts and allows separate growth segments, including possible declines around the world wars.
- 2 Methods: The exponential model defines growth rate as exp(b1)-1 and doubling time as ln(2)/b1.
- 2 Methods: Breakpoints and segment growth constants are estimated by minimizing squared residuals under ordered-breakpoint and residual-distribution assumptions.The authors describe these time-series assumptions as rather strong and did not adjust for their violations, accepting a risk of slightly higher standard errors.
- 2 Methods: Models were selected using explained variance, and three breakpoints explained 99% of annual cited-reference variance, yielding four segments from 1650–2012.
3 Results
The analysis finds segmented growth patterns in scientific publications and cited references, including distinct historical phases and discipline-level similarities. Cited-reference growth accelerates from below 1% to approximately 8%, then shows a recent database-related decline.
- Figure 1 shows exponential growth in global scientific publication output, with publication volume doubling approximately every 24 years at about 3% annual growth.
- The cited-reference curve begins flattening around 1980 and declines significantly, reflecting time-dependent database characteristics in reference registration.Later publications may not yet have accumulated citations from earlier years, contributing to the final segment.
- The regression results indicate that the period between the world wars contains a significant increase in cited references, so the approximately 8% segment begins before the Big Science period.World War II appears as a temporary low point rather than the beginning of the major growth phase.
4 Discussion
The discussion identifies three growth phases in science, with cited-reference growth rising from less than 1% to 2 to 3% and then 8 to 9% by 2012. It also emphasizes measurement limitations arising from bibliometric indicators, historical publication practices, and changes in Web of Science coverage.
- Growth phases: Three growth phases were identified: less than 1% until the middle of the 18th century, 2 to 3% until the period between the world wars, and 8 to 9% to 2012.Each phase tripled the growth rate of the previous phase.
- Growth measures: The cited-reference growth rate in the third segment was significantly higher than the rate based on publications.The discussion compares the two indicators and notes that the cited-reference rate is especially high in the latest segment.
- Measurement limitations: The study cannot directly measure scientific growth through publication volume because no database contains every publication from the beginning of modern science to today.Growth since modern science began has therefore been measured indirectly with cited references.
- Measurement limitations: Publication counts are difficult to interpret because least publishable units, disciplinary differences, work quality, journal quality, and changing publishing practices affect the data.Historical publication practices also included editors publishing letters or talks rather than scientists publishing their own work.
- Scope of growth: The study treats growth as an increase in numbers, but it is unclear whether more publications, cited references, or scientists directly represent more actionable knowledge.This perspective focuses on internal research practices rather than the external factors that have altered views of science over time.
- Database limitations: Changes in Web of Science coverage may contribute to rising publication counts, although the cited-reference results were reported as robust to substantial data restrictions.The authors assume database-characteristic changes do not exert a major influence because limiting the data to one year or field did not significantly change the results.