RESEARCH ARTICLE

Concentration of Danish research funding on
individual researchers and research topics:
Patterns and potential drivers

开放访问

杂志

Danish Centre for Studies in Research and Research Policy, Department of Political Science,
Aarhus University, Bartholins allé 7, 8000 Aarhus C

Emil Bargmann Madsen

and Kaare Aagaard

引文: Madsen, 乙. B., & Aagaard, K.
(2020). Concentration of Danish
research funding on individual
researchers and research topics:
Patterns and potential drivers.
Quantitative Science Studies, 1(3),
1159–1181. https://doi.org/10.1162/
qss_a_00077

DOI:
https://doi.org/10.1162/qss_a_00077

已收到: 01 四月 2020
公认: 23 可能 2020

通讯作者:
Emil Bargmann Madsen
ebm@ps.au.dk

处理编辑器:
Ludo Waltman

关键词: diversity, funding concentration, research funding, research policy, research priorities

抽象的

The degree of concentration in research funding has long been a principal matter of contention
in science policy. Strong concentration has been seen as a tool for optimizing and focusing
research investments but also as a damaging path towards hypercompetition, diminished
diversity, and conservative topic selection. While several studies have documented funding
concentration linked to individual funding organizations, few have looked at funding
concentration from a systemic perspective. 在本文中, we examine nearly 20,000
competitive grants allocated by 15 major Danish research funders. Our results show a strongly
skewed allocation of funding towards a small elite of individual researchers, and towards a
select group of research areas and topics. We discuss potential drivers and highlight that
funding concentration likely results from a complex interplay between funders’ overlapping
priorities, excellence-dominated evaluation criteria, and lack of coordination between both
public and private research funding bodies.

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1.

介绍

Across countries, research funding systems have undergone major changes during recent decades.
As funding plays an influential role in the governance of contemporary science, changes in
allocation mechanisms are assumed to affect the scope, 内容, 方向, and impact of public
研究 (Gläser & Velarde, 2018; Sörlin, 2007). Such changes are in turn also likely to influence
the distribution of funding across individuals and topics and hence the overall degree of funding
concentration.

Current evidence suggests that funding concentration has in fact increased as a result of these
changes and that there may be some advantages, but also important downsides, linked to high
degrees of selectivity in the distribution of funding (Aagaard, Nielsen, & Kladakis, 2020).
然而, the exact patterns and the potential drivers at aggregated levels are still underexplored.

一方面, more pervasive competition, increased performance orientation, stronger
emphasis on excellence, and higher reliance on project funding have, 跨国, been seen
as essential means to optimize the returns on public investments in science (王, 李, & Walsh,
2018). These developments are often highlighted as factors that are likely to increase concentra-
的 (Aagaard et al., 2020). 另一方面, funding landscapes have also become more diverse
and heterogeneous during this period, with research depending on, but also made possible
通过, many different extramural sources, such as public research councils, charities, 私人的

版权: © 2020 Emil Bargmann
Madsen and Kaare Aagaard. 已发表
under a Creative Commons Attribution
4.0 国际的 (抄送 4.0) 执照.

麻省理工学院出版社

Concentration of Danish research funding on individual researchers and research topics

foundations, and firms (Whitley, Gläser, & Laudel, 2018, p. 110). A more diverse set of funders,
both public and private, could be expected to ensure a more balanced and diverse distribution of
funds, because priorities may differ across funding organizations and funding instruments.

然而, how this actually plays out in broader settings, where multiple funders interact, 是
unclear. Existing studies on concentration have so far largely neglected to assess patterns, drivers,
and consequences at the systemic level. 反而, most studies focus on the concentration of
资金, to both individuals and research areas, by analyzing grants from only one funder at a time:
例如, the National Institutes of Health (最好的, 2012; Bowen & Casadevall, 2015; Hegde &
Mowery, 2008; Hegde & Sampat, 2015; Katz & Matter, 2019; 李 & 阿迦, 2015; Manton, Gu, 等人。,
2009; Stoeger, Gerlach, 等人。, 2018; Wahls, 2018乙), the National Science Foundation (Cole, Cole,
& 西蒙, 1981), the UK Engineering and Physical Sciences Research Council (Ma, Mondragón, &
Latora, 2015), the Australian Research Council (Bromham, Dinnage, & Hua, 2016), or the Veni,
Vidi, Vici Program in the Netherlands (Bol, de Vaan, & van de Rijt, 2018).

While these and other studies provide interesting findings, they are unable to address the
combined effects of multiple funders. 因此, although the need for comprehensive knowledge
about funding priorities across funders is often stressed, the issue has seldom been examined
in depth.

We improve on these studies by analyzing a set of almost 20,000 grants awarded by 15 Danish
research funders between 2004 和 2016. The data encompass almost all major research funding
bodies in Denmark. To our knowledge, our study is the first empirical study of the degree of con-
centration of research funding both for individual researchers and for fine-grained research topics/
disciplines considering the majority of relevant funders within a country. From this outset we ask
the following research question:

What patterns of concentration of research funding can be observed across individuals and
topics when the majority of funders within a national system are investigated in concert?

进一步来说, we examine the following questions:

(西德:129) How concentrated is the research funding distributed among individuals?
(西德:129) Are funding distributions markedly stratified in terms of gender?
(西德:129) What do the funding configurations of top funded researchers look like?
(西德:129) How is the funding of the top 100 most funded researchers distributed among universities?
(西德:129) How concentrated is the distribution of funding across research topics?
(西德:129) How is the research funding distributed across disease-specific research areas?
(西德:129) To what extent do the observed patterns match measures of disease burdens (which can

be seen as a partial measure of societal demand)?

In addition to providing information on these research questions, the analysis also raises a

more tentative discussion of the potential drivers of the observed developments.

The paper proceeds by briefly discussing earlier findings on concentration and diversity in
research funding in Section 2. We then outline how we combine detailed information on in-
dividual grants and grantees coupled with publication data to answer the questions posed
多于. 在部分 4, we first show the degree of funding concentration in Denmark at the in-
dividual level and examine the funding configurations of the top funded researchers.
Subsequently we proceed by investigating thematic concentration, first at an aggregated level
and second more detailed by focusing on disease-specific research. Here we match the
observed patterns with measures of disease burdens to examine whether concentration are
driven by societal demands. Based on the total set of findings, we discuss potential drivers

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Concentration of Danish research funding on individual researchers and research topics

of concentration in Section 5. In the final section, we highlight our main findings, discuss the
pros and cons of concentration, and derive a series of implications for funding policy.

2. PREVIOUS STUDIES OF CONCENTRATION IN RESEARCH FUNDING

Concentration of research funding has become a key part of the science policy debate. This is due
to multiple factors, such as efficiency concerns, austerity policies, and a general trend towards
greater reliance on grant funding, which together have sparked discussions on how best to support
scientific discovery. 尽管如此, the systematic, empirically based literature on trends in concen-
tration of grant funding is still in its infancy (Aagaard et al., 2020).

Although fragmented, the available scholarly literature in general appears to document a high
degree of concentration of grant funding at the individual researcher or group levels. 这
majority of these studies rely on grant information from the US National Institutes of Health
(NIH), and generally show that around 10% of grantees receive around 40% of all allocated
资金 (Katz & Matter, 2019; Peifer, 2017; Wahls, 2018A, 2018乙). While some concentration
of grant money consistently has been a part of the system, Katz and Matter (2019) document that
concentration has significantly increased over the past 30 年. 在 1985, the top 20% funded
researchers accumulated around twice the amount awarded to the bottom 20%, but by 2010 这
had increased to 3.5 次 (Katz & Matter, 2019, PP. 10–11). Similar developments have taken
place elsewhere. In the UK’s Engineering and Physical Science Research Council (EPSRC), 8% 的
researchers receive 50% of all funding, and also here the level of concentration rose steeply
之间 1985 和 2013 (Ma et al., 2015). Along the same lines, two studies focusing on
Quebec show how 20% of researchers amass 80% or more of total funding across a broad range
of disciplines (Larivière, Macaluso, 等人。, 2010; Mongeon, Brodeur, 等人。, 2016).

Another common finding is an apparent lack of diversity extending to both the type of researcher
and the type of research funded. At the individual level, the high concentration of funding results in
a bias towards researchers from prestigious institutions. In the NIH case, more prestigious institu-
tions receive 240% more funding per grantee compared to less prestigious institutions, have a 65%
higher success rate, and receive 50% larger award sizes on average (Wahls, 2018A). The lack of
diversity in affiliation is also evident in the EPSRC, where a small group of universities form a “rich
club,” which attracts the bulk of funding, and act as central brokers in collaborations between
different universities (Ma et al., 2015, p. 14763). 相似地, high degrees of concentration also seem
to reinforce gender biases in grant competitions. Findings from NIH grant competitions show that
women are underrepresented research project grantees, have higher risk of not transitioning to
the next level, and often transition much later in their career (Lerchenmueller & Sorenson, 2018,
p. 1011).

A second issue related to funding concentration is the possible impact on topic diversity.
Observers have long worried that increasing competition for resources, paired with low success
费率, incentivize applicants to be more conservative and mainstream oriented in the type of
research they apply for (Alberts, 克氏纳, 等人。, 2014). On a system-wide level, this may at
the same time lead funders to invest in a narrow set of topics where capacity already exists and
where the probability of obtaining results is high. Studies of biomedical research funding again
seem to confirm this notion. Funding from the NIH tends to flow towards research into a select
group of diseases, often matching allocation from previous years (Yao, 李, 等人。, 2015). 在 1996,
10% of diseases received 43% of the funding budget, with AIDS and breast cancer amassing 36%
in total (总的, 安德森, & Powe, 1999, p. 1882). 经过 2006, 10% of all disease areas still amassed
大约 40%, with AIDS and diabetes still being the top funded areas (Gillum, Gouveia, 等人。,
2011, p. 2). Certain genes are also more likely to receive attention, with up to 75% of projects

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Concentration of Danish research funding on individual researchers and research topics

funded by the NIH relating to only 5% of human protein-coding genes. This affects individual
incentives for choosing genes to study, as the probability of becoming a principal investigator
(PI) 是 10% for researchers studying the least studied genes compared to 25% for those who
studying the mainstream (Stoeger et al., 2018, p. 8).

更普遍, funding also appears to skew towards already well-funded topics. Outside
the biomedical field, a recent study of grant funding in the United States shows a considerably
skewed distribution of funding over topics (Klavans & Boyack, 2017). This concentration of
funding correlates well with the prominence of topics in the scholarly literature but also with
the amount of funding a topic has previously attained. 就其本身而言, a topic’s scholarly prominence
in one time period explains over one third of the funding variation in the subsequent period
(Klavans & Boyack, 2017, PP. 1167–1169).

While topic skew signifies a thematic concentration of funding, studies also show a concen-
tration of approaches in the way in which these topics are studied. This is visible in medical
研究, where different stages of the research pipeline receive different levels of funding.
Funding from Danish research councils has been skewed towards translational research
(39%) and basic science (21%), while clinical trials only received around 10% of all funding
之间 2012 和 2016 (Rygård, Kjær, & Perner, 2018). 相似地, focusing on infectious
disease research, Head, Fitchett, 等人. (2016, p. 185) find that 59.4% of funding in the UK is
awarded to preclinical research, while funding for phase I–III trials amounts to 5.6%.

最后, the societal impact of a disease appears to be moderately related to funding inten-
城市 (Gillum et al., 2011; Gross et al., 1999). Recent studies actually find a poor match between
estimated health needs and funding distributions (琼斯 & Wilsdon, 2018, PP. 19–20; 英国
Clinical Research Collaboration, 2015, p. 49), and this weak link disappears entirely when
funding across longer time periods is taken into consideration (Yao et al., 2015, p. 810).

总共, a growing literature shows that funding tends to be highly concentrated among few
研究人员, 主题, and approaches. 然而, the available studies are skewed towards a lim-
ited number of disciplines and countries and most importantly, there is very limited evidence
of such patterns at the systemic level. 此外, empirically based studies of drivers of con-
centration are also still lacking. These issues are examined in Sections 4 和 5.

3. METHODS AND DATA

3.1. Data on Competition-Based Grants

The present study relies on a database of 19,399 research grants awarded by 15 public and private
Danish research funders over a period of 13 years from 2004 到 2016. The group of funders
encompass both public research councils, private foundations with corporate interests, 和非-
profit foundations or societies. 此外, ERC grants are also included, as in a Danish context
they are perceived as a central part of available funding sources and as some of the most compet-
itive and prestigious grants. The total awarded grants amount to 52.9 billion kroner (A7.08 billion
or US$7.7 billion) distributed to 7,539 grantees. 这是, 然而, important to note that this sample is not a complete picture of all grants awarded by Danish research funders within the period. Many funders award money to projects that are not strictly research-related or aimed at producing a traditional scientific output. For that reason, we have excluded all grants aimed at training or education, as well as grants with a monetary value below 50,000 kroner (A6,700 or US $7,400). The bulk of these grants are small travel grants or grants to students (“skolarstipendier”).

For all grants, we standardized the grant sums to be in kroner and current prices. For grants
with a running amount paid each year, we summed these to one grant sum centered on the

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Concentration of Danish research funding on individual researchers and research topics

grant year. 此外, it is also important to highlight that grants are linked to the main recipient
仅有的 (typically the PI). For this and other reasons the database has less comprehensive coverage
of strategic and innovation-related funding, as these types of grants are often awarded to a
consortium of firms and research organizations without a single discernible PI. 最后,
some underrepresentation of these sources is likely. 此外, the focus on PIs only also
means that our analyses cannot account for how the funding is spread across researchers after
being awarded to a PI.

After establishing the database, grant recipients were manually disambiguated and linked to
grants. For common combinations of names, the grantee was identified through a combination
of data on their institutional affiliation and primary research area. If not successfully disambiguated
through this, grantees were considered separate individuals even if names matched. Throughout
the disambiguation process, we also established the gender of the grantee for 97% of all individuals.
此外, a number of infrastructure grants and PhD and postdoctoral block grants were awarded
to deans or rectors. These grants cannot reasonably be treated as grants to individuals. They were
instead assigned to an institution and kept out of the individual level analyses.

Despite these limitations, the database covers a large part of all external funding awarded to
Danish researchers from 2004 到 2016. Comparing the data from 2012–2014 to self-reported sums
spent by the funders in that period, coverage of around 2/3 of all grant sums is found (UFM, 2016).
These are likely not completely overlapping, but shows that the coverage of central funding organs
is consistent across time. Although not all funders had equally accurate data of their grant history,
we believe that the overall trends of the aggregated distribution of research funding are quite valid.
因此, while the data may not accurately depict the absolute amount of funding awarded, 他们
provide an important insight about the relative distribution of scarce resources in the Danish
系统. 再次, 然而, there is a caveat linked to strategic and innovation-oriented research
资金, where both the absolute and relative distributions are more uncertain.

3.2. Connecting Grants and Outputs

Few Danish funding organizations have consistent ways of classifying the research topics funded
by their grants. 因此, to ascertain how funding is distributed across different types of research
we rely on journal articles and reviews published by the grantees. To link each grantee to their
出版物, we use a combination of automated and manual matching, by comparing names,
email addresses and institutional affiliations in the CWTS in-house version of the Web of Science
( WoS). Using this method, we matched 5,773 grantees and 14,103 grants, to their publication
profiles. 一起, these grants account for around 80% of the combined funding amounts
attributed to individual principal investigators. Most of the nonmatched grants were awarded
to research within the humanities and social sciences, which have less extensive coverage in
the WoS (Mongeon & Paul-Hus, 2016). The full and WoS-matched samples are predominantly
similar in their composition. The WoS-matched sample has 2% fewer female grantees, 和
grants tend to be a little larger and have a higher percentage of research grants (compared with,
例如, postdoctoral grants). The differences are, 然而, negligible. Tables A1 and A2 in
the Appendix provide a more detailed comparison of the two samples.

在下面的分析中, we use the publications of each grantee to attribute them to a research
area or a specific research topic. This entails some methodological choices. We assume that a prin-
cipal investigator’s publications reveal the underlying topic, or mix of topics, of the grant. 我们也
assume that the topic mix has not changed much from grant proposal to publication output.
然而, using the publication output may also carry the advantage that we are assessing the type
of research that a grant actually resulted in, instead of just the intended results. 此外,

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because publications may span multiple areas and topics, we may better represent cross-disciplinary
research grants. A grantee’s publication output will not be a perfect representation of the topicality
in a grant, but is expected to yield a reasonably accurate estimate of topic spread at the aggregate
等级. We only consider the publications 0–4 years after a grant was received. 这种方法
leaves us with 63.3% (12,269) of all the collected grants.

To study the concentration of funding in different research areas and research topics we rely
on two categorization schemes. To categorize each grant within a research area, we use the WoS
OECD Category Scheme of 39 research areas categories.1 The categories are based on the 250
journal classifications in the WoS database. For publications in multidisciplinary journals, 我们
investigated the most common category of all references in a paper and assigned it to this.

In the article, we furthermore conduct a small case study of disease-specific research. 这
Danish system, in addition to public funders, also includes private research funding foundations
tied to pharmaceutical companies. Disease-related funding then provides the opportunity to
compare how the priorities of public and private funders overlap. Through publications, 我们
were able to match 4,108 grants, spanning 15 资助者, to one or more of the 134 disease areas
used by the WHO in assessing global burden of diseases.2 The classification of papers into
disease areas is based on data from Yegros-Yegros, Klippe, 等人. (2019), which translates
medical subject headings from the PubMed database into ICD-10 (International Classification
of Diseases) 类别, and finally into disease areas.

For each grant, we weigh both the grant sum and the grant itself according to the proportion of
publications within each research area or disease category. 例如, a grant of 1 百万
kroner with three publications within chemistry (60%) and two publications within nanotech-
科学 (40%) is divided so that 0.6 grants and 600,000 kroner are attributed to chemistry, 和
0.4 grants and 400,000 kroner are attributed to nanotechnology. 最后, following previous
学习, we use data on the burden of disease categories to investigate how funding aligns with
(imperfect) measures of societal health needs (Cassi, Lahatte, 等人。, 2017; 埃文斯, Shim, &
Ioannidis, 2014; Gillum et al., 2011; Gross et al., 1999; Yao et al., 2015; Yegros-Yegros et al.,
2019). This is done by comparing research output for a disease to its burden in Disability-
Adjusted Life Years (DALYs). DALYs are a common measure of disease burden that estimates
the equivalent number of healthy years lost due to disability or early death (Gillum et al.,
2011). It sums both the Years of Life Lost ( YLL) and Years Lived with Disability ( YLD) 估计
for each disease. We match DALY estimates from the 2017 Global Burden of Disease Study
(GBD 2017 DALYs and HALE Collaborators, 2018) 到 134 disease categories from the
WHO, and convert these to relative burdens by summing DALYs from all diseases and calcu-
lating the share of total burden attributed to each disease.

In this study, we use DALYs as a rough proxy for the societal relevance or importance of a
disease category. 然而, while widely used, DALYs are also a heavily criticized health
metric. A comprehensive critique of the DALY measure is beyond our scope, but we highlight
a few salient issues. From a methodological standpoint, the DALY calculation relies on a set of
strong assumptions of which not all necessarily are agreed upon (Anand & Hanson, 1997;
Parks, 2014). The calculations are furthermore characterized by a great deal of uncertainty
and can be an inaccurate measure of disability in high mortality regions, 例如, 因为
the underlying data are rough estimates or simply missing (Parks, 2014). DALYs also have
several shortcomings from a conceptual perspective. 第一的, by pooling YLL and YLD estimates,

1 http:// help.prod-incites.com/inCites2Live/filterValuesGroup/researchAreaSchema/oecdCategoryScheme.

html

2 https://www.who.int/gho/mortality_burden_disease/en/

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the DALY indicator conflates death and disability into one scale, with premature death as an
extreme case of disability. Each single case of a disease is also discounted based on the person’s
年龄, and case contributions to the DALY estimate thus vary. 总共, the DALY measure relies
heavily on a “cost effectiveness” rationale in both how it is calculated and what this implies
conceptually. Such a rationale can been seen as an inherent political choice, where other
rationales, such as “equity,” could be equally or more appropriate. 尽管如此, DALYs can
provide a reasonable measure of health burden in Denmark, as we are not comparing health
burdens to other contexts and expect underlying data to be reasonably well curated. Our aim is
not to argue for a distribution of research funding according to DALYs but rather to contrast the
distribution of funding to an indication of societal needs. 然而, we acknowledge that by
comparing burden and funding, there is a risk that we appear to legitimize some of the criticized
implications of the DALY.

4. ANALYSIS: CONCENTRATION OF DANISH RESEARCH FUNDING

4.1. The Danish System for Funding Research

The Danish research funding system is pluralistic and consists of many different funding chan-
内尔斯, many individual funding programs and a variety of specific funding mechanisms. This or-
ganization reflects a need to serve different societal purposes, the involvement of a broad array of
sectoral interests, and an aim to underpin a variety of different outcomes. 然而, in line with
the general international development, the Danish system has also become more competitive
随着时间的推移. Most importantly, a development was started in 2006 towards turning the existing 65/
35 balance between institutional funding and external funding into an approximately equal 50/
50 balance (Danish Government, 2006). 第二, a substantial part of this increasing share of
competitive funding was channeled into several newly established research funding organiza-
系统蒸发散, which were institutionalized alongside the traditional research council system and the
Danish National Research Foundation. 最近, these research-funding organizations have
been merged into one, namely the Innovation Fund Denmark (建立在 2014).
因此, Denmark now has a rather sharply divided research funding system with a clear
distinction between response mode funders and more mission- or innovation-oriented funders.
此外, the Danish research system has for many years benefited from a strong and varied
sector of nonprofit and private research funding foundations. This has been the case for biomed-
ical research in particular, but also most other areas have at least to some extent benefited from
these nonpublic funding organizations. The importance of the private research foundations has
surged over the past 10 年. Funding from private foundations now comprises almost 20% 的
all research funding financing public research activities, and close to 50% of all competitive
资金 (Danish Council for Research and Innovation Policy, 2020). The most recent part of this
development is, 然而, not captured in the present analysis, which only covers funding in-
formation up until 2016.

4.2. Concentration of Funding at the Individual Level

In the investigation of the concentration of competitively awarded research funding, we first
focus on the number of grants and the amount of funding for each individual grantee in the
数据库. Here we observe a significant skew of resources. Among all 7,539 grant recipients,
仅有的 3,000 have been awarded two grants, 1,600 more than two, 和 600 individual researchers
five grants or more during the period. At the absolute top end, 140 PIs have amassed more than
10 grants, and a small selection of these have close to 30. 总共, 20% of the grantees were
awarded 50% of all grants.

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Concentration of Danish research funding on individual researchers and research topics

This level of concentration is even more pronounced when focus is shifted to the total amount
of funding for each PI. 数字 1 shows the cumulative share of funding for grant recipients as a
Lorenz-curve. A straight line would signify total equality in funding amounts, but the graph instead
shows significant stratification among researchers. The blue curve shows the distribution for all
7,539 grantees, 哪里的 20% most successful receive around 75% of all funding, 而
其余的 80% share the remaining 25%. This marked concentration of funding at the individual
level does not take into account the number of researchers who have either not applied for or
not won external research funding. To estimate the concentration of funding across the entire
population of Danish researchers, we therefore identified 21,000 publishing scientists with a
Danish affiliation and at least five publications in the 12-year period in WoS. As a back-of-the-
envelope calculation, this yields a tail of more than 13,000 researchers with no external funding.
图中 1, we have included three more or less conservative estimates of the number of
研究人员: 15,000, 20,000, 和 25,000. Even when using the most conservative benchmark
的 15,000 active researchers over this period, we see a very high degree of concentration. 这
顶部 10% attracts around 75% of all funding, while the top 20% amass just short of 90% 的
total amount.

The stark degree of concentration can also be shown in terms of the average amount of fund-
ing awarded to each grantee. 数字 2 shows the mean funding amount for six ranked groups of
研究人员. The top 100 researchers each have an average of more than 90 million kroner per
人. The group from 101–500 have an average of around 30 million per person, 而
501–2,000 group on average have a little less than 10 million kroner per person each at their
处理. Further down the distribution the average funding amount per person is negligible or
nonexistent. 然而, as highlighted in Section 3, many of these researchers may indirectly
benefit from grants as team members of successful PIs.

Besides the average funding amounts, 数字 2 also shows a clear gender bias. 仅有的
16 women are among the top 100 PIs, and the next group of 400 researchers included only
60 女性. 因此, as the average amount of funding drops, the proportion of female PIs
instead rises.

This pronounced lack of gender diversity does not reflect the population of Danish re-
searchers. 数字 3 shows the proportion of female and male researchers in the population3
as full-time equivalents (FTE), and compares these to the proportions of female grantees, 这
proportion of grants awarded to female grantees, and the proportion of funding amounts
awarded to female grantees. 全面的, 40% of Danish researchers are female, while this is
the case for only 34% of the grantees. 然而, when considering the distribution of grants
and funding amounts, 仅有的 29% of all grants have a female PI, 并且只有 22% of all funding is
allocated to a female PI. Dividing these distributions into broad research areas reveals that lack
of diversity in the system trails the lack of diversity in the Natural, Technical, 和健康
科学. While the proportion of female researchers is fairly similar in the Humanities and
社会科学, the increased narrowing from FTE to funding amounts is pronounced in the
harder sciences. This also coincides with the distribution of female researchers at different ca-
reer stages. In the Humanities and Social Sciences, the proportion of female associate profes-
sors is twice as large as in the hard sciences, and the same is true for full professors.

It can also be observed that the grantees’ career stage seems to be an additional factor lead-
ing to stratification. As an imperfect measure of each grantee’s “academic age,” we calculated
the maximum number of years from their latest grant to their earliest publication for 4,047

3 Average for 2007–2015 based on numbers from Statistics Denmark.

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数字 1. Cumulative share of funding for grantees and estimated population of researchers.

researchers with 11,047 grants. A researcher with an academic age of 5 years has accumulated
a median of 1.5 million kroner in grant funding, while a researcher with an academic age of
10 years generally accumulates 4.2 百万. 而且, the distribution of funding becomes
much wider for higher academic ages. Table A3 and Figure A1 in the Appendix show that
50% of cumulative funding is contained within the interval [1,995,208–10,331,734] 为了
10 years of academic age. 为了 15 年, the interval is [3,959,349–20,939,255]. These numbers
应该, 然而, be interpreted with some caution. A significant number of grantees were not
matched to previous publications, and while these tend to have lower levels of funding, 这
distribution within this group varies a lot (see Figure A1).

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数字 2. Average amount of funding for grantees and estimated population of researchers.

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数字 3. Proportion of female researchers among population (FTE) and grantees, and proportion of grants and funding amounts for female
研究人员.

4.3. Funding Configurations of Top Funded Researchers

Returning to the small group of the top 100 funded researchers, we also note that this group of
grantees separate themselves from the rest by the configurations of their funding. 第一的, the top
100 tend to win grants with higher monetary values. 数字 4 shows the distribution of all
grants awarded to the top 100 and the remaining group of grantees, with the median funding
amount in black. The top 100 funded researchers tend to have a higher median grant amount.
Where the remaining grantees tend to win grants of around one million DKK, the central ten-
dency for the top 100 是 2.7 times that. 然而, the distribution also shows that the top 100
combines both very large grants with numerous smaller ones, as is evident from the large over-
lap between the distributions. 平均而言, the top 100 receive almost seven grants and a me-
dian of 5.5, while the remaining group receive an average of two grants but a median of one.
The top 100 also attract funding from more funders, with an average of 3.2 相比 1.3.

第二, 数字 5 shows the configuration of unique public and private funding sources among
the top 100 funded PIs and the remainder. Within the top 100, the diversity of funding sources is
much greater than in the remaining group, with an average of 1.8 private funding sources and 2.2
民众, 相比 1.2 和 1.1 among the rest of the grantees. 然而, the most interesting
pattern emerges from the configuration of funding from different sources. Outside of the top
100, 88% of grantees are funded by no more than one private and one public funder. 实际上,
77% are only funded by one funder of either domain. In the group of top funded researchers,
the configuration distribution is much more spread out: 47% of these grantees are funded by
two or more funders from both domains. 在本质上, the configuration of funding sources is much
more diverse among the well-funded scientists, and much more concentrated outside the top
100 团体. The biggest concentration within the top 100 是, 然而, still centered on one public
funder (18% of PIs). This reflects a group of grantees whose main source of funding is a large

数字 4. Distribution of funding amounts (median funding amount in black).

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Concentration of Danish research funding on individual researchers and research topics

数字 5. Configuration of distinct funding sources.

Excellence Centre grant from the Danish National Research Foundation. These grants exceed
20 million kroner, but are often much larger, with a median of 65.75 million kroner.

最后, with regard to the top 100 it is also interesting to examine to what extent the grant in-
come of these researchers is concentrated within a few universities. As highlighted in Section 2,
studies from the United States and United Kingdom have found a strong bias towards a small group
of elite universities. As can be seen from Figure 6, 然而, this is not the case in Denmark. 尽管
the largest and most research-intensive universities obviously account for the biggest share of the
total amount of grant income allocated to the top 100, they do not receive a disproportionate
分享. This likely reflects a Danish university system that is much less stratified than Anglo-Saxon
systems and the fact that the relatively low number of universities all are research universities.

4.4. Concentration of Funding on Research Topics

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.

A subsequent question is how these allocation patterns influence the systemic diversity of research
areas and topics. 数字 7 shows a disciplinary map of 12,269 of the grants in our data set. 这些都是
the grants we could link to one or more publication(s) 在里面 4 years succeeding a grant. Each bubble
or node represents a research area, 基于 39 categories from the OECD Frascati manual, 和
links between them are the citation traffic between each area. 全面的, the figure shows a marked
skewness of competitive funding towards the biological and medical sciences.

The biological research areas have, in the examined period, attracted 6.9 billion kroner,
其次是 4.6 billion kroner for basic medical research and 2.8 billion kroner to clinical

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数字 6.
staff in university sector.

Institutional distribution of funding in top 100 compared to percentage of total research

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数字 7.

Funded research areas and their citation relations.

研究. This picture, 然而, also illustrates some of the difficulties of categorizing the type of
research funded. The biological sciences, as they are defined by the OECD, comprise a broad
mix of subdisciplines spanning human, 动物, and plant biology. In our disciplinary map, 这
biological sciences are closely related to the medical research fields, as seen from the strong
citation link between these. The OECD categories may then obscure that a substantial amount
of external funding is directed towards areas with a close affinity to basic medical research, 这样的
as microbiology, biochemistry, 分子生物学, 遗传学, and virology. It is noteworthy that
this degree of concentration is relatively similar across different types of funders.

数字 8 shows the distributions of funding from public and private funders across the top
20 funded OECD areas. It is interesting to note that both types of funders largely prioritize

数字 8. Public and private funding of research areas.

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相似的, and relatively few, 地区. 再次, the biological sciences and clinical medicine are the
top funded disciplines: The top seven areas are all within natural or biomedical sciences and
amass around 70% of total funding. We also see that 25% of areas get 73% of all funding from
public funders, 和 86% from private funders. So even though both types of funders prioritize
a small set of areas, some differences still exist between their respective funding portfolios.
While public funders direct the majority of their grants towards biology, 物理, 化学,
and clinical and basic medicine, private funders focus primarily on biology and clinical med-
icine. This is not surprising given the composition of private Danish foundations, 哪里的
largest ones are linked to the pharmaceutical industry.

4.5. Concentration of Research Funding on Disease Specific Topics

At the aggregate level, the distribution of both public and private funding flows towards similar
types of research, as shown above. 然而, it is not clear whether this is a case of private
priorities that spill over into public funding, or simply a natural focus on the most important
and promising areas from both types of funders. To investigate this further, we delve deeper
into the distribution of funding within the biomedical area and compare funding of 134 疾病
categories with measures of their societal health burden.

数字 9 shows the average relative burden, in the form of a disease’s share of total DALYs
against the relative funding amount for that disease. For the measure of relative disease bur-
这, we have averaged the number of DALYs for a disease across 2004–2016, and calculated
its share of total DALYs. The first plot is the average relative burden in Denmark, 而
second shows the average relative burden at a global scale. In each plot, the diagonal shows
a proportional relationship between burden and funding. The majority of diseases attract very
little funding and pose a relatively small burden to societal health. A number of diseases are
placed below the 45° line, indicating that their relative burden in Denmark is not matched by
research investments. One example is back and neck pain, which constitutes 9% of total
health burden but under 1% of total funding. Similar patterns apply for chronic obstructive
pulmonary disease, ischemic heart disease, and stroke. Another set of diseases above the
diagonal receive a higher relative share of funding than their burden share. Diabetes is one

数字 9. Relative disease burden and funding.

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Concentration of Danish research funding on individual researchers and research topics

such disease, which receives around 11.8% of all disease-specific funding. Despite having a
health burden almost equal to chronic pulmonary disease, diabetes receives 10 times the
amount of research funding. On the global scale, a group of diseases moves further towards
the diagonal because they pose a larger health burden across the world. This is the case for
malaria, diarrheal disease, and HIV/AIDS. 相比之下, diseases such as breast cancer and skin
diseases appear more “overfinanced” because they primarily affect people in high-income
国家 (Yegros-Yegros et al., 2019).

The question is why some diseases, such as diabetes, draw so much funding relative to
other diseases. 数字 10 may provide some answers to this. We calculated the funding per-
centile of each of the 134 diseases within the group of private and public funders and plotted
these against each other.

The black regression line clearly shows the high correlation between the patterns of alloca-
tion by private and public funders with a correlation coefficient of almost 0.9 (r = 0.892).
Diabetes and breast cancer are the most funded diseases from both private and public funders.
Diabetes draws 727 million kroner from public funders and 355.5 million kroner from private
资助者, while breast cancer was awarded 331.6 million kroner from public funders and 257.7
million kroner from private funders. As both private and public funders tend to focus on a select
subset of diseases with high burdens (represented by the size of each bubble), the concentration
on a few diseases increases. The figure also shows a great overlap in diseases not prioritized by
both types of funders, which indicates both a positive feedback mechanism for high-funded
diseases and a negative feedback mechanism for low-funded diseases.

有, 然而, also differences in the revealed funding patterns between the two types of
资助者. A range of neurological and psychiatric diseases are for instance better funded by private
资助者, and while, 例如, Alzheimer’s disease and dementia are within the top 10 最多
burdensome diseases in Denmark, 57.5% of funding for these diseases is from private funders.
同样地, schizophrenia, stroke, ischemic heart disease, and some types of cancer (breast, skin,
脑) rely on over 40% of funding from private sources. 相比之下, a range of diseases prevalent

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数字 10. Funding percentiles for 134 disease areas in private and public funding bodies. 0 = lowest,
100 = highest.

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in other parts of the world, such as HIV/AIDS, lower respiratory infections, and maternal compli-
cations receive only 25–30% of funding from private funding bodies. So even though priorities
often line up across funders, some functional division between them appears to exist where private
money flows to disease areas relying on new medicine, while public resources are channeled
towards well-studied diseases with a need for large-scale prevention interventions.

5. 讨论: DRIVERS OF FUNDING CONCENTRATION

The Danish research funding system produces pronounced concentration with consequences
for the research population as a whole, gender equality, and topic selection. This degree of con-
centration is not least noteworthy, as the Danish system is considered relatively egalitarian.

然而, the scholarly literature does not offer convincing explanations of such allocation
图案. A main reason is most likely that no simple explanation exists. 相当, there may be a
number of mutually reinforcing causes interacting in various ways. In the following, we highlight
potential drivers and relate them to the empirical findings in Section 4. While this approach is
insufficient to draw clear causal conclusions, the findings raise important discussions and indi-
cate how different drivers interact in a specific national context. This may in turn inform policy
decisions and highlight needs for further comparative research.

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5.1.

Internal and External Drivers

Concentration is not a new phenomenon. The institutional structure of science has always been
biased toward concentration. Time and again, the pronounced inequality and the elitist nature of
scientific activity has been demonstrated, most clearly manifested in the highly skewed distribu-
tion of productivity and recognition among scientists (Allison, 1980; Allison & 斯图尔特, 1974;
Cole, 1970; 狐狸, 1983; Lotka, 1926; Merton, 1968; Price, 1963; Reskin, 1977; Zuckerman,
1970). Numerous historical examples have showed that even in cases where external pressures
were marginal or absent, highly stratified systems have been the rule rather than the exception
(Merton, 1968). 因此, some degree of selectivity in the allocation of funding has traditionally
been seen as both natural and justified.

然而, recent conscious and deliberate policy changes related to the funding and assess-
ment of science may have amplified this inherent bias. Larger grants, increased support for crit-
ical mass and emphasis on initiatives to create “world-leading” environments are only some of
such measures. Seen from this perspective increased funding concentration is both an intended
and desired outcome.

But increased funding concentration may at the same time also be the result of less obvious
and less deliberate factors. Two of these more hidden factors seem particularly important. 这
first concerns the dominant research quality criteria put to use when project proposals are as-
sessed in multiple sites. If different funding agencies operate with relatively uniform criteria
based on narrow notions of excellence (typically judged by elite peers and supported by met-
rics) priorities are likely to be mirrored even across different funders. 因此, if a majority of
funders all aim to pick and fund the “best” researchers based on similar excellence-oriented
quality criteria, the result is likely to be increased concentration.

This tendency can be further amplified by a second factor: a lack of oversight of allocation
decisions made elsewhere in the system. In situations with limited coordination and transparency
within and across grant bodies, the result may be higher concentration than any single funder or
policy-maker aims for. Even if each single grant decision in isolation is sound, the systemic effects
may be undesirable when the majority of funders select using identical parameters, with many

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funders inadvertently ending up funding the same researchers and the same narrow topics. If this is
the case, systems with a broad variety of funders may in fact risk ending up with higher degrees of
concentration than systems with more centrally steered allocation decisions.

5.2. Drivers in a Danish Context

The question is to what extent these potential explanations match the findings from Section 4. 和我们一样
will show in the following, all the above-mentioned factors appear to have been present and active
in the Danish case, interacting to amplify concentration. 第一的, the Danish system has experienced
deliberate policy attempts to increase the level of competition as well as the degree of selectivity in
the allocation of research funding over the past 15 年. As outlined in Section 4, the share of pro-
ject funding has increased from less than a third of the total research funding to nearly half.
Alongside this, grant sizes have grown and success rates have dropped (Aagaard, 2017). An explicit
policy aim has here been to try to raise the quality of Danish research through increased competition
and by deliberately amplifying central elements in the institutional bias towards concentration.

随着时间的推移, the explicit aim of funding only the most excellent ideas has also become much
more pronounced across all funders—public as well as private. 在这种情况下, 研究人员
who have high publication and citation performance and already have access to funding have
been disproportionally likely to be further rewarded across the board. 这是, 例如, 关于-
flected in the patterns of most of the top funded Danish researchers’ success in winning funding
from many different funders. 此外, there are also indications that such self-reinforcing
positive feedback loops initially may be set in motion by private foundations. These founda-
系统蒸发散, with their additional funding and specific priorities, are likely to give some researchers
and some topics the upper hand, which subsequently may become amplified by public funding
组织. 因此, when private foundations have specific topical interests and establish
and support visible, impactful research groups, this has self-reinforcing positive and negative
feedback effects for the system as a whole. This trend may be even further amplified when the
most successful grant recipients are subsequently rewarded with additional institutional fund-
ing via performance-based internal funding allocation criteria (Aagaard, 2017). 这样, 这
cycle may continue and perpetuate even further concentration.

Indications that self-reinforcing effects are active in the Danish system can be found not only
at the individual level but also at the topical level. As shown in the case study of disease-specific
研究, there is large overlap in the priorities set by different funders. Even though both public
research councils and private foundations focus the majority of their funds on disease areas with
a relatively high disease burden, their common focus exacerbates the skew of the resource dis-
贡品. Part of the explanation of this overlap in priorities is likely to be an overlap in selection
criteria between different funders. But it is also observed that public funding is least concentrated
in research closest to patients, and that private sponsors therefore become primary funders of
clinical research. These foundations may naturally focus on a narrow set of commercially viable
地区 (Rygård et al., 2018) and researchers working within these areas may have easier access to
资金. Funding may then concentrate even further on both individuals and research topics.

When a preliminary version of this analysis was presented in Denmark in 2019, 资助者,
政策制定者, and stakeholders expressed surprise and concern over the actual degree of
concentration on individuals and topics. 相似地, the distribution of funding across research
areas also came as a surprise to most actors. Among all involved parties there was general
agreement that better oversight and coordination are needed in the Danish system to ensure
a more balanced overall investment portfolio. The impression given was also that the degree of
selectivity and the actual priorities did not only reflect deliberate decisions made with open

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眼睛. To a large extent the results were also perceived as the result of information asymmetry to
the benefit of the most successful researchers. The observed patterns appear in other words to
be the result of both intended and unintended mechanisms reinforcing each other. 因此, 在
least in the case of Denmark, a pluralistic and decentralized funding system does not seem to
lead to increased diversity—rather the opposite.

有, 然而, two additional factors absent in this analysis, which also need to be taken
into account. The first of these is internal to science and relates to the perceived prestige of different
topics among researchers, journals, reviewers, and funders. While it is hard to conceptualize and
measure prestige at this level of aggregation, it can be assumed that prestige considerations to
some extent become internalized in assessment criteria and notions of excellence. 因此, 这
prestige factor may further contribute to amplifying the trend towards concentration. 第二
factor is mainly external and relates to grand societal challenges and other broad societal priorities.
These priorities will in most cases be made from the top down and may create other dynamics
across funders. 仍然, it is not evident whether societal priorities will amplify or weaken trends
towards concentration. The societal priorities may in some cases be in opposition to the more
science-internal dynamics. 这里, the incentive structure of science, with its emphasis on priority
and prestige, may in fact disincentivize scientists to study the most pressing societal problems.
While most scientists are likely to be motivated both by making scholarly contributions and solv-
ing pressing problems, the dominant disciplinary quality criteria may limit the types of problems
they can address. Topic choice is, 然而, a complicated phenomenon and may be influenced
by a host of factors, including expected academic returns, feasibility, possibilities to publish, 和
costs of doing research (Leisyte & Dee, 2012). So while the possibility to attract funding to some
extent may influence topic choices (Gläser & Laudel, 2016; Whitley et al., 2018), researchers in
general appear to be hard to influence in terms of research directions (迈尔斯, 日期不详。). 因此, 这
most effective instrument may not be specific programs, but rather funders’ decisions not to fund
certain topics (Gläser, 2019).

Societal priorities may thus in some cases lead to alternative research lines that would not
otherwise have been followed, resulting in increased diversity, but may also end up funding
already existing research lines under new headings. In other cases—as shown in relation to
the overlap in de facto priorities between public and private Danish funders—societal or specific
sectorial priorities may spark a self-reinforcing positive feedback circle, where successful appli-
cants to mission-oriented calls in turn also improve their chances of receiving more bottom-up
oriented funding. But because the present analysis has an underrepresentation of such societally
oriented grants it is beyond this study to shed light on these types of dynamics in more detail.

6. CONCLUSION AND PERSPECTIVES

全面的, the empirical examinations presented in this study document a strong concentration of
Danish research funding allocated by 15 of the largest Danish funders. These patterns of distribu-
tion are found in particular at the individual level, where a small proportion of the research pop-
ulation accounts for a very large share of the funding. 反过来, it also results in a skewed gender
balance as well as skewness in the relative weight of different research areas and more specialized
research topics. This Danish situation appears at least partly to be a result of increased competition
for external funding, decreasing success rates, many competing funding organizations using rather
uniform excellence criteria, and a general lack of coordination and oversight.

然而, the dynamics outlined above are not unique to Denmark but appear widespread
and rising in many national funding systems around the world. 因此, similar or even greater
funding concentration may be found in other national contexts. In this concluding section, 我们

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therefore discuss the pros and cons of further developments towards concentration. The discus-
sion first and foremost draws on a recent systematic literature review carried out by one of the
authors of this article and two other colleagues (Aagaard et al., 2020).

Some arguments in the scholarly literature clearly favor at least some degree of concentration. A
classical meritocratic argument is that the scientists with the greatest potential to produce (poten-
tially) path-breaking research should be rewarded according to their abilities. Economies of scale,
critical mass, and access to expensive instrumentation are other arguments. Funding concentra-
tion is furthermore argued to give increased flexibility to researchers, allowing them to take risks
and pursue their research process with long time horizons. 最后, positive spillovers to nearby
research environments, recruitment, and collaboration effects are also mentioned. These all seem
rather strong arguments and yet there are indications—which we return to below—that many of
these apparent benefits might be achieved with moderate degrees of concentration without the
potential systemically counterproductive effects of overly high concentration.

Arguments in favor of dispersal and diversity highlight in particular that the support of many
lines of inquiry spreads risk and increases chances of breakthroughs by allowing for a broader
variety of perspectives, 解释, and predictions. 同样地, chances of serendipity can also
be assumed to increase with a multitude of competing approaches. Dispersal is simultaneously
perceived to foster resilience in constantly changing research systems, where concentration, 在
另一方面, can lead to stagnation and reduced systemic adaptability. One reason is that large
self-perpetuating research units may reduce the systemic capacity to respond flexibly. Large units
may at the same time also turn talented group leaders into “science managers” with little time for
research and mentoring and with overly strong incentives and pressure to apply for and obtain ever
more resources than can be productively spent. Dispersal on the other hand is seen as supporting a
broader knowledge pool, creating absorptive capacity across systems as a whole and underpin-
ning research-based teaching across all disciplines. 在这样做, it may also secure a strong future
growth layer of early and midcareer researchers and keep a broader group of researchers and
students active in research. 最后, dispersal is argued as preferable, as it reduces trends towards
hypercompetition and may mitigate a peer review system that is perceived as unreliable, 主题
to a number of biases and often unable to identify the most promising projects.

While the empirical evidence for most of these arguments is scattered, one result seems to be
fairly robust. Multiple studies have shown that, 一般, there is a declining marginal return on
funding invested in research above a certain threshold. Although this threshold varies across
disciplinary and national boundaries, it is not generally very high. 然而, reducing optimal
funding to a question of evidence for or against concentration oversimplify a complex problem.
The “proper” balance between concentration and dispersal of research funding is more a matter of
程度: Both too little and too much concentration appears inefficient. Studies indicate that a
healthy research system ecology includes both large and small groups ( Wu et al., 2019).
此外, calls for greater diversity often seem to be interpreted as if all research can be per-
ceived as equally good and equally important. This is obviously not the case, and if diversity in
itself becomes a target, it may harm the overall development of science by diluting all quality con-
cerns. As we highlight below, the need for a well-functioning quality assessment system may be
even more pressing if more diversity should be pursued in a productive way, but it needs to build
on a broader and more inclusive variety of academic and societal perspectives. 尽管如此,
while the calls for diversity may be misused in certain situations, there are in general rather strong
indications that most countries and fields need less, not more, funding concentration.

A number of potential remedies can be highlighted if the aim is to reduce further concentra-
的: 第一的, better oversight is needed within and across funding organizations to ensure that

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allocations are based on broader portfolio perspectives and less on assessments of individual
applications in isolation. 尤其, there is a need to monitor the success of the older and
more established researchers, who appear to benefit the most from the lack of oversight.
第二, experiments are needed with funding mechanisms seeking to counter the current
concentration bias. A radical proposal here suggests widespread use of modified lottery
models for grant applicants who pass an initial quality screening (Fang & Casadevall, 2016).
Others suggest experimentation with new funding instruments to promote risky research—for
instance by fully blinding the review process. These suggestions may, 然而, be at odds
with aims to support more societally relevant research and should therefore only be a part of
a broader portfolio of funding instruments. But most importantly, there is a need to start
operating with broader understandings of research quality. Here it must be acknowledged
more explicitly that “excellence” is multifaceted and multidimensional. 因此, allocation
mechanisms must be better equipped to capture and reward the inherent variety of academic
and societal dimensions, and must do so without ending up in a situation where the concept of
quality disappears completely.

作者贡献

Emil Bargmann Madsen: 概念化, 数据管理, 形式分析, 调查,
方法, 项目管理, 软件, 验证, 可视化, Writing—original draft,
Writing—review & 编辑. Kaare Aagaard: 概念化, 数据管理, 形式分析,
资金获取, 调查, 方法, 项目管理, 软件, 验证,
Writing—original draft, Writing—review & 编辑.

COMPETING INTERESTS

The authors have no competing interests.

资金信息

This work was supported by the Research Council of Norway, grant number 256223.

DATA AVAILABILITY

The data on individual research grants were obtained from individual public and private re-
search funding organizations. 很遗憾, not all the funding organizations allow the data
to be publicly available in a data repository.

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APPENDIX

Table A1.

Summary statistics for full and Web of Science-matched samples

Female grantees

Funding amount

意思是

Median

Grant type

Research project

Postdoc grant

Studentship grants

Mobility grants

Infrastructure grants

Full sample
29%

WoS-matched sample

27%

2,472,936

934,001

2,650,834

1,000,000

56,2%

12, 6%

7,1%

5,8%

4,2%

59,1

10,9%

7,5%

5,3%

5,2%

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Table A2.

Percentiles of funding for full and Web of Science-matched samples

Percentiles
10th

20

30

40

50

60

70

80

90th

Full sample
120,000

200,000

350,000

513,399

970,076

1,367,621

1,824,608

2,586,948

5,573,906

WoS-matched sample
133,798.4

221,702.4

400,000

600,000

1,000,000

1,465,663.8

1,977,948.3

2,750,013.8

5,796,784.9

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Table A3.

Summary of cumulative funding amounts by academic age

Academic
年龄
1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

意思是
数量
2,059,150

1,916,986

2,359,436

2,318,330

3,560,705

3,919,500

5,212,371

5,816,947

8,104,687

9,013,589

10,519,679

11,831,184

16,941,984

12,040,523

18,532,573

Median
数量
1,394,369

1,406,368

1,281,250

1,430,635

1,471,361

1,811,427

1,975,000

2,587,626

Std. dev.
3,982,689

2,838,634

4,524,869

5,613,875

8,873,202

6,725,612

8,913,655

9,279,674

25th
percentile
465,050

491,842.2

612,500

475,133

457,283.5

700,000

678,674

759,628

75th
percentile
2,272,460

2,216,921

2,319,287

2,639,520

2,920,518

3,692,522

5,845,278

6,367,089

3,548,362

12,941,586

1,288,375.5

10,807,996

4,231,821

13,069,892

1,995,207.8

10,319,452

5,845,956

16,244,098

2,048,200

4,406,880

27,560,715

1,416,200

12,443,770

10,331,734

6,237,916

30,578,227

2,464,663.8

15,520,343

6,037,999

17,240,231

2,274,275

8,334,335

28,180,229

3,959,349

14,029,316

20,939,255

20,436,796

16+

20,350,703

10,503,805

28,182,465

4,257,937

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298

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150

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Figure A1. Distribution of cumulative funding across academic age. Boxplots show 25th, 50th,
and 75th percentiles.

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