#  Citation inequity and gendered citation practices in contemporary physics

Erin G. Teich  Department of Bioengineering, School of Engineering & Applied
Science, University of Pennsylvania, Philadelphia, PA 19104 USA  Jason Z. Kim
Department of Bioengineering, School of Engineering & Applied Science,
University of Pennsylvania, Philadelphia, PA 19104 USA  Christopher W. Lynn
Initiative for the Theoretical Sciences, Graduate Center, City University of
New York, New York, NY 10016, USA  Joseph Henry Laboratories of Physics and
Lewis–Sigler Institute for Integrative Genomics, Princeton University,
Princeton, NJ 08544, USA  Samantha C. Simon  Department of Physics &
Astronomy, College of Arts & Sciences, University of Pennsylvania,
Philadelphia, PA 19104 USA  Andrei A. Klishin  Department of Bioengineering,
School of Engineering & Applied Science, University of Pennsylvania,
Philadelphia, PA 19104 USA  Karol P. Szymula  School of Medicine and
Dentistry, University of Rochester, Rochester, NY 14642 USA  Pragya Srivastava
Department of Bioengineering, School of Engineering & Applied Science,
University of Pennsylvania, Philadelphia, PA 19104 USA  Lee C. Bassett
Department of Electrical & Systems Engineering, School of Engineering &
Applied Science, University of Pennsylvania, Philadelphia, PA 19104 USA  Perry
Zurn  Department of Philosophy & Religion, American University, Washington,
D.C. 20016 USA  Jordan D. Dworkin  Department of Psychiatry, Columbia
University College of Physicians and Surgeons, New York, NY 10019 USA  New
York State Psychiatric Institute, New York, NY 10032 USA  Dani S. Bassett
Department of Physics & Astronomy, College of Arts & Sciences, University of
Pennsylvania, Philadelphia, PA 19104 USA  Department of Bioengineering, School
of Engineering & Applied Science, University of Pennsylvania, Philadelphia, PA
19104 USA  Department of Electrical & Systems Engineering, School of
Engineering & Applied Science, University of Pennsylvania, Philadelphia, PA
19104 USA  Department of Neurology, Perelman School of Medicine, University of
Pennsylvania, Philadelphia, PA 19104 USA  Department of Psychiatry, Perelman
School of Medicine, University of Pennsylvania, Philadelphia, PA 19104 USA
Santa Fe Institute, Santa Fe, NM 87501 USA  To whom correspondence should be
addressed<EMAIL_ADDRESS>
###### Abstract

The historical and contemporary under-attribution of women’s contributions to
scientific scholarship is well-known and well-studied, with effects that are
felt today in myriad ways by women scientists. One measure of this under-
attribution is the so-called citation gap between men and women: the under-
citation of papers authored by women relative to expected rates coupled with a
corresponding over-citation of papers authored by men relative to expected
rates. We explore the citation gap in contemporary physics, analyzing over one
million articles published over the last 25 years in 35 physics journals that
span a wide range of subfields. Using a model that predicts papers’ expected
citation rates according to a set of characteristics separate from author
gender, we find a global bias wherein papers authored by women are
significantly under-cited, and papers authored by men are significantly over-
cited. Moreover, we find that citation behavior varies along several
dimensions, such that imbalances differ according to _who_ is citing, _where_
they are citing, and _how_ they are citing. Specifically, citation imbalance
in favor of man-authored papers is highest for papers authored by men, papers
published in general physics journals, and papers likely to be less familiar
to citing authors. Our results suggest that, although deciding which papers to
cite is an individual choice, the cumulative effects of these choices
needlessly harm a subset of scholars. We discuss several strategies for the
mitigation of these effects, including conscious behavioral changes at the
individual, journal, and community levels.

##  I Introduction

The under-attribution of women’s contributions to academic scholarship in
general—and scientific scholarship in particular—has been recognized for over
150 years Gage1870 ; Rossiter1993 . A broad body of work has studied this so-
called “Matilda effect” Rossiter1993 of under-attribution using a variety of
tools ranging from feminist theory Phillips2000 to statistics Caplar2017 . The
devaluing of women’s contributions in academia manifests in a decremented
interest in collaborating with women Knobloch-Westerwick2013 , the devaluation
of women’s contributions to scientific research articles chaoqun2021gendered ,
a pervasive perception that women have less academic excellence and ability
Knobloch-Westerwick2013 ; VandenBrink2012 ; Moss-Racusin2012 ; Bloodhart2020 ,
and a marked dearth of academic awards given to women Lincoln2012 ;
Lunnemann2019 . Women also face longer publication review processes
hengel2020publishing , fewer invited paper commissions Holman2018 , and lower
citation rates Sugimoto2013 ; Ghiasi2015 ; Caplar2017 ; Dworkin2020 ; Wang2021
; Dion2018 ; Maliniak2013 ; Mitchell2013 ; Fulvio2020 ; Chatterjee2021 .
Moreover, the under-attribution of women’s academic accomplishments represents
a dangerous erasure of women from the collectively built story of the history
and future of scientific progress. Exclusion of women from scientific
textbooks Phillips2000 ; Damschen2005 ; Wood2020a ; Simpson2021 , for example,
contributes to the construction of damaging stereotypes regarding who can be a
good scientist Carli2016 ; McKinnon2020 . Internalization of these stereotypes
can impact scientific performance Good2010a ; Schinske2016 and interest
Cheryan2015 ; Schinske2016 among women and girls, leading to greater exclusion
still. Exposure of the under-attribution of women’s contributions to science,
followed by mitigation, is thus a means of interrupting a historical cycle of
exclusion and hegemony within the sciences. Throughout, rather than assuming
individual intent towards exclusion, we take a consequentialist and post-
intent approach that is focused on the nature of current cultural and social
practices, and the collective effects of actions, in the spirit of other work
addressing structural oppression Kendi2019 ; perry2006post .

Here, we focus on quantifying the pervasive under-citation of woman authors
throughout the field of physics, and discuss ways in which citation inequity
may be mitigated by individual authors and journals. We use a proxy for author
gender—namely, a statistical correlation between the forename under which an
author publishes and gender identity, determined from two public databases—in
all analyses. We utilize this proxy both because the data it relies on is
immediately available and analyzable via automated means, and also
(importantly) because names have a great deal of influence over individual
perceptions of authors’ gender identities Pilcher2017 and thus over individual
assumptions (implicit or explicit) regarding the merit of authors’ scientific
works. This influence exists regardless of those authors’ self-attested,
actual gender identities. We show that the under-citation of women(’s names)
does not exist diffusely as a background effect baked into the fabric of
publication in physics, but rather depends on citation venue, citation actor,
and form of citation.

We analyze over one million papers published in 35 physics journals between
1995 and 2020, and examine citation practices of these papers as a function of
name-based author gender category, physics subfield, and publication date. We
find that, even after controlling for paper characteristics that are separate
from author gender category (including year and journal of publication), there
is a global imbalance in favor of man-authored papers. This citation inequity
is especially strong for citing papers within the broad category of “general”
physics (citation venue). It is driven primarily by the citing behavior of man
authors, whose imbalanced citation practice remains stable over time (citation
actor). Finally, global citation behavior trends more toward the over-citation
of man-authored papers when citations refer to work with which citing authors
may be less familiar (citation form). This effect is driven primarily by man
author teams, who exhibit citation preference for other man author teams when
citing both familiar and less familiar work. In contrast, among woman authors
we see evidence for distinct citation behaviors—a preference for other woman
author teams when citing familiar work, and citation equity when citing less
familiar work—consistent with practices of resistant knowledge building in
other parts of society Collins2019 .

Our results point toward specific actions that can be taken by individual
citers and publishing journals to mitigate citation inequity within physics.
For individual authors, we advocate for thoughtful engagement with the gender
make-up of every published reference list, and highlight an increasingly
common accountability measure in the form of a citation diversity statement
Zurn2020 ; Dworkin2020a . In particular, our work indicates that special care
must be taken when referencing work that lies outside one’s immediate sphere
of knowledge or scientific network; in these cases, over-citation of man-
authored papers can be especially high. We also show that longer reference
lists tend to display less over-citation of man-authored papers, for all
citing teams. These results suggest an implicit gendered meritocracy whereby
man authored papers are viewed as more deserving than woman authored papers
when resources (reference list length) are limited. While addressing this
implicit gendered meritocracy, individual researchers might also choose to
cite more papers (when allowed) to broaden engagement with other scientists
and work toward citation equity. Publishing journals, similarly, can
reconsider limitations on reference list lengths, recommend the inclusion of
citation diversity statements, and work toward more equitable representation
in their author pool, with the aim of mitigating citation imbalance in their
current and future articles.

##  II Methods

In this section we will briefly describe our methods for data acquisition,
preprocessing, and analysis. Our methods draw from and build upon the broad
and growing body of literature on gendered citation bias throughout academia
Sugimoto2013 ; Ghiasi2015 ; Caplar2017 ; Dworkin2020 ; Wang2021 ; Dion2018 ;
Maliniak2013 ; Mitchell2013 ; Fulvio2020 ; Chatterjee2021 ; in particular, we
have expanded upon the methods used for a recent study of citation bias in
neuroscience journals Dworkin2020 .

###  II.1 Data acquisition

####  II.1.1 Journal selection

In order to broadly characterize citation behavior within and across the
subdisciplines of physics, we selected a list of peer-reviewed journals guided
by several criteria. First, the journals needed to cover all major subfields
of physics, as defined by the breakdown of the _Physical Review_ family of
journals and the _Web of Science_ database categories. Second, within each
subfield we selected the central journals based on their Eigenfactor score
bergstrom_eigenfactortm_2008 (a measure that rates journals according to
incoming citations, weighted by the impact of those citations’ journals) as
reported by InCites Journal Citation Reports for the year 2018. Third, we
aimed to represent each subfield by an equal number of journals, while
allowing the number of papers to differ. This initial search resulted in 7
non-overlapping lists of 5 journals each, for a total of 35 journals. These
journals are listed in Fig. 1b.

####  II.1.2 Data collection

We downloaded all papers published in the 35 chosen journals between 1995 and
2020 from the _Web of Science_ database. We then selected all papers
classified as original research articles or review articles, and extracted
information on author names, reference lists, publication dates, and DOIs.
Each paper’s citation behavior was obtained by matching DOIs contained within
its reference list to DOIs of papers in our dataset. Authors’ last names were
included for all papers; however, for a portion of papers, authors’ first
names were not included in the database. First names are necessary for our
name-based author gender categorization scheme (see Section II.2.3), so we
attempted to find these missing first names in two ways: (i) Searching for
author first names using Crossref’s API, and (ii) Implementing a name
disambiguation scheme (see Section II.2.1) whereby authors’ initials and/or
other name abbreviations are matched to and replaced by their full first names
if possible.

###  II.2 Data preprocessing

####  II.2.1 Author name disambiguation

To maximize the number of analyzable papers for subsequent author gender
categorization by first names, we employed a method of disambiguating authors
for whom several versions of their name or initials were available across
papers, followed by assignment of the most complete version of each author’s
name to all papers they authored. Due to the size of our dataset, we performed
our name disambiguation procedure in parallel on isolated subsets of papers,
grouped according to their initially-defined subfields shown in Fig S1. This
method involved several steps. First, we identified all cases for which first
and/or last authors’ first names consisted only of initials by isolating all
authors’ first names for each paper, and then flagging the first and last of
those which contained only uppercase letters. Next, for each case of a flagged
first name that only contained initials, we gathered all other name instances
with the same first/middle initials and the same last name. If only one unique
first/middle full name matched the initials-only entry, or if all distinct
full name matches were variants of the same name, we assigned that name to the
initials. However, if multiple unique first/middle full names matched the
initials-only entry, we did not assign a name to the initials. For example, if
an entry listed an author as A. A. Griffin, and we found matches under Abby A.
Griffin and Abigail A. Griffin, we would replace the A. A. Griffin entry with
Abigail A. Griffin. If instead we found matches under Abby A. Griffin and
Arlene A. Griffin, we would not assign a name to A. A. Griffin. Initially, our
dataset contained 463,538 initials-only first and/or last author name entries.
Through the steps outlined above, we were able to assign full first names to
88,780 of these entries, for a success rate of $88,780/463,538\approx
19.15\%$.

We employed a similar strategy to match name variants in order to more
accurately determine authorship histories of individual authors. For every
author entry, we first identified sets of corresponding author entries with
matching last names and either the same first name or first names determined
to be common nicknames of each other (e.g., Abby and Abigail) according to the
Secure Open Enterprise Master Patient Index toth_soempi:_2014 . If no
corresponding matches existed, we retained the author entry name. If
corresponding matches did exist and one match occurred more often, the less
common name variant was changed to the more common name variant. Similarly, if
the corresponding matches did not have any conflicting initials, the less
common initial variants were changed to the more common initial variants. A
common non-conflicting scenario in this case was that some matches had middle
initials and others had no middle initials. If multiple corresponding matches
did have conflicting initials, however, the author entry name was not changed.

####  II.2.2 Estimation of publication month

While the year of publication was available for all 1,067,276 papers, the
publication month was not available for 38,423 papers ($\approx 3.6\%$). In
order to approximate the unknown month $m_{i}$ for each paper $i$ published in
year $y_{i}$, we considered its lower and upper bounds. The lower bound was
set to be the month of publication of the most recent paper cited by $i$ if
the most recent paper was published in year $y_{i}$, or January otherwise. The
upper bound was set to be the month of publication of the first paper to cite
$i$ if the first paper was published in year $y_{i}$, or December otherwise.
We then approximated $m_{i}$ as the midpoint between the upper and lower
bounds. To assess the validity of this approach, and to understand the
associated uncertainty, we performed the same analysis on the
$1,067,276-38,423=1,028,853$ papers for which the publication month was
available. In this test case, we found that the average absolute error between
the true month and the estimated month was $\approx 2.27$ months. In contrast,
the average absolute error of naively guessing a publication month between
June and July was $\approx 2.98$, indicating that our method provides a
reasonable approximation.

####  II.2.3 Name-based assignment of author gender categories

We assigned “author gender categories” to papers according to first names of
papers’ first and last authors. Gender was assigned to authors with available
first names using Gender API, a paid service that includes statistics for
approximately 6 million unique first names across 191 countries at the time of
writing genderAPI . We assigned the label ‘man’ (‘woman’) to each author if
their first name had a probability $\geq 0.7$ of belonging to someone labeled
‘man’ (‘woman’) according to our sources Dion2018 . Labels are assigned in the
Gender API dataset according to a combination of sex assigned to children at
birth or chosen by adults later, and gender detected in social media profiles.

Our dataset includes $n=1,067,276$ papers, for a total of $n$ first authors
and $n$ last authors. Among them, we were able to assign gender labels to both
first and last authors in 60% of papers, to only one of either first or last
author in 27% of papers, and to neither the first nor last author in 13% of
papers. Among all first and last authors with unassigned gender labels, 65.4%
were due to publishing using initials. To ensure that omitting these authors
in subsequent analyses would not significantly skew our results, we sought to
estimate the gender label distribution among these authors. As a proxy for
this author set, we examined the set of authors for which we uniquely matched
initials to first names using our name disambiguation scheme, and successfully
assigned author gender labels (see Section II.2.1). Of these 79,592 authors,
66,255 ($\approx 83.24\%$) were assigned the label ‘man’ by our algorithm and
13,337 ($\approx 16.76\%$) were assigned the label ‘woman’ (see the
_Supplementary Information_ for details). These numbers are consistent with
the ratios of assigned gender labels of all first and last authors in our
dataset, of which $\approx 87.92\%$ were labeled ‘man’ and $12.07\%$ were
labeled ‘woman.’ Hence, as far as we can measure, the distribution of genders
in unassigned author names is not radically different than that of assigned
author names.

We then subdivided papers into author gender categories according to assigned
gender labels of first and last authors. If the first and/or last author’s
name was assigned the label ‘woman,’ we categorized the paper as W$||$W. To
increase statistical power, we included all papers in this category with at
least one woman-assigned first/last author, even if the other author could not
be assigned a gender label according to our methods. If the first and last
author’s name was assigned the label ‘man,’ we categorized the paper as MM.

We emphasize that, although the phrase “author gender category” contains the
word “gender,” it need not capture the true gender identities of all authors.
Instead, it expresses a statistical correlation: By ‘woman’ we mean an author
whose name has a probability greater than or equal to 0.70 of belonging to
someone identifying as a woman on social media or in federal documents;
likewise, by ‘man,’ we mean an author whose name has a probability greater
than or equal to 0.70 of belonging to someone identifying as a man on social
media or in federal documents. True gender identity could only be learned
through careful manual research of self-attested gender identity, or already
known through kinship or conversation, and is not accessible via an automated
analysis pipeline like the one used in this paper. However, the author gender
category is nevertheless a notably useful proxy of gender for the purposes of
this paper, because it expresses a correlation between name and gender. Names
greatly influence perceptions of gender identity Pilcher2017 , with well-known
implications for a person’s perceived merit as a scientist Moss-Racusin2012 .
These perceptions have marked power to shape citation behavior, irrespective
of authors’ true gender identities.

####  II.2.4 Reference list cleaning procedure

We pared down each paper’s reference list into a “clean” version suitable for
our analysis, which we used for all investigations of citation behavior
(unless indicated otherwise). From each reference list, we removed self-
citations, citations to papers not in our dataset, and citations to papers
with authors whose names could not be assigned to a gender category. We chose
to remove self-citations from all analyses of citation behavior in order to
focus on the influence of perception of other authors’ gender category on
external citation behavior. Self-citations were defined conservatively as
references to papers for which either the cited first or last author was also
the citing first or last author. We note that in a related study of citation
behavior in neuroscience journals, it was shown that including self-citations
did not result in meaningful differences in overall over-/under-citation
trends Dworkin2020 .

###  II.3 Analysis

####  II.3.1 Probability estimation of author gender category according to
paper characteristics

To quantify over-/under-citation behavior, we first developed a gender-blind
null model predicting the probability that papers were written by MM or W$||$W
author teams according to a set of paper characteristics enumerated below.
Then, over any set of reference lists, we could tally the number of cited
papers written by MM or W$||$W author teams and compare these quantities to
the expected numbers given by the gender-blind null model. The characteristics
we used to predict MM or W$||$W authorship for each paper were (i) month and
year of publication, (ii) first and last authors’ combined number of papers in
the dataset, (iii) total number of authors, (iv) publishing journal, and (v)
categorization as a research or review article (Fig. 2a). Specifically, we fit
a generalized additive model (GAM) on the binomial outcome {MM, W$||$W} with
predictive features as defined above. We fit this model to all papers in our
dataset whose authors’ names could be assigned gender categories. To fit the
GAM, we utilized the ‘mgcv’ package in R (mgcv, ), using penalized thin plate
regression splines for estimating smooth terms of features (i), (ii), and
(iii) described above. We note that we used the logarithm of feature (iii) and
a winsorized version of feature (ii), capped at 300 (representing the top 0.6%
of papers), to ensure that we fit the GAM successfully. Univariate thin plate
splines were used for the smooth terms, and no interactions between variables
were included in the model. For each article, the GAM then yields a predicted
probability of MM or W$||$W authorship; we interpret and utilize these
probabilities as approximations of the proportion of similar articles (i.e.,
articles with comparable values of the above characteristics) written by each
group. These values thus allow us to calculate the proportions of MM and
W$||$W citations that would be expected if references were drawn in a gender-
agnostic manner from pools of characteristic-matched papers.

####  II.3.2 Calculation of over-/under-citation

For a given group of citing papers, we defined its over/under-citation of each
author gender category as the percent difference of observed citations from
gender-blind expectation. Over-/under-citation of MM papers, for example, is
given by $(o_{MM}-e_{MM})/e_{MM}*100$, where $o_{MM}$ is the (observed) number
of citations given to MM papers by the citing papers, and $e_{MM}$ is the
expected number of MM citations predicted by the gender-blind model described
in the previous section. More specifically, $e_{MM}$ is computed by summing
over the GAM-estimated probabilities that each citation given by the group
belongs to the author gender category MM.

####  II.3.3 Subfield delineation

To understand how citation practices vary between disciplines, we grouped
journals into defined “subfields.” The boundaries between subfields were drawn
according to a combination of (i) pre-defined journal categories culled from
the breakdown of the _Physical Review_ family of journals and journal
categories defined by _Web of Science_ , and (ii) _post-hoc_ citation network
clustering. The resultant subfields and their constituent journals are shown
in Fig. 1b. See the _Supplementary Information_ for further details regarding
the citation network clustering that was used to identify subfields.

##  III Results

###  III.1 Time-varying demographics of published papers

We first present a demographic overview of the data set. Our data consists of
approximately 1.07 million papers published between the years 1995 and 2020 in
35 representative and central journals (as measured by their 2018 Eigenfactor
score) across a range of 8 physics subfields. Of these papers, 668,690 could
be identified according to their name-based author gender category (see the
_Methods_ for details). The proportion of papers in each author gender
category are shown in Fig. 1a as a function of publication year. Although the
proportion of woman-authored (W$||$W) papers has increased from 17% in 1995 to
33% in 2020, it nevertheless represents a small proportion of the total number
of MM and W$||$W papers, in agreement with other studies Holman2018 .
Moreover, the proportion of papers authored by first and last authors with
names assigned to women (WW) remains significantly lower, growing from 1.7% in
1995 to only 3.6% in 2020.

Although the proportion of W$||$W papers increases in all subfields,
individual journals vary significantly in that proportion and in its rate of
change (Fig. 1b-c). The journals grouped into the general physics
subfield—which includes many of the highest impact journals in physics—and the
high energy physics subfield collectively contain the lowest proportions of
W$||$W papers. This pattern remains consistent over time. Conversely, journals
grouped into the astronomy and astrophysics subfield generally contain the
highest proportion of W$||$W papers over time, followed by the relatively
young journals grouped into the nanoscience subfield (four of which were
launched during the time period we analyze). Averaged over years, journals
with the lowest fraction of W$||$W papers are _Reviews of Modern Physics_
(0.11), _Journal of High Energy Physics_ (0.15), and _Journal of Fluid
Mechanics_ (0.15). These three journals also have the lowest fraction of
W$||$W papers published in 2020 among all journals, indicating that this trend
is not merely due to their older age and the general increase of woman authors
over time. Journals with the highest fraction of year-averaged W$||$W papers
are _Nanoscale_ (0.41), _Soft Matter_ (0.40), and _ACS Applied Materials &
Interfaces_ (0.40).

Figure 1:  Time-varying demographics of published papers according to author
gender category. (a) Proportions of papers according to author gender category
over time. The WU + UW sub-category consists of papers in which one of the
(first or last) author’s names was assigned to the woman gender category, and
the other of the (first or last) author’s names could not be assigned to a
gender category (see _Methods_). (b) Proportion of W$||$W papers published in
all journals in our dataset over time. Journals are subdivided according to
the subfield definitions used throughout the paper. Missing squares occur for
journals before their launch year. (c) Proportion of W$||$W papers published
within each subfield over time. All proportions shown here are with respect to
the per-year sum of MM and W$||$W papers (that is, not including papers with
authors whose names could not be assigned a gender category).

###  III.2 Citation imbalance exists & varies by citing venue

We next examine the citation behavior of the papers in our dataset, and find
that citation behavior is imbalanced with respect to the author gender
category of the cited papers. We consider only the citation behavior of papers
published in 2009 or later, since these papers are more likely than those
published earlier to cite other papers in our (1995 – 2020) dataset. To
increase statistical power, the citation behavior reported in this section is
aggregated over all papers published in 2009 or later, even those that could
not be assigned to an author gender category. We define over-/under-citation
of an author gender category as the percent difference between the number of
citations that papers in the category actually receive and their expected
number of received citations according to a gender-blind model (see
_Methods_).

In general, MM papers are cited _more_ often than expected by approximately
1.06%, and W$||$W papers are cited _less_ often than expected by approximately
3.17% (Fig. 2b). These results constitute an overall gender citation gap of
roughly 4.23%. This gap varies significantly across subfields (Fig. 2c) and
journals within those subfields (Fig. 2d). Papers published in journals
grouped into the general physics subfield collectively show the widest
citation gap, whereas papers in journals grouped into the astronomy and
astrophysics subfield collectively show the narrowest citation gap.

As shown in finer detail in Fig. 2d, citation behavior at the journal level
varies more widely still. Here, each point in the space of MM over-/under-
citation versus W$||$W over-/under-citation shows the collective citation
imbalance of papers grouped according to their publishing journal. The data
follow an approximately linear trend with negative slope, indicating the
correlation between over-citation of MM papers and under-citation of W$||$W
papers. Journals that lie more deeply in the lower right quadrant host papers
that collectively exhibit greater citation preference for MM papers, whereas
journals that lie in the upper left quadrant host papers that collectively
exhibit greater citation preference for W$||$W papers. Most journals are
located in the lower right quadrant, indicating their preference toward MM
over-citation, and only three journals (_Journal of Nuclear Materials_ ,
_Astronomy & Astrophysics_, and _Soft Matter_) show a statistically
significant preference for citing W$||$W papers.

Figure 2:  Over-/under-citation of physics papers is imbalanced with respect
to author gender category. (a) Illustration of the statistical model used to
estimate over-/under-citation of MM or W$||$W papers according to paper
characteristics. (b) Over-citation of MM papers and under-citation of W$||$W
papers is exhibited in aggregate over all citing papers in our data set
published between 2009 and 2020. Over-/under-citation varies when the citing
papers are grouped according to their (c) subfield and (d) journal. In panel
d, each marker reflects an individual journal colored according to subfield.
In all panels, the reported over-/under-citation values utilize the reference
lists of all relevant citing papers, including those of unknown author gender
category, to increase statistical power. Error bars representing the 95% CI of
each over-/under-citation calculation were computed via 500 bootstrap
resampling iterations.  Figure 3:  Citation behavior varies across time and
according to citing author gender category. (a) Over-/under-citation of MM and
W$||$W papers, calculated separately for MM and W$||$W citing teams published
between 2009 and 2020. Each team exhibits citation preference toward their own
author gender category. (b) Citation behavior of each citing author gender
category varies over time. MM citing teams exhibit a higher citation
preference toward other MM papers and a lower citation preference to W$||$W
papers, resulting in a citation gap that is widening over time. W$||$W citing
teams exhibit lower citation preference toward other W$||$W papers, and that
preference decreases over time. (c-d) Citation imbalance exhibited by MM teams
and W$||$W teams varies according to subfield. In both types of teams, papers
in the general physics category exhibit the highest over-citation in favor of
MM papers. (e) Overall citation imbalance within subfields is relatively
stable over time. Values reported in this panel incorporate the reference
lists of all relevant papers, including those of unknown author gender
category, to increase statistical power. In all panels, error bars
representing the 95% CI of each over-/under-citation calculation were computed
via 500 bootstrap resampling iterations.

###  III.3 Citation imbalance varies by citing actor

We further separate citation behavior according to the author gender category
of citing teams, and find that MM papers and W$||$W papers differ in their
citation behavior: MM papers tend to exhibit higher citation preference toward
other MM papers and lower citation preference toward W$||$W papers, whereas
W$||$W papers tend to exhibit higher citation preference toward other W$||$W
papers and lower citation preference toward MM papers. The extent and
existence of these citation preferences vary across subfield and across
journal. MM citing papers published in 2009 or later over-cite other MM papers
by 2.05%, and under-cite W$||$W papers by 6.53%, for a gender citation gap of
approximately 8.58% (Fig. 3a). By contrast, W$||$W citing papers published in
2009 or later over-cite other W$||$W papers by 3.56%, and under-cite MM papers
by 1.38%, for a citation preference in favor of other W$||$W papers of
approximately 4.94% (Fig. 3a).

These citation behaviors vary widely across subfields (Figs. 3c-d, S4). MM
papers in the general physics subfield show the highest citation gap, 16.47%,
in favor of other MM papers. MM papers in the nuclear and
atomic/molecular/optical subfields show the next highest citation gaps, each
above 15%. By contrast, W$||$W papers in the astronomy/astrophysics and soft
matter/biophysics subfields exhibit a citation preference toward other W$||$W
papers, resulting in citation gaps in favor of other W$||$W papers of 8.42%
and 6.53%, respectively. Interestingly, citation preference in favor of other
W$||$W papers does not exist for W$||$W citing papers in the general physics,
atomic/molecular/optical, and condensed matter subfields. Rather, papers in
these subfields show under-citation of other W$||$W papers and over-citation
of MM papers. W$||$W papers grouped into the general physics subfield show the
greatest citation gap (8.8%) in favor of MM papers.

###  III.4 Stable and growing trends in citation imbalance over time

Inspection of citation behavior as a function of time reveals that, in
general, the citation gap between over-citation of MM papers and under-
citation of W$||$W papers has remained relatively stable between the years of
2009 and 2020, and even slightly grown (Fig. 3b,e). The difference in citation
preference between MM and W$||$W citing teams, explored in the previous
section, also persists over time. However, time trends in these citation
preferences vary significantly for MM versus W$||$W citing teams. Trends also
differ across the subfield and publishing journal of citing papers; the
overall picture, however, is one of stagnant or worsening citation gaps over
time, despite the relative growth of papers authored by W$||$W teams.

The time evolution of citation imbalance for all papers in our dataset from
2009 to 2020, grouped according to citing author gender and year of
publication, is shown in Fig. 3b. The citation gap in favor of MM papers
exhibited by MM citers is larger in 2020 than in 2009 (Fig. 3b, red lines),
due to an overall increase in MM over-citation and W$||$W under-citation over
time. That this gap persists in the face of a growing fraction of published
W$||$W papers over the same time period (Fig. 1a) is notable. The fraction of
citations actually given by MM citers to MM (W$||$W) papers over time
maintains a steady positive (negative) gap with respect to the fraction
expected to be given according to our model (Fig. S5a). By contrast, W$||$W
citers show a consistent citation preference in favor of other W$||$W papers
with a markedly different trend over time (Fig. 3b, blue lines). For these
citers, the citation gap in favor of other W$||$W papers decreases over time,
in contrast to the increasing citation gap in favor of other MM papers shown
by MM citers. The fraction of citations given by W$||$W citers to MM (W$||$W)
papers over time shows a narrowing negative (positive) gap with respect to the
fraction expected to be given according to our model (Fig. S5b). The data
indicate an approach toward citation parity over time by W$||$W citers.

When grouped according to subfield, citation behavior shows a variety of
different trends over time (Figs. 3e, S6, S7). Citation gaps between MM
authored papers and W$||$W authored papers vary in magnitude according to
subfield, but are relatively stagnant over time in many cases (within error
bars). Two subfields that notably do not exhibit this behavior are the general
physics and condensed matter subfields, for which the citation gap increases
between 2009 and 2020, to 16.67% and 10.7% in 2020, respectively.

Figure 4:  Citation behavior varies according to proxies for familiarity with
cited work. Proxies are (a) whether the publishing journals of cited and
citing papers fall within the same subfield, and (b) whether the cited and
citing papers have any shared authors. In each panel, a schematic of the proxy
for familiarity is shown on the left, and citation behavior according to that
proxy is shown on the right. Markers show the citation behavior of (black) all
papers written between 2009 and 2020, including those with unassigned author
gender categories, (red) the subset of papers in the MM author gender
category, and (blue) the subset of papers in the W$||$W author gender
category. Arrows point from over-/under-citation when considering only
“familiar” citations to over-/under-citation when considering only
“unfamiliar” citations. Overall, over-citation of MM papers and under-citation
of W$||$W papers is more marked for unfamiliar citations, although this effect
is due to differing behaviors of MM and W$||$W citing teams. In both panels,
error bars representing the 95% CI of each over-/under-citation calculation
were found via 500 bootstrap resampling iterations.

###  III.5 Citation imbalance varies according to its form

The citation behaviors exhibited by MM and W$||$W teams vary significantly in
magnitude according to the form or type of each citation; more specifically,
whether the citation references work that authors are more or less likely to
be familiar with. We define proxies for familiarity between citing paper and
cited paper in two ways: (i) whether they are published in journals that fall
within the same subfield (Fig. 4a, left), and (ii) whether they are written by
at least one shared author (Fig. 4b, left, and _Supplementary Information_).
Reference lists of citing papers contain a range of reference proportions that
are deemed familiar according to these definitions (Fig. S8). We additionally
define subfield boundaries by clustering the citation network between journals
(see _Supplementary Information_), resulting in subfields distinct from those
shown here, and find that our results are robust across subfield definition
(Fig. S9).

With both proxies for familiarity, we find similar results regarding the total
citation gap between MM and W$||$W authored papers: For the set of unfamiliar
citations, the citation gap is larger, with greater over-citation of MM papers
and greater under-citation of W$||$W papers (Fig. 4a-b, black symbols). Out-
of-subfield MM papers are over-cited by 1.90%, and out-of-subfield W$||$W
papers are under-cited by -7.36%, while these rates are 0.66% and -1.80% for
within-subfield MM and W$||$W papers, respectively. Unshared-author MM papers
are over-cited by 1.29%, and unshared-author W$||$W papers are under-cited by
-4.34%, while these rates are 0.57% and -1.39% for shared-author MM and W$||$W
papers, respectively. For reference, we note that these values for all forms
of citation, independent of familiarity, are MM over-citation of 1.06% and
W$||$W under-citation of 3.17% (Fig. 2b).

The suppression of the “familiar citation gap” and the enhancement of the
“unfamiliar citation gap” together arise from the cumulative effects of two
very different citation behaviors according to citing author gender category.
Across familiar citations, both MM (Fig. 4a-b, red symbols) and W$||$W (Fig.
4a-b, blue symbols) citing teams show enhanced citation preference for their
respective author gender categories. That is, MM teams preferably cite MM
papers, while W$||$W teams preferably cite W$||$W papers. We note that these
competing effects may be partially explained by an overall homophilic
enhancement in the local co-authorship network around each paper, revealed by
higher man-author overrepresentation in co-authorship networks around MM
papers and lower man-author overrepresentation in co-authorship networks
around W$||$W papers (see _Methods_ , Fig. S10).

Across unfamiliar citations, however, MM and W$||$W teams differ in their
citation behavior. For W$||$W teams, citation preference for W$||$W papers is
approximately erased. By contrast, for MM teams, citation preference for MM
papers is not erased. Instead, this preference is enhanced for out-of-subfield
citations, and slightly reduced but still significant for unshared-author
citations. Thus, we find that W$||$W teams preferably cite familiar W$||$W
papers and cite unfamiliar W$||$W and MM papers approximately equitably. MM
teams over-cite familiar MM papers and under-cite familiar W$||$W papers, a
trend that is even more pronounced for unfamiliar papers. The overall result
is a smaller familiar citation gap, due to the competing citation behaviors of
W$||$W and MM citing teams, and a larger unfamiliar citation gap in favor of
MM papers, due to the MM citing papers’ persistent citation preference for
other MM papers even when citing unfamiliar references.

Note that, although citation imbalance across familiar citations is
approximately equal and opposite for W$||$W and MM citing teams (for both
definitions of familiarity), it is not distributed equally across W$||$W and
MM cited papers. Rather, W$||$W teams exhibit a citation preference for W$||$W
papers (vertical coordinate of the dark blue markers in Figs. 4a,b) that is
about double that of MM teams for MM papers (horizontal coordinate of the dark
red markers in Figs. 4a,b). By contrast, MM teams under-cite W$||$W papers
(vertical coordinate of the dark red markers in Figs. 4a,b) at a rate that is
about double the under-citation of MM papers by W$||$W teams (horizontal
coordinate of the dark blue markers in Figs. 4a,b).

###  III.6 Additional correlates of citation imbalance

Our dataset reveals additional correlations between citation behavior and
citing actor, venue, and form, each of which might be useful considerations
for developing individual and institutional strategies to mitigate citation
imbalance in the future. In particular, we find that citation behavior varies
on the journal level according to the relative proportion of W$||$W published
papers, and on the paper level according to the length of the reference list.
For the former, we note that the 35 journals investigated in this paper
generally show an increasing time-aggregated citation preference for W$||$W
papers with an increasing time-aggregated fraction of W$||$W papers published
(Fig. 5a). Correspondingly, the time-aggregated citation preference for MM
papers decreases with an increasing time-aggregated fraction of W$||$W papers
published (Fig. S11). These results are not unexpected given the tendency of
W$||$W papers to cite other W$||$W papers to a greater extent than MM citing
papers do (Fig. 3a-d). The data demonstrate that representation within journal
authorship pools is a meaningful correlate of citation imbalance.

For individual citing papers, we also find a collective trend whereby papers
with longer reference lists tend to exhibit increased citation preference for
W$||$W papers (see _Supplementary Information_ , Fig. S12). This trend holds
independently for both MM and W$||$W citing teams, despite the fact that
W$||$W papers in our dataset contain longer reference lists in comparison with
MM papers (Fig. S13). Notably, the trend also remains stable over time,
despite the fact that reference list length within our dataset generally
increases over time (Fig. S14). Fig. 5b demonstrates this phenomenon for
papers published in 2019. Papers are grouped according to author gender
category and reference list length, and linear fits to the data for each
author gender category show the upward trend of W$||$W citation preference
with reference list length. The slopes of these linear fits, averaged over the
years between 2009 and 2020, suggest that reference lists gain approximately
1.5% in W$||$W citation preference when they add 10 citations (Fig. S15).
Because the coefficient of determination of each linear fit is low (Fig. S16),
the relation should be considered a weak but statistically significant
collective effect rather than an exact measure of correlation for any
particular paper subset. The conceptual significance of this effect is notable
when considered in light of the global rate of MM over-citation (1.06%) and
W$||$W under-citation (-3.17%) for all (2009-2020) papers (Fig. 2b).

Figure 5:  Additional correlates of citation behavior. (a) Journals that
published a higher proportion of W$||$W papers between 2009 and 2020 generally
exhibited higher citation of W$||$W papers. Each marker represents a journal;
error bars representing the 95% CI of each over-/under-citation value
(calculated across all citing papers published in each journal between 2009
and 2020) were found via 500 bootstrap resampling iterations. Proportions of
W$||$W papers are reported with respect to total MM and W$||$W papers
published in each journal between 2009 and 2020. (b) Papers with longer
reference lists tend to exhibit higher citation of W$||$W papers. The panels
show that this trend is consistent for MM papers published in 2019 (top) and
W$||$W papers published in 2019 (bottom). Each data point shows over-/under-
citation aggregated over paper subsets of maximum size 10 at each reference
list length (see _Supplementary Information_ for details). Linear fits to the
data via ordinary least-squares are also shown, expressed approximately by
$y=0.126x-13.095$ (top) and $y=0.192x-5.911$ (bottom).

##  IV Discussion

Gender disparities exist throughout the discipline, performance, and processes
of science. While visible markers of these disparities have been detectable
for decades (or rather, centuries), other manifestations of imbalance are more
subtle, requiring the use of tools and technologies in the science of science.
Employing such tools, here we focused on evaluating the extent and drivers of
gender imbalance in the reference lists of physics papers published across a
broad range of 35 physics journals over the last 25 years. Using automated
name-based gender prediction and a model for citation behavior that estimates
over/under-citation while controlling for paper characteristics, we found that
papers within the man author category have been globally over-cited, and
papers within the woman author category have been globally under-cited. We
additionally found that this citation imbalance depends heavily on citing
author gender category, the publishing journal of citing papers, proxies for
familiarity of citing authors with cited papers, representation in journal
authorship pools, and reference list length. Our results underscore the
complexity with which gender disparities manifest in scientific publishing,
and identify correlates that could inform future actions by individuals,
journals, and collectives.

###  IV.1 Homophilic behavior and its drivers

Throughout our analyses, we observed homophilic citation behavior for both MM
and W$||$W teams, with MM citing teams tending to devote more of their
reference lists to papers published by other MM teams than predicted by our
model, and W$||$W citing teams tending to devote more of their reference lists
to papers published by other W$||$W teams than predicted by our model. For MM
citing teams, this homophilic behavior was persistent over time, pronounced
across subfields, and present for both more familiar and less familiar types
of citations. For W$||$W citing teams, homophilic behavior lessened in
magnitude over time, varied according to subfield (with some subfields not
showing homophily), and was significant only for more familiar citations.

The presence of gendered homophilic citation behavior throughout our dataset
is not surprising; indeed, homophily along numerous dimensions of similarity
is a well-studied and prominent driver of human activity and social system
development McPherson2001 . In academia, gender homophily influences patterns
of co-authorship and collaboration Boschini2007 ; Jadidi2018 ; Wang2019a ;
Holman2019 ; Kwiek2021 , citations Ghiasi2018 , invitations to give colloquia
and other talks Isbell2012 ; Debarre2018 ; Nittrouer2018 , networking
Belle2014 ; Atzmueller2018 , the nomination of Nobel laureates Gallotti2019 ,
and peer-reviewer selection Helmer2017 . We note that several of these studies
imply that gendered homophilic behavior seems unlikely to be an effective
driver of gender equity. A study of gender homophily within primatologists
Isbell2012 found significant homophily among men in invited symposium talks
even though women make up the majority of that field. Homophily has also been
shown to increase with increasing representation of women in other contexts
Boschini2007 ; Wang2019a . Moreover, a study of gender homophily in the peer-
review process Helmer2017 found different patterns of homophily for men versus
women, with men engaging in widespread homophilic behavior, and the homophilic
behavior of women due to only a few highly homophilic women editors. Authors
of that paper stressed that such a top-down approach toward engaging more
women in the peer-review process, dominated by a handful of actors, was less
likely to remain stable and effective over time than a more bottom-up approach
adopted by a range of actors.

We stress that, although homophilic behaviors of majority and minority
populations in any context (here, men and women in physics) might seem similar
on the level of quantitative analysis, they need not be driven by similar
factors. Members of a minority population may choose to take part in “activist
choice homophily,” built on the perception of shared structural barriers and a
desire to help overcome those barriers Greenberg2017 . The driver of activist
choice homophily is notably distinct from other typical drivers of homophily
based solely on similarity in perceived attributes McPherson2001 . In this
paper, the homophilic practices of women in physics are acts of citing other
women and thereby permanently embedding them into the scientific canon. These
homophilic practices, if driven by activist choice, could thus be argued to
fall under the category of resistant knowledge building and epistemic
resistance Collins2019 against a scientific narrative dominated by men, and
especially white men. In general, our results point toward the need for all
citing actors within physics to critically engage with their reference lists,
consider the historical and contemporary imbalances they seek to address
through their citation practices, and act accordingly.

###  IV.2 Toward citation equity

Gender disparities in the citation practices of physics are not surprising.
Such disparities have been reported in fields as diverse as astronomy
Caplar2017 , economics Dion2018 , neuroscience Dworkin2020 , cognitive
neuroscience Fulvio2020 , medicine Chatterjee2021 , communications Wang2021 ,
and international relations Maliniak2013 . The responses of these fields can
serve as an example for the physics community as it grapples with its own
internal culture. Such responses have spanned from individual actions to
journal stances and editorial policies. At the individual level, scholars have
taken it upon themselves to add a citation diversity statement (CDS) to their
papers, just before the reference list, stating (i) the importance of citation
diversity, (ii) the percentage breakdown (or other diversity indicators) of
citations in the paper, (iii) the method by which percentages (or other
indicators) were assessed and its limitations, and (iv) a commitment to
improving equitable practices in science Zurn2020 . In a retrospective
analysis, papers published with a CDS have been found to display citation
practices in line with expected rates, without any statistically detectable
gender disparities oudyk2021cleanbib . This finding is notable, and
underscores the efficacy of the CDS as an individually-led tool for the
mitigation of disparities.

At the journal level, responses have ranged from statements of support (e.g.,
from _Nature Reviews Physics_ and others Budrikis2020 ; natneuroeditorial2020
; braineditorial2020 ), commentaries Fairhall2020 , and essays
davies2021promoting ; pierce2020women ; Llorens2021 , to recommendations and
formal policies. For example, the _Journal of Cognitive Neuroscience_ provides
a section in their Author Guidelines regarding citation disparity, supports
the use of a CDS, and offers authors a journal-specific tool Fulvio2020 to
estimate the gender citation balance index. In a retrospective analysis of
papers published in the year following these guideline changes, the editors
report a clear reduction of gender citation imbalances postle2021one . The
Biomedical Engineering Society, which publishes four journals, also supports
the use of a CDS, and wrote and published a call to action Rowson2021 , while
pointing authors to the following publicly available journal-general tool
dale_zhou_2020_4104748 . Even more broadly, Cell Press—which publishes over 50
journals—now uses an inclusion and diversity form to gather information on how
the values of diversity and inclusion were supported and upheld throughout the
performance of the science and development of the paper under consideration
for publication Sweet2021 .

These positive actions underscore the advances that can be attained when
individual scholars embrace the change indicated by bias research
raymond2013most , an area of scholarly inquiry that faces a discrimination of
its own; gender-bias research is generically underappreciated in academia
cislak2018bias , and viewed less favorably by men, especially men faculty in
STEM handley2015quality , which is an unfortunate irony given that bias tends
to be preferentially perpetuated by those who think it is not happening
begeny2020some . Foregrounding action-based thinking, our study provides
context for existing individual- and journal-led efforts, and new directions
for mitigation strategies. At the individual level, our work underscores the
critical need for self-education, particularly focused on the work being
published in general physics journals and in fields adjacent to or far from
the author’s primary area of expertise. This need is motivated by our
observations that gender imbalances in citations are greatest within citing
articles in general physics journals and when cited articles belong to less
familiar fields.

At the journal level, our work motivates future efforts to test the hypothesis
that increasing the number of women authors that a journal publishes would
lead to a decrease in that journal’s gender imbalance in citations. This
causal hypothesis to be tested derives from our non-causal observation that
journals publishing a higher fraction of papers authored by women tend to show
less under-citation of women. Increasing the proportion of women authors
should be relatively easy for journals like _Reviews of Modern Physics_ ,
which can solicit new reviews on topics from under-represented authors; such a
step would be particularly helpful, as _Reviews of Modern Physics_ currently
has the lowest fraction of $W||W$ papers of all journals examined in our study
(0.11). Any effort to increase the number of women authors in a journal would
also serve to combat (i) the higher writing standards for women than for men
hengel2020publishing , and (ii) the tendency for submitted work to be
perceived as better when it is associated with a man’s name compared to a
woman’s name krawczyk2016authors ; Knobloch-Westerwick2013 . Our results also
suggest the possibility that removing length limits on reference lists may be
beneficial to gender equality, as papers with longer reference lists tended to
display less disparity. However, we note that this recommendation does not
condone the implicit notion that man-authored papers are of greater value and
more deserving when resources (reference entries) are limited.

###  IV.3 Expanding the scope of equitable citation practice

Although the term “citation” in academia typically refers to an entry in a
reference list, citations take many forms and therefore conversations about
citation equity can be fruitfully expanded. Whether it is a formal reference
or an informal mention, in spoken or written communication, a citation is a
way of calling forward and raising up specific scholars or instances of
scholarship ahmed2013points ; ahmed2017living ; ahmed2019use ;
mott2017citation . Given the multiple ways in which citations can occur,
issues of citation (in)equity are likely more ubiquitous than expected.

Consider the scientist’s writing life. Whether writing articles, reviews, or
grant proposals, we can evaluate the gender balance of our reference lists,
but we can also start earlier and go deeper. Who jumps to mind (and to pen, or
whiteboard) as we generate ideas for a paper? Who is there along the way as we
develop the methods and start interpreting the results? Where do those names
ultimately show up in the paper—is it in the introduction, the methods
section, the results, or the discussion? Where does a greater (or lesser)
diversity of authors appear and what does that reveal about how we
conceptualized and contextualized the project? Are citations to women
prominent, substantial, and critical to the central questions, tools, and
interpretive frames of our work? Or are they appended as supplementary or even
as afterthoughts?

Consider, too, the scientist’s speaking life. Whether teaching, giving talks,
or informally conversing with students and colleagues, we can evaluate the
gender balance of our spoken references. Who do we teach as central figures in
the history of science? Who do we recommend to students and colleagues as
scholars of idle interest or scholars making an important contribution to the
topic under discussion? Who do we explicitly mention in our talks, write into
our slides, or acknowledge as thought collaborators? Whose work do we signal
boost through invitations to speak, to co-author, to co-investigate, or to
write a review or perspective piece for our journal? Who do we retweet in the
most mundane and most meaningful of ways? And are women scholars equitably
represented in these moments?

We look forward to future research along all these vectors, and we invite
individual and collective reflection not only on how citation imbalances,
obdurate homophily, and other dynamics explored in this paper might appear
beyond our reference lists but also on how they might be addressed
massen2017sharing ; vasarhelyi2021gender ; atir2018how .

###  IV.4 Methodological considerations

While our study expands the frontiers of our understanding of gendered
practices in physics, several limitations motivate future work. In particular
we underscore the fact that under-attribution, bias, and discrimination are
faced by individuals of many—and intersecting—identities. Future work would do
well to unpack citation practices not just along the (cisgender) man/woman
binary, but also along other dimensions of difference, including trans and/or
nonbinary status, race, ethnicity, class, sexual orientation, and disability.
For example, prior work in several areas of science provides evidence for
under-attribution according to race and ethnicity; scholars of color are
broadly undercited by their academic communities Bertolero2020 ;
chakravartty2018communication . These effects compound upon known intersecting
gender and class inequalities in hiring at all levels in the academy
Sheltzer2014 ; clauset2015systematic ; way2019productivity ; at the faculty
level, the prestige of a doctoral student’s PhD-granting institution predicts
their placement as a tenure-track faculty member, women generally place worse
than men, and increased institutional prestige leads to increased faculty
production, better faculty placement, and a more influential position within
the discipline clauset2015systematic ; way2019productivity . Furthermore,
sexual orientation is a proven axis of inequality in STEM from classrooms to
careers cech2011navigating ; gibney2019discrimination ; lesbian, gay,
bisexual, transgender, and queer (LGBTQ) STEM professionals are more likely to
experience career limitations, harassment, and professional devaluation than
their non-LGBTQ peers cech2021systemic ; cech2020lgbt . Because information
about sexual orientation is not present in a scholar’s name, efforts to
increase opportunities for self-attestation are critical to future work
seeking to evaluate impacts of sexual orientation on citation practices
freeman2018lgbtq ; langin2020lgbtq . Similarly, trans and non-binary status
cannot be predicted from names, and hence name-based assessments such as those
we use here will not be able to reveal specific discrimination faced by these
individuals due to their non-cis gender identity. Nevertheless, transgender
and non-binary individuals exist in our dataset, and their name-(binary)gender
associations are part of the probabilistic databases we employ. At the
population scale, these individuals face the same name-based citation costs
and payoffs as a cis gender scholar, which could be compounded by other costs
and payoffs not accessible to our analysis. Of course, all scholars with
marginalized intersecting identities are likely to face compounded citation
costs, as indeed supported by a recent study that evaluated the intersection
of gender and race/ethnicity Bertolero2020 . We look forward to further work
that could complexify our understanding of citation practices, and their
ethics, along these diverse lines of difference.

##  V Conclusion

Our work represents an analysis of the gendered demographics and citation
practices of papers published in 35 physics journals over the last 25 years.
We found that citation practices skew toward the over-citation of man-authored
papers (and the under-citation of woman-authored papers), and that citation
behavior is heavily influenced by citing actor (the predicted gender makeup of
the citing author team), citing venue (the subfield and journal in which the
citation appears), and citing form (whether the citation pertains to work with
which authors are likely to be familiar). Our results highlight correlates
with citation imbalance at the population level that are suggestive of actions
that individuals and journals can take immediately to mitigate citation
imbalance in physics, including (for individuals) acknowledging and disclosing
the demographics of constructed reference lists, considering expanding said
reference lists, and being mindful when citing outside one’s specialty; and
(for journals) increasing representation of woman authors, relaxing reference
list length limits, and encouraging disclosure in the form of citation
diversity statements. Thoughtful engagement with citation imbalance at all
levels of the publishing hierarchy will contribute to the inclusion of women
in the current and future story (and reality) of scientific progress. We
invite readers to consider these and other ways they can make visible the
contributions of all scholars to the scientific endeavor.

##  VI Citation diversity statement

Recent work has identified a bias in citation practices such that papers from
women and other marginalized scholars in STEM are under-cited relative to the
number of such papers in the field. Here we sought to proactively consider
choosing references that reflect the diversity of the field in thought, form
of contribution, gender, and other factors. We use databases that store the
probability of a name being carried by people of different genders to mitigate
our own citation bias at the intersection of name and identity. Based on the
databases used, the set of names assigned the “woman” label will contain a
predominance of women and the set of names assigned the “man” label will
contain a predominance of men, but both sets may also contain other genders.
By this measure (and excluding self-citations to the first and last authors of
our current paper, and papers whose authors’ first names could not be
determined), our references contain 44.58% woman(first)/woman(last), 19.28%
man/woman, 15.66% woman/man, and 20.48% man/man categorization. This method is
limited in that names, pronouns, and social media profiles used to construct
the databases may not, in every case, be indicative of gender identity.
Furthermore, probabilistic studies of names cannot be used to detect citation
costs that are specific to intersex, non-binary, or transgender people who are
out to a large number of their colleagues. We look forward to future work that
could help us to better understand how to support equitable practices in
science.

##  VII Acknowledgments

E.G.T, L.C.B. and D.S.B. are supported by the National Science Foundation
Materials Research Science and Engineering Center at University of
Pennsylvania (NSF grant DMR-1120901). J.Z.K. is supported by a National
Science Foundation Graduate Research Fellowship. C.W.L. is supported by a
James S. McDonnell Foundation Postdoctoral Fellowship. S.C.S. acknowledges
support from the University Scholars program at the University of
Pennsylvania. P.S. is supported by the Swartz Foundation. P.Z. and D.S.B also
acknowledge support from the Center for Curiosity.

##  VIII References

## References

  * [1] Matilda Joslyn Gage.  Woman as inventor; issued under the auspices of the New York State Woman Suffrage Association.  F. A. Darling, Fayatteville, N.Y., 1870.
  * [2] Margaret W. Rossiter.  The Matthew Matilda Effect in Science.  Social Studies of Science, 23(2):325–341, may 1993.
  * [3] Jaime Phillips and Kathryn Hausbeck.  Just Beneath the Surface: Rereading Geology, Rescripting the Knowledge-Power Nexus.  Women’s Studies Quarterly, 28(1/2):181–202, 2000.
  * [4] Neven Caplar, Sandro Tacchella, and Simon Birrer.  Quantitative evaluation of gender bias in astronomical publications from citation counts.  Nature Astronomy, 1(6):0141, jun 2017.
  * [5] Silvia Knobloch-Westerwick, Carroll J. Glynn, and Michael Huge.  The Matilda Effect in Science Communication: An Experiment on Gender Bias in Publication Quality Perceptions and Collaboration Interest.  Science Communication, 35(5):603–625, 2013.
  * [6] Chaoqun Ni, Elise Smith, Haimiao Yuan, Vincent Larivière, and Cassidy R Sugimoto.  The gendered nature of authorship.  Sci Adv, 7(36):eabe4639, 2021.
  * [7] Marieke van den Brink and Yvonne Benschop.  Gender practices in the construction of academic excellence: Sheep with five legs.  Organization, 19(4):507–524, 2012.
  * [8] Corinne A. Moss-Racusin, John F. Dovidio, Victoria L. Brescoll, Mark J. Graham, and Jo Handelsman.  Science faculty’s subtle gender biases favor male students.  Proceedings of the National Academy of Sciences of the United States of America, 109(41):16474–16479, 2012.
  * [9] Brittany Bloodhart, Meena M. Balgopal, Anne Marie A. Casper, Laura B. Sample McMeeking, and Emily V. Fischer.  Outperforming yet undervalued: Undergraduate women in STEM.  PLoS ONE, 15(6):1–13, 2020.
  * [10] Anne E. Lincoln, Stephanie Pincus, Janet Bandows Koster, and Phoebe S. Leboy.  The Matilda Effect in science: Awards and prizes in the US, 1990s and 2000s.  Social Studies of Science, 42(2):307–320, 2012.
  * [11] Per Lunnemann, Mogens H. Jensen, and Liselotte Jauffred.  Gender bias in Nobel prizes.  Palgrave Communications, 5(1):17–20, 2019.
  * [12] Erin Hengel.  Publishing while female: Are women held to higher standards? Evidence from peer review, pages 80–90.  CEPR Press, 2020.
  * [13] Luke Holman, Devi Stuart-Fox, and Cindy E. Hauser.  The gender gap in science: How long until women are equally represented?  PLoS Biology, 16(4):1–20, 2018.
  * [14] Vincent Larivière, Chaoqun Ni, Yves Gingras, Blaise Cronin, and Cassidy R Sugimoto.  Bibliometrics: Global gender disparities in science.  Nature, 504(7479):211–213, dec 2013.
  * [15] Gita Ghiasi, Vincent Larivière, and Cassidy R. Sugimoto.  On the Compliance of Women Engineers with a Gendered Scientific System.  PLOS ONE, 10(12):e0145931, dec 2015.
  * [16] Jordan D. Dworkin, Kristin A. Linn, Erin G. Teich, Perry Zurn, Russell T. Shinohara, and Danielle S. Bassett.  The extent and drivers of gender imbalance in neuroscience reference lists.  Nature Neuroscience, 23(8):918–926, aug 2020.
  * [17] Xinyi Wang, J. D. Dworkin, D. Zhou, J. Stiso, E. B. Falk, D. S. Bassett, P. Zurn, and David M. Lydon-Staley.  Gendered citation practices in the field of communication.  Annals of the International Communication Association, 45(2):134–153, apr 2021.
  * [18] Michelle L. Dion, Jane Lawrence Sumner, and Sara Mc Laughlin Mitchell.  Gendered Citation Patterns across Political Science and Social Science Methodology Fields.  Political Analysis, 26(3):312–327, 2018.
  * [19] Daniel Maliniak, Ryan Powers, and Barbara F. Walter.  The gender citation gap in international relations, volume 67.  2013\.
  * [20] Sara Mclaughlin Mitchell, Samantha Lange, and Holly Brus.  Gendered Citation Patterns in International Relations Journals.  International Studies Perspectives, 14(4):485–492, 2013.
  * [21] Jacqueline M. Fulvio, Ileri Akinnola, and Bradley R. Postle.  Gender (Im)balance in citation practices in cognitive neuroscience.  Journal of Cognitive Neuroscience, 33(1):3–7, 2020.
  * [22] Paula Chatterjee and Rachel M. Werner.  Gender Disparity in Citations in High-Impact Journal Articles.  JAMA Network Open, 4(7):1–8, 2021.
  * [23] Ellen I. Damschen, Kristen M. Rosenfeld, Mary Wyer, Deena Murphy-Medley, Thomas R. Wentworth, and Nick M. Haddad.  Visibility matters: Increasing knowledge of women’s contributions to ecology.  Frontiers in Ecology and the Environment, 3(4):212–219, 2005.
  * [24] Sara Wood, Jeremiah A. Henning, Luoying Chen, Taylor McKibben, Michael L. Smith, Marjorie Weber, Ash Zemenick, and Cissy J. Ballen.  A scientist like me: Demographic analysis of biology textbooks reveals both progress and long-term lags.  Proceedings of the Royal Society B: Biological Sciences, 287(1929), 2020.
  * [25] Dasia Y. Simpson, Abby E. Beatty, and Cissy J. Ballen.  Teaching between the Lines: Representation in Science Textbooks.  Trends in Ecology and Evolution, 36(1):4–8, 2021.
  * [26] Linda L. Carli, Laila Alawa, Yoon Ah Lee, Bei Zhao, and Elaine Kim.  Stereotypes About Gender and Science: Women != Scientists.  Psychology of Women Quarterly, 40(2):244–260, 2016.
  * [27] Merryn McKinnon and Christine O’Connell.  Perceptions of stereotypes applied to women who publicly communicate their STEM work.  Humanities and Social Sciences Communications, 7(1):1–8, 2020.
  * [28] Jessica J. Good, Julie A. Woodzicka, and Lylan C. Wingfield.  The effects of gender stereotypic and counter-stereotypic textbook images on science performance.  Journal of Social Psychology, 150(2):132–147, 2010.
  * [29] Jeffrey N. Schinske, Heather Perkins, Amanda Snyder, and Mary Wyer.  Scientist spotlight homework assignments shift students’ stereotypes of scientists and enhance science identity in a diverse introductory science class.  CBE Life Sciences Education, 15(3):1–18, 2016.
  * [30] Sapna Cheryan, Allison Master, and Andrew N. Meltzoff.  Cultural stereotypes as gatekeepers: Increasing girls’ interest in computer science and engineering by diversifying stereotypes.  Frontiers in Psychology, 6(FEB):1–8, 2015.
  * [31] Ibram X. Kendi.  How to Be an Antiracist.  One World, New York, NY, 2019.
  * [32] Imani Perry.  Post-intent racism: A new framework for an old problem.  National Black Law Journal, 19:113–148, 2006.
  * [33] Jane Pilcher.  Names and “Doing Gender”: How Forenames and Surnames Contribute to Gender Identities, Difference, and Inequalities.  Sex Roles, 77(11-12):812–822, 2017.
  * [34] Patricia Hill Collins.  Intersectionality as Critical Social Theory.  Duke University Press, Durham, 2019.
  * [35] Perry Zurn, Danielle S. Bassett, and Nicole C. Rust.  The Citation Diversity Statement: A Practice of Transparency, A Way of Life.  Trends in Cognitive Sciences, 24(9):669–672, 2020.
  * [36] Jordan Dworkin, Perry Zurn, and Danielle S. Bassett.  (In)citing Action to Realize an Equitable Future.  Neuron, 106(6):890–894, 2020.
  * [37] Carl T. Bergstrom, Jevin D. West, and Marc A. Wiseman.  The EigenfactorTM Metrics.  Journal of Neuroscience, 28(45):11433–11434, nov 2008.
  * [38] Csaba Toth, Elizabeth Durham, Murat Kantarcioglu, Yuan Xue, and Bradley Malin.  SOEMPI: A Secure Open Enterprise Master Patient Index Software Toolkit for Private Record Linkage.  AMIA … Annual Symposium proceedings. AMIA Symposium, 2014:1105–1114, 2014.
  * [39] Gender API, 2021.
  * [40] Simon N. Wood.  Generalized Additive Models: An Introduction with R.  Chapman and Hall/CRC, 2 edition, 2017.
  * [41] Miller McPherson, Lynn Smith-Lovin, and James M. Cook.  Birds of a feather: Homophily in social networks.  Annual Review of Sociology, 27:415–444, 2001.
  * [42] Anne Boschini and Anna Sjögren.  Is team formation gender neutral? Evidence from coauthorship patterns.  Journal of Labor Economics, 25(2):325–365, 2007.
  * [43] Mohsen Jadidi, Fariba Karimi, Haiko Lietz, and Claudia Wagner.  Gender disparities in science? Dropout, productivity, collaborations and success of male and female computer scientists.  Advances in Complex Systems, 21(3-4), 2018.
  * [44] Y. Samuel Wang, Carole J. Lee, Jevin D. West, Carl T. Bergstrom, and Elena A. Erosheva.  Gender-based homophily in collaborations across a heterogeneous scholarly landscape.  pages 1–33, 2019.
  * [45] Luke Holman and Claire Morandin.  Researchers collaborate with same-gendered colleagues more often than expected across the life sciences.  PLoS ONE, 14(4):26–29, 2019.
  * [46] Marek Kwiek and Wojciech Roszka.  Gender-based homophily in research: A large-scale study of man-woman collaboration.  Journal of Informetrics, 15(3), 2021.
  * [47] Gita Ghiasi, Philippe Mongeon, Cassidy R. Sugimoto, and Vincent Larivière.  Gender Homophily in Citations.  23rd International Conference on Science and Technology Indicators (STI 2018), pages 1519–1525, 2018.
  * [48] Lynne A. Isbell, Truman P. Young, and Alexander H. Harcourt.  Stag Parties Linger: Continued Gender Bias in a Female-Rich Scientific Discipline.  PLoS ONE, 7(11):2–5, 2012.
  * [49] Florence Débarre, N. O. Rode, and Line Vej Ugelvig.  Gender equity at scientific events.  Evolution Letters, 2(3):148–158, 2018.
  * [50] Christine L. Nittrouer, Michelle R. Hebl, Leslie Ashburn-Nardo, Rachel C.E. Trump-Steele, David M. Lane, and Virginia Valian.  Gender disparities in colloquium speakers at top universities.  Proceedings of the National Academy of Sciences of the United States of America, 115(1):104–108, 2018.
  * [51] Deborah Belle, Laurel Smith-Doerr, and Lauren M. O’Brien.  Gendered networks: Professional connections of science and engineering faculty.  Advances in Gender Research, 19(October):153–175, 2014.
  * [52] Martin Atzmueller and Florian Lemmerich.  Homophily at Academic Conferences.  The Web Conference 2018 - Companion of the World Wide Web Conference, WWW 2018, pages 109–110, 2018.
  * [53] Riccardo Gallotti and Manlio De Domenico.  Effects of homophily and academic reputation in the nomination and selection of Nobel laureates.  Scientific Reports, 9(1):1–12, 2019.
  * [54] Markus Helmer, Manuel Schottdorf, Andreas Neef, and Demian Battaglia.  Gender bias in scholarly peer review.  eLife, 6:1–18, 2017.
  * [55] Jason Greenberg and Ethan Mollick.  Activist Choice Homophily and the Crowdfunding of Female Founders*.  Administrative Science Quarterly, 62(2):341–374, 2017.
  * [56] Kendra Oudyk, Isil Poyraz Bilgin, Samuel Guay, Léa Michel, François Paugam, Céline Provins, and Adina Wagner.  Cleanbibimpact: Do papers with Citation Diversity Statements have more gender-balanced reference lists?  BrainHack 2021 Proceedings, 2021.
  * [57] Zoe Budrikis.  Growing citation gender gap.  Nature Reviews Physics, 2(7):346–346, Jul 2020.
  * [58] Nature Neuroscience Editors.  Widening the scope of diversity.  Nature Neuroscience, 23(8):903–903, Aug 2020.
  * [59] Dimitri M Kullmann.  Editorial.  Brain, 143(3):715–715, 03 2020.
  * [60] Adrienne L. Fairhall and Eve Marder.  Acknowledging female voices.  Nature Neuroscience, 23(8):904–905, Aug 2020.
  * [61] Sarah W Davies, Hollie M Putnam, Tracy Ainsworth, Julia K Baum, Colleen B Bove, Sarah C Crosby, Isabelle M Côté, Anne Duplouy, Robinson W Fulweiler, Alyssa J Griffin, et al.  Promoting inclusive metrics of success and impact to dismantle a discriminatory reward system in science.  PLoS biology, 19(6):e3001282, 2021.
  * [62] Susan K Pierce, Pamela L Schwartzberg, Nirali N Shah, and Naomi Taylor.  Women in immunology: 2020 and beyond.  Nature immunology, 21(3):254–258, 2020.
  * [63] Anaïs Llorens, Athina Tzovara, Ludovic Bellier, Ilina Bhaya-Grossman, Aurélie Bidet-Caulet, William K Chang, Zachariah R Cross, Rosa Dominguez-Faus, Adeen Flinker, Yvonne Fonken, Mark A Gorenstein, Chris Holdgraf, Colin W Hoy, Maria V Ivanova, Richard T Jimenez, Soyeon Jun, Julia W Y Kam, Celeste Kidd, Enitan Marcelle, Deborah Marciano, Stephanie Martin, Nicholas E Myers, Karita Ojala, Anat Perry, Pedro Pinheiro-Chagas, Stephanie K Riès, Ignacio Saez, Ivan Skelin, Katarina Slama, Brooke Staveland, Danielle S Bassett, Elizabeth A Buffalo, Adrienne L Fairhall, Nancy J Kopell, Laura J Kray, Jack J Lin, Anna C Nobre, Dylan Riley, Anne-Kristin Solbakk, Joni D Wallis, Xiao-Jing Wang, Shlomit Yuval-Greenberg, Sabine Kastner, Robert T Knight, and Nina F Dronkers.  Gender bias in academia: A lifetime problem that needs solutions.  Neuron, 109(13):2047–2074, 2021.
  * [64] Brad Postle and Jacqueline Fulvio.  One-year update from the Editor-in-Chief.  Journal of Cognitive Neuroscience, In Press, 2021.
  * [65] Bethany Rowson, Stefan M. Duma, Michael R. King, Igor Efimov, Ann Saterbak, and Naomi C. Chesler.  Citation diversity statement in bmes journals.  Annals of Biomedical Engineering, 49(3):947–949, Mar 2021.
  * [66] Dale Zhou, Jennifer Stiso, Eli Cornblath, Erin Teich, Ann Sizemore Blevins, Kendra Oudyk, Cleanthis Michael, Anne Urai, Virtualmario, and Christopher Camp.  dalejn/cleanbib: v1.1.1, oct 2020.
  * [67] Deborah J. Sweet.  New at cell press: The inclusion and diversity statement.  Cell, 184(1):1–2, Jan 2021.
  * [68] Jennifer Raymond.  Most of us are biased.  Nature, 495:33––34, 2013.
  * [69] Aleksandra Cislak, Magdalena Formanowicz, and Tamar Saguy.  Bias against research on gender bias.  Scientometrics, 115(1):189–200, 2018.
  * [70] Ian M Handley, Elizabeth R Brown, Corinne A Moss-Racusin, and Jessi L Smith.  Quality of evidence revealing subtle gender biases in science is in the eye of the beholder.  Proc Natl Acad Sci U S A, 112(43):13201–6, 2015.
  * [71] Christopher T Begeny, Michelle K Ryan, Corinne A Moss-Racusin, and Gudrun Ravetz.  In some professions, women have become well represented, yet gender bias persists-Perpetuated by those who think it is not happening.  Sci Adv, 6(26):eaba7814, 2020.
  * [72] Michał Krawczyk and Magdalena Smyk.  Author’s gender affects rating of academic articles: Evidence from an incentivized, deception-free laboratory experiment.  Eur. Econ. Rev., 90:326–335, 2016.
  * [73] Sara Ahmed.  Making feminist points.  Feministkilljoys.com, 2013.
  * [74] Sara Ahmed.  Living a Feminist Life.  Duke University Press, 2017.
  * [75] Sara Ahmed.  What’s the Use? Duke University Press, 2019.
  * [76] Carrie Mott and Daniel Cockayne.  Citation matters: Mobilizing the politics of citation toward a practice of ’conscientious engagement’, 2017.
  * [77] Jorg J M Massen, Lisa Bauer, Benjamin Spurny, Thomas Bugnyar, and Mariska E Kret.  Sharing of science is most likely among male scientists.  Sci Rep, 7(1):12927, 2017.
  * [78] Orsolya Vásárhelyi, Igor Zakhlebin, Staša Milojević, and Emőke-Ágnes Horvát.  Gender inequities in the online dissemination of scholars’ work.  Proc Natl Acad Sci U S A, 118(39):e2102945118, 2021.
  * [79] Stav Atir and Melissa J Ferguson.  How gender determines the way we speak about professionals.  Proc Natl Acad Sci U S A, 115(28):7278–7283, 2018.
  * [80] Maxwell A Bertolero, Jordan D Dworkin, Sophia U David, Claudia López Lloreda, Pragya Srivastava, Jennifer Stiso, Dale Zhou, Kafui Dzirasa, Damien A Fair, Antonia N Kaczkurkin, Bianca Jones Marlin, Daphna Shohamy, Lucina Q Uddin, Perry Zurn, and Danielle S Bassett.  Racial and ethnic imbalance in neuroscience reference lists and intersections with gender.  bioRxiv, page 2020.10.12.336230, 2020.
  * [81] Paula Chakravartty, Rachel Kuo, Victoria Grubbs, and Charlton McIlwain.  #communicationsowhite.  Journal of Communication, 68(2):254––266, 2018.
  * [82] Jason M. Sheltzer and Joan C. Smith.  Elite male faculty in the life sciences employ fewer women.  Proceedings of the National Academy of Sciences of the United States of America, 111(28):10107–10112, 2014.
  * [83] Aaron Clauset, Samuel Arbesman, and Daniel B Larremore.  Systematic inequality and hierarchy in faculty hiring networks.  Sci Adv, 1(1):e1400005, 2015.
  * [84] Samuel F Way, Allison C Morgan, Daniel B Larremore, and Aaron Clauset.  Productivity, prominence, and the effects of academic environment.  Proc Natl Acad Sci U S A, 116(22):10729–10733, 2019.
  * [85] Erin A. Cech and Tom J. Waidzunas.  Navigating the heteronormativity of engineering: the experiences of lesbian, gay, and bisexual students.  Engineering Studies, 3(1):1–24, 2011.
  * [86] Elizabeth Gibney.  Discrimination drives lgbt+ scientists to think about quitting.  Nature, 571(7763):16–17, 2019.
  * [87] Erin A Cech and Tom J Waidzunas.  Systemic inequalities for LGBTQ professionals in STEM.  Sci Adv, 7(3):eabe0933, 2021.
  * [88] Erin A. Cech and William R. Rothwell.  LGBT workplace inequality in the federal workforce: Intersectional processes, organizational contexts, and turnover considerations.  Industrial and Labor Relations Review, 73(1):25–60, 2020.
  * [89] Jon Freeman.  LGBTQ scientists are still left out.  Nature, 559(7712):27–28, 2018.
  * [90] Katie Langin.  LGBTQ researchers say they want to be counted.  Science, 370(6523):1391, 2020.