Authorship in top-ranked mathematical and physical journals: Role of gender on self-perceptions and bibliographic evidence

Despite increasing rates of women researching in math-intensive fields, publications by female authors remain underrepresented. By analyzing millions of records from the dedicated bibliographic databases zbMATH, arXiv, and ADS, we unveil the chronological evolution of authorships by women in mathematics, physics, and astronomy. We observe a pronounced shortage of female authors in top-ranked journals, with quasistagnant figures in various distinguished periodicals in the first two disciplines and a significantly more equitable situation in the latter. Additionally, we provide an interactive open-access web interface to further examine the data. To address whether female scholars submit fewer articles for publication to relevant journals or whether they are consciously or unconsciously disadvantaged by the peer review system, we also study authors’ perceptions of their submission practices and analyze around 10,000 responses, collected as part of a recent global survey of scientists. Our analysis indicates that men and women perceive their submission practices to be similar, with no evidence that a significantly lower number of submissions by women is responsible for their underrepresentation in top-ranked journals. According to the self-reported responses, a larger number of articles submitted to prestigious venues correlates rather with aspects associated with pronounced research activity, a well-established network, and academic seniority.


INTRODUCTION
A strong publication record ranks among the most powerful determinants of academic career success in many disciplines, exerting significant influence on decisions about tenure, funding, and promotions (Krantz, 2007;McGrail, Rickard, & Jones, 2006). While monographs and edited books predominantly drive research in the humanities and social sciences, in math-intensive fields, the most relevant deliverable is the peer-reviewed article in a scholarly journal. Analyses of the dedicated mathematics and astrophysics databases zbMATH and ADS show that this type of publication constitutes over 80% of their indexed content from 1970 to date. Journal articles have effectively become not only a vehicle for communicating knowledge in these areas, promoting the exchange of ideas and advancing science, but also a tool for research assessment, a development that is not without criticism (Hicks, Wouters, et al., 2015;Taubes, 1993). It is not just the number of authored articles that matters, but especially the venues where they appear and their perceived quality, which are often used as a proxy for the relevance of the a n o p e n a c c e s s j o u r n a l Mathematics is a relatively small field with even narrower subfields. Journals of high perceived quality within the community ideally base their decisions on manuscript acceptance on Littlewood's precepts of novelty, correctness, and interest (Krantz, 1997, p. 125). The thorough examination of proofs is a key expectation of peer review in the discipline. Linked to it is the assumption that all statements in a peer-reviewed paper can be regarded as true, despite the fact that such a requirement is often extremely hard to fulfill within reasonable time and effort (Geist, Löwe, & Van Kerkhove, 2010, pp. 160-163;Grcar, 2013;Krantz, 2007Krantz, , p. 1510. Aside from some exceptions, such as extremely prestigious journals like the Annals of Mathematics or particularly difficult research results where additional expertise might be sought, a common practice is to engage a single referee in the peer review process (Andersen, 2017;Krantz, 2007). The London Mathematical Society, which publishes many top-ranked journals in particular in pure mathematics, refers to the referee in singular form in its Author Guidelines, noting that "in mathematics it is common for the Referee to know the Authors personally," thus "fine judgement" is required to handle potential biases (London Mathematical Society Guide to Authors, 2020). The survey of mathematical journal editors in Geist et al. (2010) stresses that "the mathematical peer review is largely a communication between an editor and one referee based on trust due to a personal relationship." The standard to which proofs in submissions are scrutinized by the reviewer is not homogeneous across journals, ranging from cases where all claims in a demonstration are fully checked by the peer to others where the responsibility for mathematical correctness is placed mostly on the author (Nathanson, 2008). The promptness and thoughtfulness with which a manuscript is handled might depend on the reputation of the author, the perceived novelty of the topic, or other potentially nonobjective considerations (Krantz, Kuperberg, & van der Poorten, 2003). Given that the correctness of proofs is so important to accept or reject a manuscript, the fact that peer review in mathematics lacks homogeneity and relies substantially on the authors' credit and the level of trust between editors and reviewer(s) merits a thorough investigation of the potential existence of structural biases. Although a large body of research on the peer review system has been published in the past decades, so far only one systematic study exists that focuses on the particularities of mathematics, namely that by Geist et al. (2010); cf. Andersen (2017) and Auslander (2008).
Physics is a larger research field that spans numerous subfields with very different organizational styles, from small theoretical groups that operate in a way closely resembling that of mathematicians, to big-science collaborations that involve thousands of researchers around a common experiment. Many physics papers, most significantly in the fields of astrophysics and high-energy physics, appear first as preprints, which has been shown to increase the number of citations (Gentil-Beccot, Mele, & Brooks, 2009). The arXiv has long been used to communicate research results and establish priority claims, in fact relegating journals to outlets for "secondary distribution, archiving, and peer-review" (Brooks, 2009). Peer review in physics is a relatively modern practice. Originally, traditional authoritative German journals such as Annalen der Physik did not seek external referees and published based on the sole opinion of an identifiable editor instead (Lalli, 2016). Peer review became standard within the English-speaking world around the mid-20th century and it was only towards the late 20th century that it "came to be seen as a process central to scientific practice" (Baldwin, 2018). The currently established process in most physics journals involves the selection of two referees "in parallel" from a curated pool of reviewers (Gordon, 1979). If reports on a manuscript conflict, the staff editor normally seeks an adjudicating referee. Rejection decisions might involve the journal's editor-in-chief and editorial board. Physics fields organized around small research groups do operate within the triangular relationship authors-editor-referees. However, scholarly communication in large collaborative disciplines such as high-energy physics, observational astronomy, or gravitational physics differs significantly. Big-science collaborations that rely on access to large facilities to perform research "increasingly resemble organizations in themselves" (Birnholtz, 2008). Typically, all of their members, in a growing number that often creeps into the thousands, are listed as authors on any paper published by the collaboration: see, for example, Smith (2016) for astronomy and Pritychenko (2016) for nuclear and particle physics. Credit attribution in such a setting poses a distinct set of challenges: There is no differentiation for the first or last author as most significant contributor (Birnholtz, 2008) and acknowledgment of individual ownership is ambiguous or directly impossible (Birnholtz, 2006). The peer review process in big-science disciplines entails the particularity that manuscripts have generally been internally reviewed and vetted ahead of submission; sometimes finding external reviewers with comparable expertise and no conflicts of interest becomes arduous for journal editors (A. Day, personal communication, June 21, 2020).
From the exposition above, it becomes apparent that professional networks, personal connections, and trust relationships are pivotal elements in scholarly communication in mathematics and physics. According to the norms of modern science though, truth-claims cannot be judged on the basis of personal or social attributes of their authors. This includes race, nationality, religion, affiliation, class, and of course gender. And yet, at the core of the discussion is the recognition that "the institution of science is part of a larger social structure with which it is not always integrated" (Merton, 1973). Consequently, we consider the entire process from manuscript submission until final decision on acceptance or rejection an excellent use case for the assessment of the impersonal character of science. However, only a few studies exist that investigate the complete peer review mechanism comprehensively, mainly due to lack of access to extensive data from academic publishers.
For this reason it is convenient to consider additional perspectives on the intricacies of the publication process. The authors' perceptions of their own submission practices provide one such important source of information. In this article, we analyze the answers of almost 10,000 worldwide scientists from the physical sciences and mathematics who participated in an online snowball-sampled survey and answered the following question: "During the last five years, how many articles have you submitted to journals that are top-ranked in your field?" We show that the respondents' gender does not play a significant role in their perceived submission practices. Instead, a higher number of manuscripts submitted to top-ranked journals correlates rather with factors associated with pronounced research activity, a well-established network, and academic seniority, such as being a journal editor, member of a grant committee, or conducting research abroad.
Furthermore, we use bibliographic databases to analyze the distribution of authors' gender in selected journals in mathematics, astronomy and astrophysics, and theoretical physics. We compute and model longitudinal trends in the proportion of publications authored by women over time. Our analysis shows that the percentage of female authors in top-ranked astronomy and astrophysics journals has grown steadily over recent decades, reaching numbers well comparable to their overall presence in the discipline. This is in stark contrast to most high-profile journals in mathematics and even more so in theoretical physics. Additionally, we provide an interactive open-access web interface that allows us to examine all journals indexed in the dedicated databases zbMATH and ADS and the arXiv preprint server similarly.
Although our two analyses of survey responses and bibliographic data are not directly comparable, it is useful to discuss their implications for the existence of potential imbalances in the peer review process in mathematics and physics altogether. This is even more the case given that the respondents' perceptions of their own submission practices are very similar across disciplines, which is in discrepancy with the measured outcomes in the considered topical journal publications.

Related Work
The situation of women in academia, especially in the so-called "hard sciences," is a massively researched topic. The literature that examines its causes presents contradictory conclusions, yet the one mostly agreed-upon fact is that women are underrepresented in all math-intensive fields at the level of college, graduate studies, and the professoriate: see Ceci, Ginther, et al. (2014), Williams (2011), Hill, Corbett, andRose (2010), Kahn and Ginther (2017), and Wang and Degol (2016) for reviews. More controversial is the debate about the underlying causes. Arguments based on early biological differences in mathematical ability among the sexes do not seem to be supported by current experimental evidence (Hutchison, Lyons, & Ansari, 2018;Kersey, Csumitta, & Cantlon, 2019); actually, sociocultural influences rather than biological factors appear more likely to have an impact (Andreescu, Gallian, et al., 2008;Wang & Degol, 2016). Regardless, gender segregation concerning career preferences already manifests by high school and continues through college major choices. By graduation, men outnumber women in nearly every STEM field; particularly in physics, engineering, and computer science the latter earn a mere 20% of bachelor's degrees (Hill et al., 2010). Perceptions and unconscious beliefs about gender in mathematics and science seem to play a role in women's choices, as evidenced by their underrepresentation in fields believed to emphasize brilliance as key to success (Meyer, Cimpian, & Leslie, 2015). Once in possession of a doctorate in a math-intensive field, there is no clear consensus about the existence of biases in academic interviewing, hiring, and promotion. For astronomers in the United States, for instance, no gender differences are found in career outcomes, the proportion of graduates starting postdocs and the proportion of those hired into long-term positions being comparable for men and women (Perley, 2019). In fact, Ceci et al. (2014) argue that more pipeline leakage is observed in life and social science fields, where women are already prevalent, than in math-intensive ones, where they are underrepresented but in which the number of women holding assistant professorships is commensurate with that of men.
One potential reason for the dearth of women in math-intensive fields that is supported by data is the fact that female researchers publish fewer papers on average than their male counterparts (Larivière, Ni, et al., 2013) and are less likely to be listed as either first or last author (West et al., 2013). This extends to top-ranked journals, as evidenced in Bendels et al. (2018)'s analysis of publications spanning various scientific fields from the Nature Index (Nature, 2014). Discipline-specific studies report analogous findings in high-rank serials in mathematics (Mauleón & Bordons, 2012). Female mathematicians are significantly underrepresented in the most prestigious journals: The amount of publications by women has remained in the single-digit percentage range over the last decades, despite the fact that they have been entering the field at a higher rate over that time period (Mihaljević-Brandt et al., 2016). Whether women submit fewer manuscripts is difficult to confirm in the absence of transparent statistics on submission rates. What seems to hold is that women are underrepresented when it comes to being invited to submit to prestigious venues, as shown in statistics of commissioned authors to journals in the life and physical sciences (Conley & Stadmark, 2012).
The topic of whether the peer review system is intrinsically biased against women is highly disputed, with some studies challenging its robustness, albeit without consistent outcomes. A comprehensive review from an epistemiological perspective is that of Lee et al. (2013), who characterize and examine the empirical, methodological, and normative claims of bias in peer review. Results showing lack of evidence for bias in peer review in science are quoted for instance in Fox, Burns, and Meyer (2016), who conclude that gender, seniority, and geographic location affect the particularities of the refereeing process but not its outcome. Squazzoni, Bravo, et al. (2020) find no evidence of gender imbalance in the acceptance rates of 145 journals in biomedicine, life, physical, and social sciences, yet their conclusions emphasize the complexity of the problem, as distortions are extremely difficult to account for. Ceci and Williams (2011) argue that there is "no sex discrimination in publishing" and conclude that the critical variable for bias in peer review is not gender per se, but rather access to resources, which correlates with the former because women are more likely to work as adjuncts or at teaching-intensive institutions with limited means. Upon analysis of diverse sources in math-intensive disciplines, Ceci et al. (2014) agree that "manuscript reviewing and grant funding are gender neutral." Per contra, divergent conclusions can also be found in the literature. Recent analyses of journals in the physical and life sciences hint at the existence of gender-and geography-based biases: IOP Publishing (2018) shows that women are less likely to receive acceptance for publication in half of the subdisciplines covered by their 50+ journals and are less frequently invited to review. An evaluation of submissions to the eLife journal by Murray, Siler, et al. (2019) reveals a homophilic effect between the gender and the affiliation country of gatekeepers (editors and referees) and authors regarding the outcome of the review. Given the underrepresentation of women in editorial boards (Topaz & Sen, 2016) and reviewer pools (Lerback & Hanson, 2017), it is not unrealistic to suspect that the chances of manuscript acceptance for female authors might be lessened, even if this mechanism occurs at a subconscious level. Helmer, Schottdorf, et al. (2017) reach similar conclusions in their analysis of the Frontiers journals, stressing the need for increased efforts to fight against subtler forms of gender bias and not just focus on numerical underrepresentation alone. A reasonable strategy to limit bias in peer review is the implementation of the double-blind strategy. Tomkins, Zhang, and Heavlin (2017a) confirm that single-blind reviews confer a notable advantage to papers with famous authors and authors from high-prestige institutions in conference proceedings, the standard publication outlet in computer science. A meta-analysis indicates that the overall effect against women can be considered statistically significant (Tomkins, Zhang, & Heavlin, 2017b), followed by the recommendation that double-blind reviewing be implemented as a means to control for biases.
Most of the existing literature on bias in peer review concerns the natural, medical, and life sciences. Comparatively few articles are devoted to mathematics and physics, even though publication practices vary considerably, a fact that would merit further field-specific analyses. To the best of our knowledge, no systematic studies exist that look into hidden biases possibly introduced by publication practices in large collaborations, such as those in experimental physics. The lack of homogeneity in peer review for mathematics and its implications for the publication rates of underrepresented groups is likewise seldom addressed. Regarding the potential implementation of double-blind mechanisms in mathematics and physics, editors doubt that every single author identity can be successfully hidden in such small fields (Palus, 2015). Almost no journal in these areas currently offers double-blind review in any case, which is regarded as difficult to manage and maintain. To what extent the lack of double-blindness is hindering women and other underrepresented groups in mathematics and the physical sciences remains largely unknown.
This article addresses the scarcity of targeted studies on gender bias in scholarly communication in mathematics and the physical sciences by looking at discipline-specific bibliographical databases to select and study publications in distinguished topical journals. Additionally, we leverage the responses to a global survey of scientists by specifically selecting answers from mathematicians, physicists, and astronomers to questions about their perceived submission practices to top-ranked journals in their disciplines. The data offers novel insights into (a) the ways that female and male scientists perceive to behave regarding prestigious publication venues and (b) the evidence provided by publication rates split by gender obtained from the bibliographical sources themselves.

Selection of Journals and Perceived Quality
The quality of academic journals is often estimated by one of the available rankings that try to infer scientific prestige from various metrics, in particular citations. Perhaps the most widespread of them is the Journal Impact Factor ( JIF) (Garfield, 2006), with the Eigenfactor (West, Bergstrom, & Bergstrom, 2010) and the CiteScore (da Silva & Memon, 2017) as known alternatives. In some disciplines, journals are categorized using manually compiled lists, usually curated by fieldspecific academic organizations, as for instance the so-called ERA indicator developed by the Excellence in Research for Australia. For a review of bibliometric indices see, for example, Roldan-Valadez, Salazar-Ruiz, et al. (2018).
Aside from the convenience of having an accessible categorization to assess quality, it is by no means clear that journal rankings can encapsulate said information meaningfully. Against the JIF numerous well-argued critiques have been formulated on the basis of both technical issues, such as its concrete definition and implementation (Kiesslich, Weineck, & Koelblinger, 2016), which is problematic because the calculation is based on the arithmetic mean of a highly skewed distribution of citations, and of interpretative concerns . Similarly, concerns about potential biases have been raised against the ERA indicators (Haslam & Koval, 2010;Vanclay, 2011), which eventually led to their discontinuation. A consensus seems to be emerging that research quality should not be measured based just on the one-dimensional scale of a journal ranking (Callaway, 2016;DORA, 2012;Shanta, Sharma, & Pradhan, 2013;Verma, 2015). This development is in agreement with the views of the majority of the mathematical community, namely that "citation data provide only a limited and incomplete view of research quality, and the statistics derived from citation data are sometimes poorly understood and misused" (Adler, Ewing, & Taylor, 2009). In astrophysics, a field characterized by the pattern of communicating results as preprints ahead of publication, survey data showed that researchers rate "the quality of the journal as perceived by the scientific community" as more important than the JIF (Polydoratou & Moyle, 2007).
Accordingly, we have decided to refrain from employing any such ranking scheme in our analyses and instead leverage expert domain knowledge to select and prioritize some topical journals above others. For every analyzed discipline we justify our choices in the respective subsections under Subsection 3.2. Our selection of journals is intended to be representative of top-ranked outlets across disciplines and in agreement with the views of the respective scientific communities. Nevertheless, readers are encouraged to query the entire database used in this study to analyze publication statistics from their journals of interest in mathematics, astronomy and astrophysics, and theoretical physics using the custom web interface provided at http:// gender-publication-gap.f4.htw-berlin.de/journals/.

Data Sources
Our analysis is based on two distinct types of data sources: (a) bibliographic records of published articles in mathematics, astronomy and astrophysics, and theoretical physics, enriched by inferred author gender labels, and (b) answers from participants in a global survey of scientists, carried out in 2018 by the American Institute of Physics as part of an international and interdisciplinary project ("A Global Approach to the Gender Gap in Mathematical, Computing, and Natural Sciences: How to Measure It, How to Reduce It?", https://gender-gap-in-science.org/).

Bibliographic records
The data on published journal articles stems from three bibliographic repositories managed by scientific organizations with (partially, at least) open-access data policies. All three are regarded as high-quality, curated, comprehensive bibliographic collections for the respective disciplines, and have often served as data basis for specialized scientometric analyses (Brisbin & Whitcher, 2018;Caplar, Tacchella, & Birrer, 2017;Mihaljević-Brandt et al., 2016;Smith, 2016).
1. Mathematics: Zentralblatt MATH (zbMATH https://zbmath.org), founded in 1931, is the longest standing and one of the two most comprehensive abstracting and reviewing services in pure and applied mathematics. Edited by the nonprofit institution FIZ Karlsruhe, a member of the Leibniz Association, its contents will be made freely accessible in 2021. It places high value on its completeness, containing about 4 million bibliographic entries with reviews or abstracts drawn from about 3,000 journals and 180,000 books. Its author database comprises 950,000 author profiles. Every year, approximately 120,000 mathematical publications are indexed, and about 100 new journals and 3,000 research monographs and conference proceedings are added to the database (Hulek, 2016). For all practical purposes, regardless of the subfield within mathematics and its applications, every relevant publication can be found in zbMATH (Hansen, 2018). Our analyses of zbMATH entries capture the database at the end of July 2019. 2. Astronomy and astrophysics: The SAO/NASA Astrophysics Data System (ADS, https://ui .adsabs.harvard.edu) is a digital library for research in astronomy and astrophysics operated by the Smithsonian Astrophysical Observatory under a NASA grant. It is the main discovery platform for scientific literature used by the community of astronomers and astrophysicists, providing both disciplinary completeness and enriched data features (Accomazzi, Kurtz, et al., 2018). The ADS maintains three bibliographic databases covering publications in astronomy and astrophysics, physics, and the arXiv e-prints. For our analyses in astrophysics we have restricted ourselves to the first one, which contains over 2.5 million publications, 1.1 million of which are peer-reviewed. About 25,000 new entries are added yearly to the collection. The coverage of major journals of astronomy is complete, and those account for a large fraction of the research contained in the database (Santamaría, 2018). We analyze data from ADS as of at the end of March 2018. 3. Theoretical physics: The arXiv (https://arxiv.org), funded by Cornell University, the Simons Foundation, and member institutions, provides open access to electronic preprints in various fields, most notably physics. Contrary to mathematics and astronomy and astrophysics, where curated databases such as zbMATH and ADS ensure access to a mostly complete corpus of bibliometric metadata, no comparable repository exists for the entire field of theoretical physics. Standard publication practices of physicists, especially in theoretical subfields, include the upload of preprints to the arXiv prior to or concurrently with manuscript submission. In fact, this is so common that in fields such as high-energy physics, many peer-reviewed journals allow direct submissions from the arXiv via the e-print number. This preprint repository is "an indispensable mode of scientific exchange" (Jackson, 2002), "covering the majority of publications in subfields like astronomy, astrophysics, and nuclear and particle physics" (Larivière, Sugimoto, et al., 2014). Because arXiv e-prints do not include standardized information on the posterior appearance in peer-reviewed journals, we have cross-referenced the data with CrossRef (https://www .crossref.org) to enrich the information on serials as well as on authors' first names that we use for gender inference. Nevertheless, it should be noted that the analyzed content of selected journals from physics taken from the arXiv might differ from the full published records. We base our study on data gathered from the arXiv at the end of July 2019.

Survey responses
Answers to the question about the perception of submission practices were collected through the "2018 Global Survey of Mathematical, Natural, and Computing Scientists" (http://statisticalresearchcenter.org/global18), developed within the aforementioned Gender Gap in Science project with the goal of obtaining a broader picture of the status of mathematicians and scientists worldwide. The questionnaire addressed the researchers' impressions of their early years, university studies, doctoral studies, and professional careers.
Data was sampled via a snowball method that targeted affiliates and contacts from partnering institutions of the project. Due to the far-reaching network of 11 professional societies and scientific organizations it was possible to reach almost 30,000 respondents across the globe. The main reason for the choice of a snowball sampling technique was the lack of a single network to reach all targets; thus the creation of a statistically representative sample was not feasible. This poses certain limitations on the proper interpretation of the collected data, most notably the fact that answers cannot be assumed to be representative of the (sub-)populations as a whole. Rather, they should be considered indicators of trends observed among participating individuals in the survey.
Our analyses are based on the replies of participants with at least a Master's degree that are primarily working in mathematics, physics, or astronomy and that entered a valid answer to the question: "During the last five years, how many articles have you submitted to journals that are top-ranked in your field?" This selection yields 9,984 responses. Figure 1 shows the number of respondents per discipline and gender. Physicists are the largest group, with 4,392 answers, while mathematicians amount to 3,734 and astronomers to 1,858. In physics, women make up about 34% of all participants, whereas they reach 45% in astronomy and mathematics. The gender breakdown is also country-dependent. As shown in Figure 2, women represent 35% to 50% of all survey respondents in the majority of countries, with the notable exceptions of Japan and South Korea, where their proportion is much smaller. Overall, the percentage of women in the data set is significantly larger than in their respective disciplines, estimated from the figures of the UNESCO Institute for Statistics (http://data.uis.unesco.org), which report less than 30% of scientific researchers worldwide being women, cf. by the proportions of active authors per discipline over time (https://gender-publication-gap.f4.htw-berlin.de /cohorts/authors). Women were possibly more inclined to respond to a survey that they perceived to deal with gender issues, even though the call explicitly stated that the entire scientific community was encouraged to contribute.
In Figure 3 we show the age distribution broken down by gender and discipline. Note that the median lies between 40 and 50 years in all three fields. Whereas in physics and astronomy female respondents tend to be younger than their male counterparts, in mathematics the age distribution  is almost gender independent. In physics, we observe a second bulge in the range of 45 to 55 years, which indicates that the survey was answered by comparatively more female than male physicists in the second half of their academic career, a fact that might be relevant for the correct interpretation of the data.

Gender Inference
Bibliographic metadata does not include the authors' gender, hence this information needs to be inferred. Usually, an author's name is the only piece of information capable of providing an indication. In our analyses we have combined assessments from different gender assignment services maximizing the recall (i.e., the proportion of names that can be assigned a gender), while keeping the error rate under a certain threshold. Our algorithm is based on the benchmark of Santamaría and Mihaljević (2018), where we compared five dedicated web services and software packages. Roughly speaking, in our first stage we use the results from Gender API (https://gender -api.com) featuring a high probability score. For names leading to gender assignments with probability values between 75 and 90 in Gender API we combine responses with those from genderize.io (https://genderize.io). All remaining unidentified first names are processed with Python package gender guesser (https://github.com/lead-ratings/gender-guesser), which attains high precision but low recall. For authors without a first name but with last names contained in a curated list of Soviet surnames (https://en.wikipedia.org/wiki/List_of_surnames_in_Russia), we apply surname-ending rules to infer the gender. It is also important to note that more than 70% of the first names of authors in ADS are abbreviated as initials; thus direct gender inference via first names would hardly be useful. Therefore, we have trained an algorithm which clusters authorships into author profiles and increases the percentage of identifiable authorships enormously (Mihaljević & Santamaría, 2020).
Following the gender assignment procedure, all author names are tagged with a "female," "male," or "unknown" qualifier. The percentage of nonlabeled records is generally large and primarily affects names from certain regions; for instance, authors of Chinese ancestry are more often assigned unknown labels due to loss of gender marking during transliteration. In our gender analyses we remove all authorships labeled as "unknown," which in itself introduces a selection bias. An agnostic estimation of the incurred error would assume that the percentage of men and women in the "unknown" group mimics the ratio between the groups identified as male and female. Yet we know from our previous studies that the proportion of women in the group of authors labeled unknown is smaller than the share of identified women (Mihaljević-Brandt et al., 2016). This means that "unknown" names are more likely to be men than women. We conclude that our estimated percentage of women among all authorships when removing unknown authors is always an upper bound with respect to the entire data set of authors. When possible, we have added error regions to our plots to reflect this fact.
Numerous challenges arise in connection with automated gender recognition (AGR). To name a few, the association of a name with gender is not unique and also depends on the cultural and regional context; hence relying solely on the first name can be error-prone and lead to biases towards certain countries. Furthermore, all AGR approaches that build on names or other physiological features, such as facial images or voice, assume a binary gender paradigm that reinforces noninclusive preconceptions. Despite these (and other) critiques, we have performed a namebased gender inference because academia is notoriously not gender agnostic and because gender disparities are indeed observed and need to be explained. We have discussed various concerns related to AGR in Mihaljević, Tullney, et al. (2019) and would welcome ideas towards more inclusive schemas, preferably based on self-identification. Those would allow fairer, sustainable, and statistically significant analyses of bibliographic corpora in terms of gender.

Authorships
Academic publications are authored by one or more people (i.e., authors); formally speaking, we consider each one-to-many pairing of publication and author as one instance of authorship. For instance, an article authored by three individuals yields three different authorships.
Authorships might be counted in various ways: They can be weighted equally, regardless of the total number of authors in the paper and with no distinction on the order of appearance. This leads to a counting scheme that does not discriminate between authorship in single-author versus large-collaboration articles. Alternatively, one can incorporate the importance of individual publications by computing so-called fractional authorships, where each authorship is assigned a weight of 1/n, with n being the total number of authors. For example, in the example above, the weight would be 1/3. Furthermore, analyses might consider only one specific position in the list of authors as relevant, and often it is the first or the last slot that is particularly significant.
The sensible choice of a counting schema for authorships is field-specific and depends on the peculiarities of each discipline. In mathematics there are few large collaborations, most articles being written by a handful of authors. In that situation, statistics on publication patterns remain roughly unchanged when using equal or fractional authorship counts. This is not the case in other fields such as astronomy or high-energy physics, where sizable collaborations abound; hence for those it makes more sense to proceed using fractional authorships.
The global survey of scientists yields further insights on name ordering practices, specifically the following question: "In your field, which criteria are usually used to determine who will be the first, middle, or last author?" Almost half of the 10,219 respondents answered with "relative contribution," followed by "alphabetical ordering." Details are displayed in Figure 4.
Conventions regarding the assignment of author order in a publication vary per discipline: In mathematics the dominant criterion is alphabetical, but this is uncommon elsewhere, even almost unheard of in astronomy. In the physical sciences it is mostly the relative contribution that determines the author list order, at least within small research groups. In fact, astronomy has its particular unspoken publication policies, whereby whoever did (or claims to have done) most of the work becomes first author, usually followed by a few major contributors. Equal (smaller) contributors are listed next in alphabetical order. Generally speaking, when subsequent authors are not alphabetical, the order reflects the importance of their contributions. Both first and leading (second or third) authors play important roles. Large collaborations on the other side abide to the rules described in Section 1 and also tend to favor alphabetical ordering, sometimes inserting a handful of leading authors at the forefront. See Figure 5 for actual numbers obtained from the global survey's respondents.

Self-reported Publication Practices: Perceptions on Submission to Top Journals
In the global survey of scientists the following question was asked: "During the last five years, how many articles have you submitted to journals that are top-ranked in your field?" Respondents were expected to provide a number between 0 and 30; larger values were clustered together. 9,984 researchers in astronomy, mathematics and physics who hold at least a Master's degree provided a valid answer to this question, among them 3,981 women, 5,861 men, and 142 individuals who . Distribution of answers to the question "In your field, which criteria are usually used to determine who will be the first, middle, or last author?" from the global survey of scientists. Figure 5. Heatmap displaying the distribution of answers to the question "In your field, which criteria are usually used to determine who will be the first, middle, or last author?" from the global survey of scientists, broken down by academic discipline. did not disclose their gender. The respondents had the possibility to choose between "Female," "Male," and "prefer not to respond." They could also select none of them.
The majority of respondents quoted a small number: the median amounted to four submissions in the last 5 years, regardless of gender. The mean values in all three groups were very much alike, with 6.21 for women, 6.5 for men, and 6.64 in the unlabeled group. Figure 6 displays the histogram of responses by women and men split by gender. Note that peaks at multiples of five most likely indicate a rounding effect on the participants' side. Both distributions are similar, with a slight shift of answers from women towards lower numbers of submitted articles to what they consider top-ranked journals, except for the answer that no article was submitted to such a journal. Correspondingly, a somewhat higher proportion of men is visible in the long tail.
As a first assessment of the effect of gender on the perceived number of submissions, we test the null hypothesis that there is no statistical difference between the self-reported rates of women and men. For this purpose we use the nonparametric Mann-Whitney U test and compute two socalled "rank scores," (i.e., the number of times a score from group A precedes in rank order a score from group B, and vice versa (controlling for the minimum possible value for the rank sum)). This is appropriate to decide whether two data sets have been sampled from populations with the same distribution. We apply the test to the following data sets: (a) total answers of all women and all men, (b) answers subdivided by discipline, and (c) answers subdivided by world region. We set a significance level = 0.05 and apply the Bonferroni correction, yielding = 0.017 for the subgroup analysis (b) and = 0.004 in case (c), respectively.
In almost all scenarios, the null hypothesis cannot be rejected using the applied test method. The only exception occurs in subgroup analysis (c) for the region "Northern Europe" with a p value <0.0019 based on 715 respondents. However, the effect size is rather small, with the Rank-Biserial correlation having a very low value of 0.13. The Rank-Biserial correlation equals the difference of the proportions of the two rank sums, where the proportion is meant with respect to the number of all possible comparisons between groups 1 and 2. This indicator can have a maximum value of 1, in which case in all pairwise comparisons between both groups the score of one of them would be smaller than the other's. A correlation value close to 0, on the other hand, implies that the effect is very small, as is the case here.
To complete the picture we have built a multivariate linear model using an ordinary least squares (OLS) fit to predict the logarithm of the number of articles submitted to top-ranked Figure 6. Histogram of the number of publications submitted to top-ranked journals in the last 5 years as self-reported by the respondents to the global survey's question "During the last five years, how many articles have you submitted to journals that are top-ranked in your field?" Dark (light) bars encode answers from women (men). journals in the last 5 years (the target variable) taking the following attributes as independent variables: • highest academic degree (Master's/Doctoral) • primary discipline (Astronomy/Physics/Mathematics) • gender (Female/Male/Prefer not to respond) • age • country • parent or guardian of children ( Yes/No) • number of total/successful grant applications in the last 5 years • participation in 14 types of academic activities (e.g., journal editor, supervision of graduate students) We have applied a logarithmic transform to the target variable to achieve a roughly normal distribution and have preprocessed the data by removing rows with missing values and replacing rare countries by dummy values. To test for multicollinearity among all predictor variables, we have performed a fivefold cross validation as follows: For each predictor, we use the remaining ones to fit a tree-based ensemble model. Depending on the type of target (categorical/numerical) we either fit a classifier with accuracy as the loss function or a regression by minimizing the mean squared error. Furthermore, we introduce additional random variables, which serve as baseline to estimate the impact of the predictors. For each of the target variables, we evaluate the fivefold validation score, which measures the goodness of fit and thus the collinearity of the variable with other predictors of the initial OLS model, and we analyze the relevance of the most important ones. The procedure does not show significant mutlicollinearity for the variable gender. The most important predictor of gender is age, followed by the randomly distributed variables with almost the same values for feature importance. The variable age, however, shows mutlicollinearity with the highest academic degree and with being the parent or guardian of children. Thus, we have excluded age as a predictor in the OLS model for the number of articles submitted to top journals. The resulting OLS model is overall significant, yielding an adjusted R 2 value of 0.422, which means that the model explains around 42% of the variation in the data. Such an R 2 can be considered satisfactory for this kind of fit, as our data clearly do not include all relevant predictors, such as place of work, teaching load, or the exact meaning of "renowned" or "top-ranked" journals, that could explain the amount of submissions. We can look at the model's coefficients to estimate the effect of gender on the number of submitted articles while controlling for the other predictors. As suggested by the previous exploration, while gender is statistically significant for the overall model, its effect is comparatively small and yields an increase of around 6% for men versus women when controlling for the other predictors. The difference is measured for the overall median number of four submissions. The relative difference decreases to 5% or 4%, when taking five or 10 submissions, respectively, as the baseline. Conversely, the field of expertise has a much greater impact. When controlling for the other variables, submission numbers in mathematics and physics are predicted to be significantly lower than in astronomy. In particular, mathematicians are found to submit merely half as many articles as astronomers. The country of residence also plays a role: For example, Japan has the largest negative contribution in the resulting linear model. Indeed, in all three disciplines, 50% of the respondents from Japan claim to have submitted one or no manuscripts to a top-ranked journal. This might be an indication that the term top-ranked is understood differently across countries, possibly due to varying ranking schemes. Among the factors that correlate positively with submissions is the holding of certain academic functions associated with strong research activity and a solid network, such as conducting research abroad, delivering talks, and co-organizing conferences, or with seniority and academic prestige, as is typically the case for scientists who serve as journal editors, supervise graduate students or are members of grant committees. It is worth noting that a restricted model (based on highest academic degree, primary field, gender, age, country, parenting of children) that does not take into account the latter set of predictors associated with overall academic success results in only slightly higher impact of the respondents' gender, indicating that gender is not strongly correlated with such variables and thus not implicitly encoded.
We deduce that the selected female and male survey participants perceive their submission practices to journals they consider to be top-ranked in a similar way, with no evidence that women appreciate major differences with respect to men. What matters much more for the regression model, beyond the discipline-specific differences, is strong research activity, a network, and overall academic success. A closer look at the data further indicates that the proportion of women and men among those who participate in committees or pursue active international collaborations is very similar among the survey respondents.

Bibliographic Analysis of Top-Ranked Journals
In all three disciplines analyzed in this article, the proportion of women among actively publishing researchers has steadily increased in recent decades. Using data from the bibliographic services zbMATH, ADS, and arXiv we estimate that the proportion of authorships by women in mathematics and astronomy has grown from around 6% in 1970 to around 25% nowadays. The temporal trend in theoretical physics papers from the arXiv is less positive, yielding percentages around 5% in the early 1990s towards 20% nowadays. The figures are considerably lower, with proportions between 8% and 16%, in subfields other than astrophysics, as can be explored at our website.
In this section we analyze aggregated publication statistics in various high-ranked journals grouped by discipline. The selection was primarily driven by recommendations of senior researchers, taking into account additional field-specific information that we spell out in the following subsections. In all figures, dots represent the percentage of fractional authorships attributed to women among all authorships with inferred gender (i.e., after removing unknown gender assignments). Solid curves are the result of fitting a locally weighted scatter plot smoothing regression (LOWESS) model to the data. We count fractional authorships; however, the trends remain roughly the same when considering full or first authorships.

Mathematics
In the course of the professionalization of mathematics during the 19th century numerous national mathematical societies were formed, the oldest being the Moscow Mathematical Society, founded in 1864 (Cooke, 2011, p. 73). Akin to academic institutions, professional societies soon established their own journals, in which some of the most profound works of the discipline are still published today. We have thus decided to consider nine prestigious mathematical journals that are (co-)published by national societies. We have selected an additional nine journals that are particularly favored in certain subfields of mathematics and can be used as a proxy for what is considered high-quality research in those areas. All journal names are listed in Figure 7. Figure 7 displays percentages of fractional authorships from women in distinguished mathematics journals since 1970. In all considered serials the numbers are predominantly constrained below 20%. A solid half of the society journals displayed on the left column show a positive tendency over time. The Bulletin de la Société Mathématique de France shows a rather noisy behavior and no clear chronological trend, with proportions of women ranging from almost 0% to over 20%. The average share is around 10%, similar to the Journal of the European Mathematical Society. The lowest percentages are found in the Journal of the American Mathematical Society, where the proportion of women is around 5% or less and shows no noticeable increase over time. Topical journals in the right column are arranged roughly following the MSC 2010 (http://msc2010.org/msc2010final2-Aug10.pdf). The last three journals, which mainly feature work in areas of applied mathematics, display a rising development over time with shares above 10% in recent years. Except for the Journal of Differential Geometry, all journals reveal a slight positive trend. The particularly renowned journals Inventiones Mathematicae and Annals of Mathematics, which for the most part publish work in pure mathematics, stand out with numbers predominantly in the single-digit range.
In addition to the few selected journals shown above, we wish to obtain a more comprehensive picture of the correlation between journal quality and gender distribution of their authors by looking at a larger data set. As baseline for journals representing international mathematical research, we employ the Mathematics Subject Classification (MSC 2010), a tree-like, three-level alphanumerical scheme used by researchers, publishers, and the two main reviewing services in mathematics to label publications according to their subject matter. For every journal we compute the percentage of articles primarily classified into a core MSC class, namely between 03 and 65. A serial is considered a core mathematics journal if said percentage is larger than 90%. Journals indexed cover-to-cover in zbMATH are included in this group too, based on the expert opinion of their editorial board. Finally, all articles published before 1970 are also tagged as core mathematics, as that was the focus of the indexing service back then. This "Core Math" selection comprises 1,716 journals and around 2.9 million authorships.
Rather than using standard but questionable journal rankings to differentiate among perceived quality of mathematics serials, we adopt the internal ranking schema used by zbMATH instead. This journal categorization, which consists of a handful of labels, is updated on a regular basis by zbMATH's editorial staff, which comprises experts from most mathematical disciplines and engages in active communication with zbMATH's reviewer community to reflect the relevance of the journals' content. Editorial prioritization can certainly change over time, and a journal that was not considered particularly valuable 20 years ago may well have a different reputation today. However, experience shows that the corresponding fluctuations are rather small in mathematics, so that we can assume a relatively high stability in this classification. This selected group of 175 "priority" serials, named "Core Math Priority," is given preferential treatment due to their assumed novelty and special relevance. The latter is deemed to contain only prominent publication venues of proven quality. To give an estimate of the relative volume, articles in "Core Math Priority" contribute almost 900,000 authorships and make up about 25% of the "Core Math" data set in the last 10 years.
All 18 journals presented in Figure 7 belong to the Core Math Priority data set. In Figure 8 we observe that the proportion of authorships from women has been growing steadily in both the Core Math and Core Math Priority data sets, which confirms the trend from Figure 7. However, a gap remains between the percentage of women publishing in top-ranked journals and their overall representation as scientific authors in the entire field of mathematics.
To quantify the chronological evolution of the gap shown in Figure 8 more accurately, we have calculated the relative deviation from the mean per year; that is, for each year we measure the difference between the proportions of female authorships in both data sets and normalize it by dividing by the proportion of women in the Core Math baseline set. The relative deviation from the mean is displayed in Figure 9. Starting with a relative deviation of almost −25%, the gap becomes progressively narrower until the early 2000s, reaching a relative deviation of −10% to −15%. However, this trend does not seem to carry on: Since 2010, the values have declined and are back in the range of almost −20%.

Astronomy and astrophysics
In contrast to mathematics and its plethora of prestigious journals, there seems to be a consensus that the six serials showcased in Figure 10 encompass the vast majority of noteworthy research in astronomy and astrophysics (Caplar et al., 2017). This list comprises the five journals covered in Caplar et al. (2017) plus The Astronomical Journal, which the senior astronomers consulted considered a distinguished publication venue as well. Figure 10 displays the percentage of fractional authorships from women in said journals since 1970. Using first author counts yields very similar results, with slightly fewer female first authors in Science but overall exhibiting the same trends.
Unlike in mathematics and theoretical physics, authored contributions from female astronomers and astrophysicists in top-ranked journals have clearly increased since the 1970s. All six analyzed serials present female percentages around 20% in recent years, with a continuous increment and comparable little noise.
As mentioned, these six journals cover the majority of the publications in astronomy and astrophysics. To quantify this more precisely, we attempt to extract from ADS those journals with a specific focus in astronomy or astrophysics. To this extent, we implement a simple method: We create the "Astro" data set by considering all serials that contain "astro" in their name, plus Nature and Science, as they also publish high-quality research in the field. The advantage of this straightforward approach is that it works in most languages, thus enabling a country-agnostic selection. We find that the six manually selected journals shown in Figure 10 cover the majority, meaning about 70%, of the publications in the Astro data set. Figure 11 illustrates a noteworthy phenomenon: In the 1970s and 1980s, when the six journals accounted for about 50% of all publications in astronomy and astrophysics, female authorships were underrepresented when compared to all Astro journals. But in recent years the proportion of authorships by women in top journals no Figure 9. Relative deviation of the annual share of fractional authorships from women in the Core Math Priority data set from that in Core Math, fitted using LOWESS smoothing. longer deviates from the overall mean in the negative direction. In fact, women's share in the six renowned journals nowadays even slightly exceeds their proportions in the entire Astro data set.

Theoretical physics
Theoretical physicists consulted for this analysis suggested that the 10 journals listed in Figure 12 can be regarded as highly prestigious while offering a broad insight into different specialization areas. Figure 12 displays the percentage of fractional authorships from women in them over the past 20 years, according to indexed records in the arXiv. When using first author counts instead, the obtained results are very similar, showing more noise for first authors in Reviews of Modern Physics but overall exhibiting the same trends.
The situation in theoretical physics appears to be static all throughout the 2000s and 2010s, with average percentages of women barely reaching 10% and displaying little to no rising tendency. A minor exception is the International Journal of Theoretical Physics, which shows an upward shift but overall rather low figures for women's contributions. The situation in Advances in Theoretical and Mathematical Physics is rather dismal, showing practically no female representation.
It should be kept in mind that the development in physics, especially if astrophysics is excluded from the consideration, is not as positive as in the other disciplines. Nevertheless, the trends in these journals remain clearly behind the development of the proportion of women in the total number of physics articles indexed in the arXiv. It is important to remark that our statistics for Figure 10. Percentage of fractional authorships from women in prestigious astronomy and astrophysics journals per year since 1970. Figure 11. Relative deviation of the annual share of fractional authorships from women in the top six astronomy and astrophysics journals with respect to the entire Astro data set, fitted using LOWESS smoothing. theoretical physics are based on arXiv data, meaning that only submissions to the preprint service rather than the final published records are considered. Although the practice of submitting preprints to the arXiv is widespread in physics, we cannot guarantee that our data basis is comprehensive for all journals displayed above. Nevertheless, we argue that the general evolution in the discipline can be roughly captured by using the arXiv data as proxy for publications in theoretical physics.

Additional resources
Apart from the results shown above, further adhoc analyses of journals and gender can be informed by the resources displayed in our visualization website. In http://gender-publication -gap.f4.htw-berlin.de/journals/collection it is possible to group selected journals (e.g., the most representative serials in a given discipline), and study how the contributions of female authors in that collection have evolved over time. We encourage the interested reader to take advantage of this feature to inform their own understanding of publication dynamics in their field.

CONCLUSIONS
Motivated by the undeniable role that high-impact publications play in the making or breaking of academic careers, we have analyzed the gender distribution of authorships in prestigious mathematics, physics, and astronomy journals in the past 50 years. Dedicated open-access bibliographic databases and a custom gender inference algorithm allow us to perform this analysis at scale rather than manually. All other factors being equal, the expectation is that the proportion of women among all authors should roughly resemble the percentage of established female researchers in the profession, a number that has been steadily growing and that is estimated to be currently above 20% on average in mathematics and astronomy and astrophysics, and between 10% and 20% in other theoretical physical sciences. Remarkably, several of the analyzed journals in the most mathematical disciplines exhibit meager female representation and no signs of turnaround over the last couple of decades. The situation in astronomy and astrophysics, to the contrary, aligns better with the supposition that male and female authors are to be published in top-ranked journals at a comparable rate.
A search for potential causes for this phenomenon leads us to ask whether submission rates to prominent venues in mathematics and theoretical physics differ significantly when broken down by gender (i.e., perhaps women are underrepresented in the aforementioned journals because they do not submit as many manuscripts for consideration as men). A second explanation might lie in the process of peer review itself, which in the case of these disciplines favors close interactions and trust relationships between editors and reviewers. Maybe structural biases against women hinder their acceptance rates in high-ranked journals, which are known to be already very stringent. It is almost impossible to establish to which extent any of these hypotheses may account for the lack of female representation in top mathematics and physics journals, as relevant submission and acceptance rates are hard to obtain from academic publishers.
Alternative data sources that could shed light on this topic include self-reports such as classical survey methods. We have leveraged the 2018 Global Survey of Mathematical, Natural, and Computing Scientists to obtain answers from almost 10,000 mathematicians, physicists, and astronomers about their submission practices to top-ranked journals in their disciplines. Our analysis of their responses indicates that women and men report similar numbers of submitted articles in the past 5 years, with no major statistically significant differences in subgroup analyses broken down by disciplines or world regions. Therefore, the first of the two conjectures mentioned in the above paragraph is at least not supported by the survey's data.
The comparison of responses from the global survey regarding self-reported number of submissions to prestigious journals with the actual publication statistics from selected top-ranked serials results in a conflicting picture for mathematics and theoretical physics. On one side, there is no statistically significant difference between women and men regarding perceptions of their own publication practices; both quote comparable figures for their manuscript submission rates, as shown in Subsection 3.1. Per contra, such reports do not harmonize with the observed percentage of authorships from women in the selected top journals in mathematics and theoretical physics, as exposed in Subsection 3.2. The answers to the survey cannot explain the low number of women that are published in these renowned venues, as for instance the percentage of women in multiple distinguished mathematics serials is shown to be comparatively smaller than the overall ratio of female mathematicians in the complete field. The gap between female-authored publications in very prestigious journals and in the totality of core mathematics journals, that had been closing before the 2000s, has astonishingly grown larger again ever since. We don't observe a similar phenomenon in astronomy and astrophysics. Coincidentally, a major difference between peer review in both fields is a missing homogeneous standard for acceptance criteria in the former, which leaves room for factors such as author's prestige or institutional pedigree to affect the decision-making process, consciously or unconsciously. This could be one of the ways in which women are at a disadvantage regarding high-impact publications in small fields. One of the rare self-evaluations by one of the major publishers in physics suggests at least a gender-and workplace-based bias in physics (IOP Publishing, 2018).
However, it cannot be concluded from the survey results that peer review in top-ranked mathematics and theoretical physics journals discriminates against women. Ultimately, the global survey and the bibliographic databases cannot be directly aligned with each other: Because participation in the survey was not randomized but built on snowball sampling, its results cannot be considered representative of the entire population of researchers and scholars. For instance, it might be plausible to expect that female respondents to the survey are among those that submit to renowned venues comparatively more frequently. According to the survey answers, a higher number of manuscripts submitted to top-ranked journals correlates with factors associated with pronounced research activity, a well-established network, and academic seniority. While these aspects do not significantly depend on gender among the surveyed scientists, this might well be a confounding factor in the overall population of researchers in these disciplines, as suggested by, for example, Ceci and Williams (2011). Additionally, the survey question itself does not provide a definition of what a "top-ranked" journal is, leaving that characterization to the individual perceptions of respondents, which potentially induces gender-related as well as other types of bias, such as the use of a countryspecific scheme for the ranking of journals, as suggested by the consistently lower numbers in responses from scientists from Japan. Similarly, an unbalanced distribution of authorship in topranked journals at the country level and, even more granularly at the institutional level, is to be expected. We were only able to investigate these superficially, as the coverage of affiliations, from which entities such as countries and institutions can be extracted, was not suffiently ensured by zbMATH. Moreover, a certain bias was present towards larger publishers such as Springer and Elsevier; this is a topic to be addressed in depth elsewhere. Nonetheless, the survey encodes the impressions of a sizable number of actual scientists and this confers its significance despite the lack of statistical representation.
As it could not be ruled out that potential biases in the peer review process in mathematics and physics are a cause for the underrepresentation of female authors in top-ranked journals, we recommend increasing the transparency in the submission and acceptance practices of scholarly communicators as well as implementing any measures to alleviate conscious and unconscious biases. The onus is on academic publishers to conduct and make available their own investigations on rejection and publication rates in relation to the gender, as well as other potentially important social and demographic features, of their submitting authors.