Peer review has an important role in improving the quality of research papers. It is the “lifeblood of research in academia […] the social structure that subjects research to the critical assessment of other researchers” (Bourdieu, 1975). This structure relies on self-regulated interactions within the scientific community, in which a journal editor appoints peer reviewers with expertise in the subject of a particular manuscript to report on the quality of that manuscript and to provide recommendations for its improvement. Other attributes of the peer reviewer, such as their gender, should be irrelevant (Moss-Racusin et al., 2012; Nature, 2013). However the identities of peer reviewers and editors are usually confidential, so previous work on gender balance in the peer-review process has relied on small, monodisciplinary data sets and these studies have given partly contradictory reports (Lloyd, 1990; Gilbert et al., 1994; Budden et al., 2008; Borsuk et al., 2009; Knobloch-Westerwick et al., 2013; Larivière et al., 2013; Buckley et al., 2014; Demarest et al., 2014; Handley et al., 2015b; Fox et al., 2016).

Frontiers journals (www.frontiersin.org) differ from most journals in that they generally disclose the identities of peer reviewers and associate editors alongside each published article in an attempt to increase the transparency and quality of the publication process (Poynder, 2016). This allowed us to extract the names of associate editors, peer reviewers and authors for articles published in Frontiers journals between 2007 (when the first Frontiers journal was published) and the end of 2015. This data set included the names of more than 9000 editors, 43,000 reviewers, and 126,000 authors for about 41,000 articles published in 142 journals in Science, Health, Engineering and the Humanities and Social Sciences (see Materials and methods). This data set is one of the largest available to date, and contains at least an order of magnitude more information than most data sets used in previous studies of peer review (see Supplementary file 2 for comparison).

Analysis of this data set reveals that women are underrepresented in the peer-review process, and that editors of both genders operate with substantial same-gender preference (homophily) when appointing reviewers. Moreover, our analysis suggests that this homophilic tendency will persist even when men and women are fairly represented in the peer-review process. Our results confirm the need for increased efforts to fight against subtler forms of gender bias in scholarly publishing and not just focus on numerical under-representation alone.

To assess whether our data set was representative of an active and mature research community, we created directed networks (Figure 1a₁), in which individual scientists appeared as vertices, while arrows denoted interactions between them (“is appointing” in the editor-to-reviewer network, and “is editing (reviewing) a manuscript of” in the editor (reviewer)-to-author network). As a whole, the networks had an exponentially fast growth in time, with a large fraction of people participating in a connected component of the graph reaching 90% of the total network size. Furthermore, graph theoretical metrics such as shortest path length, small-world index as well as several other network properties have changed little in the 3-5 last considered years (Figure 1—figure supplement 1). Thus, peer-reviewing interactions in the Frontiers journal series gave rise to a mature, topologically stable and integrated community, even though its contributors constitute only a small subset of researchers worldwide.

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We then looked for signatures of gender bias and of its evolution across time in the structure of these large networks. We study first the fractions of assignments for reviewing or editing given to female or male scientists and, for comparison, we also show the fractions of author contributions. Figure 1b reveals that the fractions of authoring, reviewing and editing contributions by women — amounting to 37%, 28% and 26%, respectively, in the complete accumulated data until 2015 — are always significantly smaller than the corresponding fractions for men. The unbalance between male and female contributions thus worsens when gradually ascending through the peer-review hierarchy. Apart from a few outlier countries, this pattern was dominant worldwide (Figure 1—figure supplement 2). It was also largely present in all the considered journals when looking at them individually (Figure 1c). Overall, the number of contributions by female authors varies between about 15% (Frontiers in Neurorobotics) and 50% (Public Health), by female reviewers between about 15% (Surgery) and 50% (Public Health), and by female editors from ca. 5% (Robotics AI) to 35% (Aging Neuroscience). Globally, we observed a trend towards gender parity across time. The rates of change were, however, very slow. Linear extrapolation based on the fractions observed from 2012 to 2015 would predict that exact parity could be achieved as late as 2027 for authoring, 2034 for reviewing and 2042 for editing.

We wondered whether these lower fractions of contributions to the different roles were just due to the fact that overall there are numerically less female than male authors, reviewers and editors (39%, 30% and 28% out of all available authors, reviewers and editors, respectively, were women, closely mirroring the observed fractions of assignments). To test this hypothesis, we took the exact same network of peer-review interactions in the Frontiers journals for given, and randomly permuted gender labels among scientists of a given role (Figure 1a₂). This procedure maintained the ratio of female and male scientists acting in the different roles, but destroyed all direct correlations between gender and numbers of contributions. Repeatedly drawing random genders for the scientists in the network generated a surrogate ensemble that we used to estimate the expected number of contributions in a gender-blind control network. Author and reviewing contributions by women lay significantly below the confidence intervals obtained through this permutation testing procedure since 2009 and 2011, respectively. For female editing contributions we found the same, though non-significant, trend. Thus, the mere overall smaller number of female actors cannot explain the observed unbalanced fractions of female contributions to the peer-review chain.

We then looked for possible differences over the entire distributions of the number of peer-review tasks and authoring contributions for men and women. These distributions are fat-tailed (Figure 2a-c), indicating that some individuals provided a large number of contributions to the publication chain, while a majority of scientists authored, reviewed or edited only a small number of manuscripts. Moreover, comparing the observed degree distributions to the expectations derived from the same null hypothesis used above, women had a significantly smaller than chance probability to review (and author) more than one article, while their probability to act as single-time reviewer or author exceeded the expected chance level (Figure 2e-f). In the editing role, women underrepresentation was significant only for a high number of contributions. Furthermore, we found significant deviations from chance-level expectations across the entire studied time-span (Figure 2—figure supplement 1).

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The differences in assignment numbers may reflect behavioral or psychological differences between the groups of male and female scientists — either intrinsic or due to sociocultural context (Moss-Racusin et al., 2012; Nature Neuroscience, 2006; Ceci et al., 2009; Ceci and Williams, 2010; Goulden et al., 2011; Ceci and Williams, 2011; Bloch, 2012; Raymond, 2013; Shen, 2013; Handley et al., 2015a). Nevertheless, assignment numbers are also ultimately influenced by the editors’ active choices. To reveal whether any bias exists in the reviewer assignment relation, we first analyzed gender correlations between directly connected pairs of nodes in the editor-to-reviewer appointment network (Figure 3a) and found a marked gender homophily bias for both male and female editor nodes. Specifically, 73% of reviewers appointed by men were also men, 33% of reviewers appointed by women were women, but, importantly, both these numbers laid above the expectations drawn from the assumption that genders were randomly distributed in the given editor-to-reviewer network topology. Similarly, in the reviewer-to-author network (Figure 3b), male (female) reviewers assessed articles authored by male (female) authors significantly more often than expected.

Figure 3

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While these findings seem to point at homophily created by choices, they might also stem from “baseline” homophily (McPherson et al., 2001), i.e. subtle but unavoidable bias caused by disproportions in the number of reachable male and female nodes due to heterogeneous network structure. We first checked for the influence of local subnetwork structure on apparent gender bias by looking at different scientific fields, including those with relatively mild underrepresentation of women, and found homophily widespread across disciplines (Figure 3c). Second, a more detailed analysis of inter-node gender correlations in the editor-to-reviewer appointment network detected a clear tendency to gender homophily already at the level of the narrow neighborhood of individual nodes (Figure 3d). Specifically, to control for baseline homophily at the level of a narrow local neighborhood, we measured, for each editor node, the actual number of reviewer assignments given to women. We then subtracted from this number its chance expectation, derived individually for every node from the frequency of locally reachable female reviewers, i.e. reviewers situated at most five links away (which is a short distance relative to the average shortest path length of 12 steps for the editor-to-reviewer network, cf Figure 1—figure supplement 1e). Even at this local neighborhood level, we continued to find that male (female) editors generally appointed female reviewers at a lower (higher) rate than expected. Both independent analyses – by topic or localized – validate the existence of a so-called “inbreeding” homophily, i.e. an active preference to connect with same-gender network nodes, on top of “baseline” homophily (McPherson et al., 2001).

Finally, we wondered whether the observed inbreeding homophily in the network was due to the presence of a few strongly homophilic editors or whether, alternatively, homophilic attachment was a feature shared by most editors. To that end, we defined an index of inbreeding homophily at the local level of each editor node. For each considered editor node, we first evaluated the number k of connected same-gender reviewers. We then evaluated the probability 0 ≤ Φ_hom ≤ 1 that k (or more) homophilic connections could arise by baseline homophily only, taking into account the editor-specific basin of locally reachable male and female reviewers (defined as for Figure 3d). Such Φ_hom can serve as an index tracking the strength of inbreeding homophily in shaping the actual reviewer appointments by an editor. Large values of Φ_hom approaching 1 indicate that the observed gender homophilic choices of a given editor are plausibly just due to “passive” baseline homophily. In contrast, small values of Φ_hom approaching 0 hint at a stronger tendency to “active” – consciously or unconsciously, see Discussion – inbreeding homophily. Figure 3e shows the histograms of the index Φ_hom for male and female editors, compared with expectations from gender-shuffled networks. For male editors, most histogram bins for Φ_hom < 0.6 displayed node counts significantly larger than gender-shuffled estimations. The histogram of Φ_hom for female editors showed much fewer significant overrepresentation and most of them at very low values of Φ_hom, however it remained compatible with gender-shuffled estimations for most of the Φ_hom range.

These different distributions of inbreeding homophilic tendencies resulted in a gender-dependent impact of the reviewer-appointment choices of male and female editors in determining the overall number of female reviewer appointments. To determine this impact we pruned links originating from editors with inbreeding homophily index Φ_hom below a growing threshold Φ_thr (retaining only editors whose Φ_hom satisfies 0 ≤ Φ_thr ≤ Φ_hom ≤ 1) and we did so separately for male and female editors (Figure 3f). After pruning the most homophilic male or female editors, we evaluated the new resulting probabilities of appointing a female reviewer. On the one hand, we found that it was enough to remove the few most homophilic female editors with the lowest values of Φ_hom from the network, to bring the probability for a female editor to appoint a female reviewer back to chance-level. On the other hand, the probability for a male editor to appoint a female reviewer increased only very slowly by pruning more and more male editors. In particular, it remained significantly below chance expectations for all the considered thresholds for inclusion, 0 ≤ Φ_thr ≤ 0.5. This means that the overall smaller-than-chance probability of appointing female reviewers for male editors is due to inbreeding homophilic tendencies that are widespread among male editors, although at varying degrees of strength. In contrast, the overall larger-than-chance probability to appoint female reviewers for female editors is driven by the action of just a small number of strongly homophilic female editors, with most other female editors showing only “passive” baseline homophily.

In this study, we found that apart from a few outliers depending on country and discipline, women are underrepresented in the scientific community with a very slow trend towards balance, which is consistent with earlier studies (Larivière et al., 2013; Fox et al., 2016; Topaz and Sen, 2016; Lerback and Hanson, 2017; Nature Neuroscience, 2006; Shen, 2013; Nature, 2012). In addition, we found that women contribute to the system-relevant peer-reviewing chain even less than expected by their numerical underrepresentation, revealing novel and subtler forms of bias than numeric disproportion alone. We reported clear evidence for homophily beyond the expected baseline levels in both genders (Figure 3) using a very large trans-disciplinary data set that allowed us to clarify a previously ambiguous picture (Lloyd, 1990; Gilbert et al., 1994; Borsuk et al., 2009; Buckley et al., 2014; Fox et al., 2016). This network-level inbreeding homophily is driven by a large fraction of male editors, together with only a few highly homophilic female editors.

Ideally, all scientific interactions are gender-blind. A scientist's status and the provision of resources to scientists should not be influenced by gender but solely depend on the value of the scientific contributions. Access to the publication systems is a critical determinant of a scientist’s success. Accordingly, reviewers and editors, the gatekeepers of the scientific canon, should be particularly sensitive to base their judgment solely on the merit of scientific work. This merit, however, is difficult to determine and any assessment is necessarily influenced by the assessor's view of the field, including his or her personal position in the network of colleagues and the interactions with them (Mulkay, 1979; Cole, 1992).

Inbreeding homophily, an increased affinity between persons with similar attributes, appears to be a sociological, population-level trait of human societies. It is only natural, thus, that we find gender homophily in interactions between editors, reviewers and authors. Nonetheless, this inbreeding homophily is damaging to female scientists, whose work ends up being overlooked, due to unconscious negative bias. The phenomenon of inbreeding homophily is also likely not restricted to the peer review of manuscripts, so it needs to be taken into account for grant evaluation, hiring, or when designing mentoring programs. Importantly, it is likely to persist even when numerical balance between genders is achieved (Isbell et al., 2012). Altogether, inbreeding homophily negatively affects science as a whole because a stronger involvement of women would increase the quality of scientific output (Merton, 1973; Woolley et al., 2010; Nature, 2013; Campbell et al., 2013). Consequently, all scientists should wholeheartedly support the endeavor to remove gender bias from science - but how could that be achieved?

Initiatives to remove gender-based inequality can roughly be divided into two different categories. On the one hand, “gender mainstreaming” (Special Adviser on Gender Issues and Advancement of Women, 2002) promotes the consideration among actors at all levels of every action’s and policy’s implications on women and men and is geared towards creating long lasting “bottom-up” changes. On the other hand, fast progress could be attempted through “top-down” implementation of technocratic instruments such as quota. This politically issued ‘state feminism’ (Mazur and McBride Stetson, 1995), is suboptimal in that it might even “provide an alibi” for not modifying attitudes in depth (Squires, 2008). As inbreeding homophily is an expression of a state of mind it is likely little amenable to change by externally enforced measures. Raising awareness, in comparison, seems to be the most promising route. The goal should be to motivate all scientific actors to “integrate thinking about gender discrimination in every decisional process” (translated from Woodward, 2008). Educative actions should be conducted with tact, not based uniquely on inducing feeling of guilt and shame, in order not to be perceived as annoying (Woodward, 2003). At the same time, existing formal actions to reduce bias should be upheld.

In the field of peer review two more specific strategies are available to reduce bias: blind review and automated editorial management. However, both strategies are of limited acceptance and use. First of all, removing the authors’ names is often not sufficiently blinding. References to the authors’ previous publications or to the approving ethics committee all but spell out the authors. Second, while removal of the authors’ names does indeed blind the reviewers to all irrelevant attributes, it also blinds them to relevant meta-data, such as the scientific experience of the authors, which might be considered as relevant by many reviewers. In an attempt to assist editors of Frontiers journals, keyword-based reviewer suggestions are automatically provided to them but the editors remain free to make their own choices. While these gender-blind automated suggestions could already contribute to an assignment that is less influenced by homophily, an editorial management software is also the ideal platform to routinely direct the editor’s attention to the issue of homophily. It could display statistics similar to our Figure 3 and encourage non-homophilic choices of reviewers. Such a strategy maintains full editorial freedom and could easily be evaluated, either internally or, in the case of open review as in the Frontiers journals, through analysis of the publicly available data.

Given how engrained homophily is in our nature, the path towards a gender-blind science will be arduous. Yet, with the joined effort of the scientific community to overcome partisanship and discrimination, a merit-based system with equal opportunities for all scientists might just be within reach. After all, which social enterprise would be more apt to follow ratio over instinct than science?

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Thank you for submitting your article "Gender bias in scholarly peer review" to eLife for consideration as a Feature Article. Your article has been reviewed by three peer reviewers, and the evaluation has been overseen by a Senior/Reviewing Editor. The reviewers have discussed the reviews with one another and the Reviewing Editor has drafted this decision to help you prepare a revised submission.

Summary:

This is an interesting and high quality manuscript on a topic that is important and timely. The manuscript (which is based on a novel data set) merits publication after revision to improve readability and replicability.

Essential revisions:

1) To maintain high standards of research reproducibility, and to promote the reuse of new findings, eLife requires all major data sets associated with an article to be made freely and widely available (unless there are strong reasons to restrict access, for example in the case of human subjects’ data), in the most useful formats, and according to the relevant reporting standards. (See below for more details).

2) How representative is the population studied by the authors? It would be interesting to compare the population studied by the authors with other large-scale studies to enhance the generalizeability of their findings. For example, it seems as if the authors could compare Figure 1—figure supplement 2 to Lariviere et al. (2013) in order to determine whether the population they study is significantly different to traditional scientometric populations. Also, there are several studies that show that women are less productive than men. This might be useful for explaining Figure 2.

3) The authors should more fully acknowledge the limitations of the data set. For example, the authors mention that the names are publicly disclosed (this is what allows this analysis). However, several studies have shown that open peer review significantly affects the willingness of certain populations to conduct reviews (e.g., by age, rank, gender, minority status). Could the fact that names are disclosed make this less generalizable? The limitations of this should be discussed.

4) The analyses only included reviewers who agreed to review (understandably, as there is no publicly available data for reviewers who declined to review). However, women might be more likely to say no to requests to reviews for various reasons (e.g. they might have less time to review, or they might feel less qualified to comment on their peers' work). Hence, might their underrepresentation stem from self-selection rather than discrimination?

5) It would be interesting to comment on the possible effect of age on gender discrepancies at different levels. Specifically, editors might (on average) be older than reviewers, who in turn might (on average) be older than authors (although with large variability). Is it possible that higher gender discrepancy among editors and reviewers is because women might be less represented in older age groups?

6) There is sparse information on author name disambiguation (for those that lacked a UID). More information should be provided on this. The authors state that they cannot guarantee a "completely error-free parsing" – could they run a validation test to give an estimate of the error? And was any validation exercise conducted on the name-gender algorithm? How does this compare with other name-gender algorithms?

7) Several seminal books on peer review and articles specifically focused on bias in peer review are omitted here. Furthermore, the article fails to engage with the previous literature in a substantial way. Given that this work is one of the largest peer-review studies to-date, it would be useful for the authors to establish how their work refutes or confirms previous work.

8) Regarding the third paragraph in the Results section: please include a figure which shows that the gender gap in various contributions cannot be fully explained by population.

9) There are many interesting results that warrant more explanation in the text. At present, some of the most interesting results are buried in the figure captions. It would be great to see the authors embed some of these results, in more detail, in the main text.

10) Overall, the differences between observed and chance-level participation of women (for instance in Figure 2) are not that large, even though they are statistically significant. How concerned should we be about them in the first place?

11) The authors advise that editors should be encouraged to make non-homophilic reviewer selection. But if the goal is to increase gender parity, shouldn't women editors be 'allowed' to be more homophilic, at least until the parity achieved? Might it be better to suggest that all editors should try to recruit more women reviewers?

Essential revisions:

1) To maintain high standards of research reproducibility, and to promote the reuse of new findings, eLife requires all major data sets associated with an article to be made freely and widely available (unless there are strong reasons to restrict access, for example in the case of human subjects’ data), in the most useful formats, and according to the relevant reporting standards. (See below for more details).

We thank the reviewer for the reminder. We have included the anonymized raw data in the revised submission.

2) How representative is the population studied by the authors? It would be interesting to compare the population studied by the authors with other large-scale studies to enhance the generalizeability of their findings. For example, it seems as if the authors could compare Figure 1—figure supplement 2 to Lariviere et al. (2013) in order to determine whether the population they study is significantly different to traditional scientometric populations. Also, there are several studies that show that women are less productive than men. This might be useful for explaining Figure 2.

We thank the reviewer for these suggestions. We have now augmented the Discussion section with a comparison of the Frontiers population with other scientometric populations (subsection “How representative are the Frontiers journals?”) and included two tables (Supplementary files 1 and 2) summarizing previous studies. Specifically, we find that gender composition of Frontiers articles authors is similar to that of Lariviere et al. (2013), although when broken down by country outliers do exist. We also included a comparison with (1) a large data set for the gender composition of editors in mathematical journals (Topaz and Sen, 2016) and (2) a recent study (Lerback and Hansen, 2017) with data from 20 journals of the American Geophysical Union. We find that, overall, our study provides a global account on the prevalence of women among editors and reviewers and ranks these previous reports in a continuum of field-specific participation numbers.

While our data does not allow inferring the reasons for why women contribute less, some studies indeed suggested that women are less productive. These results are now mentioned and discussed as a potential reason in the revised Discussion (subsection “Evolution of participation rates by gender and causes for remaining inequity”, second paragraph). However, for completeness, we also refer to other partially conflicting studies indicating that women may have different, not necessarily lower productivity patterns than men (e.g. Gilbert et al., 1994; Pan & Kalinaki, 2015). Furthermore, we stress that the key new findings of our study concern homophily (Figure 3) and that the smaller number of women has been taken into account in the analysis leading to these findings.

3) The authors should more fully acknowledge the limitations of the data set. For example, the authors mention that the names are publicly disclosed (this is what allows this analysis). However, several studies have shown that open peer review significantly affects the willingness of certain populations to conduct reviews (e.g., by age, rank, gender, minority status). Could the fact that names are disclosed make this less generalizable? The limitations of this should be discussed.

We thank the reviewer for pointing this out. We agree that open peer review could potentially have effects other than the intended increase in transparency and quality. These effects are now explicitly discussed in the revised manuscript (subsection “How representative are the Frontiers journals?”, first paragraph). Despite extensive search we could not find any study that specifically assesses whether open peer review affects the gender specific acceptance rate of reviewer assignments. Should we have missed a crucial publication, we would be very grateful for a reference.

We also now systematically compare our findings to a large number of previous studies which considered smaller sample-sizes but had access to more meta-data, since they were initiated journal-side. Overall, as we comment in the extended Discussion, we find women’s participation rates among editors, reviewers and authors of Frontiers journals to be comparable to previous reports, indicating that the Frontiers community is well representative of a general situation.

4) The analyses only included reviewers who agreed to review (understandably, as there is no publicly available data for reviewers who declined to review). However, women might be more likely to say no to requests to reviews for various reasons (e.g. they might have less time to review, or they might feel less qualified to comment on their peers' work). Hence, might their underrepresentation stem from self-selection rather than discrimination?

The reviewer is correct in suggesting that it is critical to distinguish between self-selection and discrimination. Our data set does not allow inferring the reasons for women’s underrepresentation and therefore self-selection (due to various motivations) could potentially play a role. This possibility, along with others, is now acknowledged and discussed in the revised manuscript (subsection “Evolution of participation rates by gender and causes for remaining inequity”, second paragraph). Besides this discussion, we also performed a more detailed analysis of the different prevalence of homophily in the male and female subpopulation. Taken together we feel that the data clearly point to same-gender preference of mostly male editors as a contribution to the under-representation of female scientists across the Frontiers series of journals. This conclusion is particularly strengthened by our new analysis of the different patterns of gender homophily for male and female editors (Figure 3e-f).

5) It would be interesting to comment on the possible effect of age on gender discrepancies at different levels. Specifically, editors might (on average) be older than reviewers, who in turn might (on average) be older than authors (although with large variability). Is it possible that higher gender discrepancy among editors and reviewers is because women might be less represented in older age groups?

Our data set does not include scientists’ ages and we are, therefore, unable to analyze how age affects women’s participation in the peer-review system. However, as the number of female scientists decreases with age and rank, the differences seen in the gender fraction of editors, reviewers and authors could well be influenced by the age distribution in these populations. The revised manuscript now mentions this possibility (subsection “Evolution of participation rates by gender and causes for remaining inequity”, second paragraph) and we further discuss our results in light of a recent study with access to age data (Lerback and Hansen, 2017; subsection “How representative are the Frontiers journals?”, last paragraph).

6) There is sparse information on author name disambiguation (for those that lacked a UID). More information should be provided on this. The authors state that they cannot guarantee a "completely error-free parsing" – could they run a validation test to give an estimate of the error? And was any validation exercise conducted on the name-gender algorithm? How does this compare with other name-gender algorithms?

We thank the reviewer for pointing this out. The gender assignment is a critical step of the analysis and we have now included both a more detailed description of the name-gender algorithm and a validation test in the Materials and methods section (subsections “Collection and parsing of data” and “Determination of gender”). While errors are in principle unavoidable when identifying people based on their names, Newman (2001) estimated their rate to be only few percent. Combined with our reliance on user IDs for the vast majority of people, we expect that errors due to name disambiguation are uncommon.

To estimate the error rate in gender assignment, we have validated the genders of a random selection of 924 scientists through a manual web search (as described in subsection “Determination of gender”, second paragraph) and compared our assignment error with the supplemental material of Lariviere et al. (2013). Notably, our algorithm’s error rate is smaller than the reported error rate of the name-gender algorithm of Lariviere et al. (2013). Independent of the error rate, we would like to stress that mis-assigning gender can never increase the homophily that we see. Random mis-assignments have the same effect as a small rate of random permutation of gender labels. This would reduce evidence for inbreeding homophily rather than spuriously inducing it Thus, although we cannot reach a 100% correct gender assignment, the finding of inbreeding homophily is robust against this type of uncertainty.

7) Several seminal books on peer review and articles specifically focused on bias in peer review are omitted here. Furthermore, the article fails to engage with the previous literature in a substantial way. Given that this work is one of the largest peer-review studies to-date, it would be useful for the authors to establish how their work refutes or confirms previous work.

We thank the reviewer for pointing this out. It is true that our previous version had the style of a short letter, rather than that of an extended article. We now rewrote and substantially extended the Discussion section of the manuscript, including generous paragraphs of comparison with other empirical work, the current state of the art and detailed discussions about why our study can clarify previously ambiguous pictures.

Despite these comprehensive additions and expanded reference section (99 references cited, while in the previous version we had just 31) we have failed to include the crucial references the reviewer had in mind; we would be keen to receive more explicit guidance.

8) Regarding the third paragraph in the Results section: please include a figure which shows that the gender gap in various contributions cannot be fully explained by population.

Every figure in our article clearly indicates comparison with confidence intervals associated to a null hypothesis of no bias effects besides numerical differences between male and female populations. Therefore, our figures already showed the requested information.

Indeed, our statistical assessment – random shuffling of gender labels – leaves the network structure and the fraction of females at every level intact. In essence, we ask whether the observed contributions could have occurred randomly, if all actors of different gender behaved identically with respect to the contribution in question.

We apologize if this important procedural aspect was not clear enough. We have now better highlighted the concept of the shuffling method (cf. Figure 1A) for the generation of gender-blind control networks, and edited the third paragraph of the Results section (third paragraph) in an attempt to make it more understandable. Furthermore, we have also improved figure captions.

9) There are many interesting results that warrant more explanation in the text. At present, some of the most interesting results are buried in the figure captions. It would be great to see the authors embed some of these results, in more detail, in the main text.

We thank the reviewer for this suggestion. Former Figure S3, now Figure 1C, as well as former Figure S5, now Figure 3D are now presented in more detail in the Results section, (second and sixth paragraphs, respectively). We also better highlighted the homophily findings, which are a key novel contribution of our study. In particular, we have added a completely new section and figure panel about the observed different mechanisms of homophily for male and female editors (Figure 3E and 3F) in the main manuscript.

We further rewrote and substantially extended the Discussion section of the manuscript to now include a discussion of these findings.

10) Overall, the differences between observed and chance-level participation of women (for instance in Figure 2) are not that large, even though they are statistically significant. How concerned should we be about them in the first place?

We agree with the reviewer that it is important to discern statistical significance, effect size, and relevance. First, while the differences, for the most part, seem small, they can reach up to a factor of 2 between the observed fraction of females with 10 contributions and the chance range. Given the large range in the number of occurrences, visualized in Figure 2, we had to use a logarithmic scale. This requires care when attempting to judge the magnitude of the bias just from the visual inspection of those graphs, while statistics are precise. Second, to highlight why our findings are concerning, we now include several sections in the revised Discussion that:

A) Argue why we are confident, in the light of previous findings, to state that discrimination is a critical reason for the remaining inequity (subsection “Evolution of participation rates by gender and causes for remaining inequity”, second paragraph);

B) List direct results of subtler forms of gender bias. Notably, even a slight homophily can influence and alter the way in which information spreads and is damaging to female scientists, whose work is perceived with a negative bias by the majority (subsection “Homophily in society and science”, last paragraph) and;

C) Translate the findings to specific structural disadvantages for women (subsection “Conclusions”, second paragraph).

11) The authors advise that editors should be encouraged to make non-homophilic reviewer selection. But if the goal is to increase gender parity, shouldn't women editors be 'allowed' to be more homophilic, at least until the parity achieved? Might it be better to suggest that all editors should try to recruit more women reviewers?

The reviewer is asking an interesting question and we agree: on first glance, it might seem like a prudent policy to support homophily among female editors to reach equity.

In response to question 1, we would like to highlight, however, that the goal of scientific policy is not equity per se, but equal opportunity and scientific meritocracy. To this end homophily should be reduced, too, as homophily, even in a situation when parity is reached, prevents equal opportunity. This is now detailed in the revised Discussion in the first two paragraphs of the subsection “Conclusions”.

In response to question 2, encouraging editors of both genders to recruit more women might foster the advance of excellent female scientists and advertise that women do good science. We stress however that a broad literature corpus in sociology of work environments have shown that the efficacy of top-down measures aiming at enforcing equal representation is poor if not paired with policies aiming at educating deciders about the importance of fighting gender discrimination (i.e. healing “from within” network construction mechanisms, rather than just artificially “transplanting” more female nodes into the network).

Considering both sides of the medal, it is unclear whether the positive effects (faster route to equity) or negative effects (undesirable behavioral trait) prevail in the long run. We added a corresponding paragraph to the Discussion (last paragraph) and the subsection “Conclusions” (third paragraph).

Author details

1. Markus Helmer

   1. Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany
   2. Bernstein Center for Computational Neuroscience, Göttingen, Germany
   3. Yale University, New Haven, United States

   Contribution

   MH, Conceptualization, Data curation, Software, Formal analysis, Validation, Investigation, Visualization, Methodology, Writing—original draft, Writing—review and editing

   For correspondence

   markus.helmer@yale.edu

   Competing interests

   The authors declare that no competing interests exist.

   "This ORCID iD identifies the author of this article:" 0000-0001-9680-0595

2. Manuel Schottdorf

   1. Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany
   2. Bernstein Center for Computational Neuroscience, Göttingen, Germany

   Contribution

   MS, Conceptualization, Formal analysis, Validation, Investigation, Methodology, Writing—original draft, Writing—review and editing

   Competing interests

   The authors declare that no competing interests exist.

   "This ORCID iD identifies the author of this article:" 0000-0002-5468-4255

3. Andreas Neef

   1. Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany
   2. Bernstein Center for Computational Neuroscience, Göttingen, Germany

   Contribution

   AN, Conceptualization, Formal analysis, Validation, Investigation, Methodology, Writing—original draft, Writing—review and editing

   Competing interests

   The authors declare that no competing interests exist.

4. Demian Battaglia

   1. Bernstein Center for Computational Neuroscience, Göttingen, Germany
   2. Institute for Systems Neuroscience, Aix-Marseille University, Marseille, France

   Contribution

   DB, Conceptualization, Formal analysis, Validation, Investigation, Methodology, Writing—original draft, Project administration, Writing—review and editing

   For correspondence

   demian.battaglia@univ-amu.fr

   Competing interests

   The authors declare that no competing interests exist.

   "This ORCID iD identifies the author of this article:" 0000-0003-2021-7920

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