Abstract
Evidence suggests that women in academia are hindered by conscious and unconscious biases, and often feel excluded from formal and informal opportunities for research collaboration. In addition to ensuring fairness and helping to redress gender imbalance in the academic workforce, increasing women’s access to collaboration could help scientific progress by drawing on more of the available human capital. Here, we test whether researchers tend to collaborate with same-gendered colleagues, using more stringent methods and a larger dataset than in past work. Our results reaffirm that researchers co-publish with colleagues of the same gender more often than expected by chance, and show that this ‘gender homophily’ is slightly stronger today than it was 10 years ago. Contrary to our expectations, we found no evidence that homophily is driven mostly by senior academics, and no evidence that homophily is stronger in fields where women are in the minority. Interestingly, journals with a high impact factor for their discipline tended to have comparatively low homophily, as predicted if mixed-gender teams produce better research. We discuss some potential causes of gender homophily in science.
Introduction
Women are severely underrepresented in many branches of science, technology, engineering, mathematics, and medicine (STEMM), and face additional challenges and inequities relative to men [1–5]. On average, women occupy more junior positions [6, 7] with lower salaries [8, 9], receive less grant money [10, 11], are promoted more slowly [12–15], and are allocated fewer resources [16] and less research funding [17–19]. Experimental evidence suggests that bias against women plays a major role in generating these differences [20, 21].
Writing papers, networking, and collaboration are all instrumental to research productivity and academic career advancement [22–25], and dozens of studies have tested for gender differences in these areas [5, 26–29]. For example, studies have concluded that women tend to be less involved in international collaboration [19, 28, 30–32], collaborate less within their own university departments [31], have less prestigious collaborations [33], and fewer collaborations in total [34]. These gender differences in collaboration presumably have multiple causes, which might include implicit and explicit gender bias [20], differential family obligations [33, 35, 36], gender differences in confidence or self-esteem [37], concerns relating to sexual harassment [38], and unequal access to conferences [39] or travel funds [32].
A high, steadily increasing proportion of research papers is written by more than one author [3], making collaboration a key predictor of publication output, and thus of career prospects [40, 41]. Additionally, empirical studies imply that mixed-gender or otherwise diverse teams produce better outputs on collaborative tasks than less diverse teams [42–48]. For reasons such as these, multiple studies have examined the author lists of published research articles in order to test for gender differences in collaboration frequency or pattern. To our knowledge, most or all such studies imply that men co-publish with men, and women with women, more often than expected if collaborators assort randomly with respect to gender [49–58]. This non-random assortment is often termed ‘gender homophily’.
We believe that most or all earlier studies of gender homophily were hindered by a largely unacknowledged statistical issue that we will refer to as the Wahlund effect (Fig 1), by analogy with the conceptually similar Wahlund effect in population genetics [59]. The Wahlund effect makes it deceptively difficult to test for gender-based co-author choice simply by counting the relative number of same- and mixed-gender coauthorships. Essentially, the Wahlund effect means that whenever coauthorship data are sampled from two or more discrete sets of literature, which vary in the author gender ratio and which are largely unconnected by collaboration, the number of same-gendered coauthors will be inflated. This can give the impression that authors preferentially publish with same-gendered colleagues even if no gender preferences exist, or if the true preference is for opposite-gendered colleagues (‘gender heterophily’). For example, a sample of literature containing a mixture of bioinformatics and cell biology papers will probably contain an excess of mostly-male and mostly-female author lists, simply because researchers usually collaborate within their own discipline, and because the author gender ratio is more male-biased in bioinformatics than in cell biology [5].
In the present study, we test whether life sciences researchers tend to co-publish with same-gendered colleagues, while controlling for the Wahlund effect as strictly as we are able. We use a recently-published dataset describing the gender of 35.5 million authors from 9.15 million articles indexed on PubMed [5]. Holman et al. [5] reported large differences in the gender ratio of authors across research disciplines, journals, countries, and across the years 2002-2016. We therefore tested for gender homophily while restricting our analysis to particular journals (a proxy for research specialties), time periods, and countries. We quantified gender assortment using a metric called α′ [60], which is positive when same-gender authors publish together more often than expected (gender homophily), negative when opposite-gender authors publish together more often than expected (heterophily), and equal to zero when authors assort randomly with respect to gender (see Methods).
Results
Gender homophily by discipline, time period, and authorship position
Fig 2 shows the distribution of α′ estimates in 2015-2016 across all journals for which we recovered sufficient data, when α′ was calculated for all authors, first authors only, or last authors only. Most journals had positive values of α′ (77-92%, depending on time period and author type; S1 Data), and for many of these the false discovery rate (FDR)-corrected p-values suggested that α′ was significantly greater than zero (1469/2077 journals were significant in 2015-16, and 404/1192 in 2005-6; S1 Data). Only 2/2077 journals had statistically significant heterophily (i.e. α′ < 0) in 2015-16, and 1/1192 in 2005-6 (S2 Table). The remaining 606 or 787 journals (in 2015 and 2005 respectively) had a value of α′ not significantly different from zero, consistent with the null hypothesis of random assortment with respect to gender. We also confirmed that in most journals (S2 Data) and most research disciplines (S3 Data, S1 Fig), the majority of papers had multiple authors.
α′ was significantly higher in the literature sample from 2015-16 relative to 2005-6, though the difference in means was small (S2 Fig; Effect of the fixed factor ‘Time period’ in a linear mixed model of the data for all author positions: Cohen’s d = 0.091±0.04, t953 = 2.42, p = 0.016).
When comparing pairs of α′ values estimated for the first and last authors for the same journals, we found that α′ tended to be higher for first authors than for last authors (S3 Fig; Effect of the fixed factor ‘Authorship position’ in a linear mixed model: Cohen’s d = 0.065±0.02, t2024 = 4.28, p < 0.0001). This suggests that the gender of the first author was a slightly stronger predictor of the remaining authors’ genders than the gender of the last author, i.e. the opposite of what is predicted if senior scientists are causally responsible for homophily.
Variance in homophily between disciplines
Fig 2 illustrates the variance in journal homophily values (α′) across scientific disciplines. All disciplines had positive mean α′ (averaged over journals), although homophily appeared somewhat stronger in some disciplines than others (e.g. mean α′ was 0.12±0.02 for Urology journals and 0.03±0.01 for Veterinary Medicine journals; Fig 2, S4 Data). However, there was no formal evidence for consistent differences in α′ between disciplines: the random factor ‘Discipline’ explained around 1% of the variance in α′ in the two linear mixed models described in the previous section (see Fig 2 and mixed models in Online Supplementary Material). Thus, the causal mechanisms underlying the observed positive α′ values appear to be similarly strong in all the disciplines we examined.
There was no indication that journals publishing on a wide range of topics have higher α′ values than more specialised journals due to the Wahlund effect (Fig 1). For example, the journal category ‘Multidisciplinary’—which includes general interest journals like PLOS ONE, Nature, Science, and PNAS—did not have markedly elevated α′ (Fig 2). This result suggests that our estimates of homophily, and estimates from some of the earlier studies of homophily listed in the Introduction, are probably not markedly inflated by the presence of disparate research topics (with variable author gender ratios) being published within individual journals.
Nevertheless, when we calculated α across all non-single-author papers in our entire 15-year PubMed dataset (as before, excluding papers where at least one author’s gender was unknown; n = >3 million papers, >16 million authors), we found that α was 0.126. This figure is almost double the median value of α′ for individual journals (Fig 2; α′ = 0.070 for ‘All authors’), suggesting that lumping together papers from different fields and different time periods can indeed produce spurious evidence for gender homophily as outlined in Fig 1.
Relationship between gender homophily and number of authors
Papers with two authors had significantly lower (but still positive) α′ values relative to papers with more than two authors, while papers with 3, 4 or ≥ 5 authors had essentially identical average α′ values (Fig 3). Specifically, the posterior estimate of mean α′ was 0.014 (95% CIs: 0.002—0.026) for 2-author papers and 0.065 (95% CIs: 0.056—0.074) for 3-author papers (and roughly the same for 4- and ≥ 5-author papers; Fig 3). One possible explanation for this finding is that 2-authors papers are more likely to have an author list that is evenly split between career stages (e.g. a postgraduate student and their supervisor), increasing the chance that the authors are mixed gender (see section ‘Theoretical expectations for α when the gender ratio differs between career stages’). The result also suggests that the causal mechanisms responsible for gender homophily are similar in small (e.g. 3-author) and larger (≥ 5 author) collaborations (and across disciplines where small versus large collaborations are the norm).
Relationship between gender homophily and gender ratio
We next tested whether researchers are more or less likely to publish with same-gendered colleagues in strongly gender-biased disciplines (e.g. Surgery or Nursing), relative to disciplines with a comparatively gender-balanced workforce (e.g. Psychiatry). We found a positive, non-linear relationship between the gender ratio across all the authors publishing in a particular journal [5], and the estimated value of α′ for all authors and for first authors, but not last authors (S4 Fig). Journals with a balanced or female-biased author gender ratio tended to have higher α′ (i.e. stronger homophily) than journals with a male-biased author gender ratio (GAM smooth term p = 0.0002 for all-author homophily, p < 0.0001 for first-author homophily, and p = 0.13 for last-author homophily).
Relationship between journal impact factor and gender homophily
We observed a noisy but statistically significant linear relationship between standardised journal impact factor and α′, such that journals with a high impact factor for their discipline had weaker gender homophily than did journals with a low impact factor for their discipline (Fig 4; linear regression: R2 = 0.043, t1415 = -8.0, p < 0.0001). The slope of the regression was −0.012±0.0015, indicating that increasing the discipline-standardised impact factor by one standard deviation is associated with a reduction in α′ of 0.012. The Spearman correlation coefficient was -0.19 (p < 0.0001).
Analysis accounting for differences in author gender ratio between countries
When we restricted the analysis by country, we observed statistically significant homophily for 72 of the 325 journal-country combinations tested (64 unique journals and 18 unique countries), and no significant heterophily (S5 and S6 Figs). Additionally, the values of α′ calculated for each journal-country combination were only very slightly lower than the α′ values calculated for the journal as a whole (i.e. when pooling papers from different countries, as was done to make Fig 2): on average, the difference in α′ was only 0.002 (S7 Fig). These results suggest that our findings of widespread homophily in the main analysis were not driven solely by a Wahlund effect resulting from gender differences between countries.
Theoretical expectations for α when the gender ratio differs between career stages
Given that we cannot identify individual researchers or their career stages, we used a simple model to derive the theoretical expectations for α when the gender ratio differs between career stages (see Methods). As shown in Fig 5, we predict that α is expected to be non-zero, even if collaborators are randomly selected with respect to gender, provided that there is a gender gap between career stages. The extent to which α deviates from zero depends on the relative frequencies of collaboration within and between career stages (rows and columns in Fig 5), and the size of the gender gap between stages (x- and y-axes in Fig 5). When >50% of coauthor pairs comprise one early-career and one established researcher, we expect gender heterophily (α < 0) whenever the gender ratio differs between career stages. Conversely, when >50% of collaborations are between people at the same career stage, we expect gender homophily (α > 0). In a few parameter spaces (shown in red; Fig 5), α was quite high, and overlapped with the values that we estimated (Fig 2).
Despite this overlap, Fig 5 suggests that our main conclusions (and those of other studies of gender homophily) are probably robust to this career stage issue. We only expect strongly positive α when A) the gender ratio is highly skewed across career stages (e.g. a 5-fold difference), and B) collaborations between early and established researchers are very rare (e.g. <10% of the total). Both of these conditions seem unlikely to be true for most fields: the gender gap across careers stages is generally less pronounced [1, 5], and it is very common for early-career researchers to co-publish with an established mentor [61]. However, one can get α > 0 for realistic combinations of parameters, e.g. a moderate shortage of women in senior positions coupled with a moderate excess of within-career stage collaboration, suggesting this effect might contribute to some of the homophily observed by this and previous studies.
Lastly, we note that if there is a gender gap between career stages and coauthorships between early-career and established researchers comprise >50% of the total, then the baseline expectation for α is actually less than zero (blue areas in Fig 5). Therefore, it is possible that researchers preferentially assort with same-gendered collaborators even more strongly than implied by our results, at least for certain journals or research disciplines.
Discussion
We found evidence that researchers work with same-gendered coauthors more often than expected under the null model, even after implementing stringent controls for Wahlund effects of the kind illustrated in Fig 1. Our study therefore reaffirms earlier studies’ conclusions [49–57, 62] using stricter methodology, and generalises their results across the life sciences. Relatively few journals had α′ values below zero, and almost no journals showed statistically significant gender heterophily after controlling for multiple testing. The excess of same-gender coauthorships was quite large: many journals had α′ > 0.1, indicating that the gender ratio of men’s and women’s coauthors differs by >10% in absolute terms. In relative terms, our findings are even more striking: for example, if men have 20% female coauthors and women have 30% (i.e. α′ = 0.1 in a field with a typical gender ratio [5]), then women publish with women 50% more often than men do.
An important limitation of our study is that we cannot reliably determine the cause(s) of the observed excess of same-gender coauthorships. As well as the obvious interpretation—conscious or unconscious selection of same-gendered collaborators by men, women, or both genders—our results could be partly explained by uncontrolled Wahlund effects. However, we suspect the contribution of these uncontrolled artefacts to be minor, for four reasons: we found positive α′ after controlling for three obvious sources of Wahlund effect; there was no inflation of α′ in highly multidisciplinary journals relative to specialised journals; restricting the data by country yielded similar estimates of α′; and our modelling work suggested that differences in gender ratio between career stages are unlikely to fully explain our results. On balance, we believe the data suggest that it is likely that some researchers preferentially select same-gendered collaborators, although it is difficult to ascertain what proportion of people show such a preference, or how much the strength of the preference varies between individual researchers. We also note that even in a world in which everyone selected their collaborators at random with respect to gender, a high proportion of individual researchers would have entirely same-gendered collaborators by chance alone (especially in gender-biased disciplines); thus, individuals who only have same-gendered co-authors are not necessarily doing anything differently from people with gender-balanced co-authors.
We hypothesised that disciplines with a strongly skewed gender ratio might show the strongest gender homophily, e.g. because being in the minority might increase one’s motivation to seek out same-gendered colleagues. Contrary to this hypothesis, we found no evidence that gender homophily is restricted to particular disciplines: α′ was similarly high across the board (Fig 2). Interestingly, gender homophily was weakest for journals with a male-biased author gender ratio, and strongest in journals with a female-biased author gender ratio. One possible reason is that men are more likely to preferentially seek out male collaborators in fields where men are a minority, relative to the homophily displayed by women in fields where women are a minority. However, this latter result only has tentative statistical support since our sample contains few journals in which most authors are women (S4 Fig).
We also found that gender homophily was marginally stronger in 2015-2016 relative to 2005-2006. Although this trend might reflect a change in the gender preferences of researchers seeking collaborators, there are alternative (and perhaps more likely) explanations. For example, this trend might result from the increasing number of women working in senior positions in STEMM over the past decade [63–65]. As shown in Fig 5, if enough coauthorships are between junior and senior researchers, a large gender gap between career stages can give the appearance of heterophily. As this gender gap between career stages lessens, the observed values of α′ may increase.
Regarding our finding of weaker homophily among 2-author papers, we suspect that many 2-author teams comprise a student/postdoc and a senior staff member, making these teams especially likely to be mixed-gender, due to the greater shortage of women among senior researchers [1, 5]. Assuming this interpretation is correct, this result suggests that our reported α′ values may underestimate the strength of peoples’ preferences for same-gendered collaborators; essentially, women seeking a senior collaborator could be constrained to work mostly with men, meaning that people’s ideal and realised gender preferences would be mismatched. On a related note, Ghiasi et al. [51] argue that women in engineering are “compliant [in reproducing] male-dominated scientific structures” because they do not collaborate often enough with other women (for reference, Figure 7 in [51] implies that coauthorships involving two women are c. 30% more frequent than expected under random assortment). By contrast, we feel that it may be counter-productive to recommend that women collaborate primarily with other women, e.g. because this constrains women’s options (particularly in fields like the one studied by Ghiasi et al.—engineering—where 90% of professors are men [1]). Instead, we suggest that researchers of both genders can help to close the gender gap in STEMM. In the context of collaboration, one way to do this is to undertake self-examination to ensure that one is not inadvertently overlooking or excluding women among potential students and colleagues. One should also take care to treat male and female collaborators equally, e.g. in terms of training and mentoring, allocation of work, and how one descibes the collaboration to other people (e.g. in conference presentations, on the lab website, or in the ‘Author contributions’ section of a paper). Experimental work suggests that unconscious bias causes people to undervalue women’s research achievements [20], and a study of author contribution statements found observational evidence that menial or under-valued tasks are more often assigned to women while more prestigious tasks are assigned to men [61].
Our study begs two questions: what causes gender homophily in science, and are our results cause for concern? We believe that the answers to these questions are closely related. For example, some of the homophily we observed might be caused by women seeking to avoid harassment or sexism from men [38], which would clearly be very concerning. Additionally, Sheltzer and Smith [66] concluded that ‘elite’ male academics (defined as recipients of major honours) have a higher proportion of male students and postdocs than non-elite male academics. This finding could contribute to the homophily we observed, and is cause for concern since the results might reflect discrimination against women during hiring [20], or avoidance by women of elite research groups (e.g. due to gender differences in confidence, or a perception that some groups are sexist). We also found a little evidence that gender homophily is detrimental to research quality, in that high-impact journals tended to have weaker homophily (though the relationship was very noisy). Assuming that papers published in high-impact journals are of higher average quality (which is contentious; [67]), our results provide non-experimental support for the hypothesis that mixed-gender teams produce better research than single-gender teams [42–48]. Another issue is that if many collaborations are between established researchers, there will be an excess of male-male collaborations in fields where women in senior positions are rare; some of the observed homophily might therefore reflect the elevated gender gap among senior researchers.
On the other hand, homophily might have more benign causes. Collaboration is often most enjoyable and productive when working with like-minded people, who might tend to be same-gendered more often than not. We also suppose that some people consciously choose to preferentially collaborate with women in order to help close the gender gap in the workforce; this would create homophily if women adopt this strategy more often than men. In support of this interpretation, there is some evidence that women are more likely than men to promote the work of female colleagues by inviting them to give talks [68, 69]. Given that many collaborative research projects unfortunately involve a gendered division of labour [61], working with a same-gendered colleague may provide exposure to new parts of the research process.
Methods
The dataset
We used the dataset of PubMed author lists from Holman et al. [5]. Briefly, that dataset was created by downloading every article indexed on PubMed and attempting to infer gender from each authors’ given name using computational methods. Each journal was assigned to one of 107 scientific disciplines, using PubMed’s journal categorisations in the interests of objectivity. Because the present study focuses on co-authorship, all single-author papers were discarded. We also discarded all papers for which we could not determine the gender of every author with ≥95% certainty, in order to simplify the statistical analysis. To mitigate Wahlund effects caused by variation in the gender ratio of researchers over time (see below), we only kept papers with publication dates falling in two one-year time periods, namely 0-1 or 10-11 years prior to the collection date of the PubMed data (i.e. 20th August 2016). Lastly, we excluded journals with fewer than 50 suitable papers. Detailed sample size information is given in S1 Table.
Calculating α, the coefficient of homophily
Following Bergstrom et al. [60], we defined the coefficient of homophily as α = p − q, where p is the probability that a randomly-chosen co-author of a male author is a man and q is the probability that a randomly-chosen co-author of a female author is a man. Like the Wahlund effect, α is borrowed from population genetics; for a set of 2-author papers, it is equivalent to Wright’s coefficient of inbreeding [70]. Mathematical work illustrates that α is closely related to alternative network-based methods for quantifying homophily [71].
To estimate α for a particular subset of the scientific literature, we estimated p as the average proportion of men’s co-authors who are men (averaged across all papers with at least one man author), and q as the average proportion of women’s co-authors who are men (averaged across all papers with at least one woman author). To estimate the 95% confidence intervals on α for a given set of n papers, we sampled n papers with replacement 1000 times, estimated α on each sample, and recorded the 95% quantiles of the resulting 1000 estimates.
As well as calculating α for all authors, we calculated α for first or last authors only. α was again defined as p − q, but this time p was estimated as the average proportion of male co-authors on papers with a male first (or last) author, and q was estimated as the average proportion of male co-authors on papers with female first (or last) authors. We did not calculate α for other authorship positions (e.g. second or third authors) because this would necessitate culling the dataset to include only papers with a sufficiently long author list, complicating interpretation of the results.
We also calculated α for papers with 2, 3, 4 or ≥5 authors, for all journals that had at least 50 suitable papers from 2015-2016 with the specified author list length.
Our test assumes that the expected value of α is zero if authors randomly assort, but for small datasets this assumption is not always true. Essentially, this issue arises because a person cannot be their own co-author. In a small dataset comprising m men and f women authors, a man can co-author with m − 1 men while a woman can co-author with m men. Thus, the null expectation for α is a negative number—potentially a large one if m and f are very small.
To control for the fact that the null expectation for α is not zero for small datasets, we devised an adjusted version of the coefficient of homophily, which we term α′. Every time we calculated α for a set of papers, we also determined the expected value of α under the null hypothesis that authors assort randomly with respect to gender. This was accomplished by randomly permuting authors across papers 1000 times, recalculating α, and taking the median. We then calculated α′ by subtracting the null expectation for α from the observed value. We also used the null-simulated α values to calculate a two-tailed p-value for the observed value of α; the p-value was defined as the proportion of null simulations for which |αnull| > |αobs|. We applied false discovery rate (FDR) correction to each set of p-values to account for multiple testing [72].
As expected, α′ was usually almost identical to α (S8 Fig), but α was downwardly biased relative to α′ for the smallest datasets (S9 Fig). Additionally, the correlation between α′ and sample size was negligible (R2 < 0.01), suggesting that our calculation of α′ effectively removed the dependence of α on sample size. We therefore used α′ in all analyses.
Minimising the Wahlund effect: Research discipline and time period
To minimise bias in α′ due to the Wahlund effect, we restricted each set of papers to a single research specialty to the greatest extent allowed by our data. Specifically, we only calculated α′ for individual journals, since papers from the same journal typically focus on closely related topics. Although some journals, e.g. PLOS ONE, publish research from diverse disciplines with very different author gender ratios [5], calculating α′ for these highly multidisciplinary journals is still useful as a contrast. The difference in α′ between highly multidisciplinary and more specialised journals, e.g. PLOS ONE versus PLOS Computational Biology, gives an estimate of the extent to which multidisciplinarity within journals inflates α′.
As well as varying between disciplines, the gender ratio of authors has changed markedly over time [5]. Because the gender ratio was more male-biased in the past, α′ would be inflated if we calculated it for a sample of papers published over a long enough time frame. To minimise this effect, we only sampled papers from two one-year periods (namely 2005-6 and 2015-16). The median change per year in % (fe)male authors across journals is below 0.5% [5], and so restricting our dataset to a single year should prevent temporal changes in gender ratio from noticeably affecting our estimates of α′.
Minimising the Wahlund effect: Author country of affiliation
A Wahlund effect could arise even if one calculates α′ for a single discipline and time period, because of variation in the gender ratio of researchers from different countries. For example, Holman et al. [5] found that PubMed-indexed authors based in Serbia are far more likely to be women than are authors based in Japan. Therefore, a dataset containing a mix of papers from teams of authors based in these two countries would contain an excess of same-sex coauthorships, even if collaboration were random with respect to gender within each country.
To address this issue, we also analysed every combination of journal and author country of affiliation for which we had enough data (i.e. 50 or more papers published in 2015-16). For simplicity, we restricted the dataset to only include papers for which Holman et al. [5] had identified the country of affiliation for all authors on the paper, and all authors shared the same country of affiliation. Restricting the dataset in this fashion produced enough data to measure α′ for 325 combinations of journal and country (median: 70 papers and 273 authors per combination).
Calculating standardised journal impact factor
We obtained the 3-year impact factor for each journal from Clarivate Analytics (formerly ISI). To account for large differences in impact factor between disciplines, we took the the residuals from a model with log10 impact factor as the response and the research discipline of the journal as a random effect. Thus, journals with a positive standardised impact factor have a higher mean number of citations than the average for journals in their discipline. We then used linear regression and Spearman rank correlation to examine the relationship between α′ and impact factor across journals.
Statistical analysis
Previous authors [66, 73] have hypothesised that senior scientists preferentially recruit staff and students of the same gender, and/or that junior researchers preferentially select same-gendered mentors. In the majority of PubMed-indexed disciplines, authorship conventions mean that the first-listed author is often an early-career researcher, while the author listed last is more likely to be a senior researcher leading a research team [74]. Assuming that senior researchers are the main drivers of homophily and that there are enough papers with three or more authors, we predict that the last author’s gender will be the strongest predictor of the remaining authors’ genders (i.e. the gender of the last author will be more salient than that of the first author, or any other authorship position). This is because the first author’s gender would simply be an imperfect correlate of the true causal effect, while the last author’s gender would be the causal effect itself.
To test whether α′ for last authors tends to be higher than α′ for first authors for any given dataset, we used a linear mixed model implemented in the lme4 and lmerTest packages for R, with authorship position (first or last) as a fixed factor, and journal and research discipline as crossed random effects. The response variable was α′, and we weighted each observation by the inverse of the standard error from our estimate of α′, meaning that more accurate measurements of α′ had more influence on the results. We used a similar model to test for a difference in α′ between the 2005-6 and the 2015-16 datasets, with two differences: we fit year range as a two-level fixed factor (instead of authorship position), and we used α′ estimated for all authors (not first/last authors) as the response variable.
The relationship between the gender ratio of authors publishing in a journal and its α′ value appeared nonlinear (S4 Fig). We therefore fit a generalised additive model with thin plate regression spline smoothing, implemented using the mgcv package for R.
To model the relationship between α′ and the number of authors on the paper, we used a meta-regression model implemented in the R package brms [75]. The model incorporated the standard error associated with each estimate of α′, had author number as a fixed effect, and journal as a random intercept (to control for repeated measures of each journal). We also fit a random slope of author number within journal, thereby allowing the response to author number to vary between journals. We used the default (weak) priors. The full output of this model can be viewed in the Online Supplementary Material.
Theoretical expectations for α when the gender ratio differs between career stages
In most STEMM disciplines, the gender ratio is more skewed among established researchers relative to early-career researchers, due both to women leaving STEMM careers at greater rates (the ‘leaky pipeline’), and to historical shortages of women studying STEMM subjects at university (‘demographic inertia’) [1, 5]. We hypothesised that this difference in gender ratio between career stages could potentially create both Wahlund effects and ‘reverse’ Wahlund effects. For example, imagine that the majority of collaborations in a particular field are between students and professors, and that the gender ratio differs between career stages: we would then see an excess of mixed-gender coauthorships (heterophily, α < 0), even if gender has no direct, causal effect on the choice of coauthors. Similarly, a hypothetical field in which students work only with students, and professors with professors, would have apparent gender homophily (α > 0).
We can think of no tractable method of controlling for this issue using our dataset, which contains no reliable information on career stage. Therefore, we instead decided to derive theoretical expectations for α when there is a difference in gender ratio across career stages, in order to determine if and how this effect should alter our inferences. For simplicity, our calculations assume there are only two career stages (‘early-career’ and ‘established’), though we expect that the general conclusions would also apply to a multi-tier career ladder. Under the null model that gender has no causal effect on collaboration, we calculated α for various combinations of the four free parameters in our simple model. These parameters are: the gender ratio among early-career researchers (x-axis of Fig 5), the gender ratio among established researchers (y-axis of Fig 5), the frequency of within- versus between career stage collaborator pairs (rows in Fig 5), and lastly the frequency of within-stage collaborations that are between two early-career researchers as opposed to two late-career researchers (columns in Fig 5). When these four parameters are specified, one can easily calculate the relative frequencies of collaborator pairs that involve two men, two women, or a man and a woman. In short, if we have specified the frequency of women at both career stages, as well as the frequency of the three possible types of collaboration with respect to career stage (early-early, early-established, and established-established), then we can calculate the frequency of collaborators pairs comprising two women, or a woman and a man, and thus calcualte α (see the Online Supplementary Material for the annotated R code).
Supporting information
Acknowledgments
We thank Devi Stuart-Fox and Dominique Potvin for their very helpful comments on the manuscript.
Data Availability
The raw input data from Holman et al. [5] is archived at https://osf.io/bt9ya/, and all the derived data are contained within the paper and its Supporting Information files. The R scripts used to produce all results, figures and tables are freely available at https://github.com/lukeholman/genderHomophily, and a report explaining this R code and its outputs can be viewed online at https://lukeholman.github.io/genderHomophily/.
Funding Statement
Funding was provided by Biotieteiden ja Ympäristön Tutkimuksen Toimikunta (252411 and 284666) to CM. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
References
- 1. Shaw AK, Stanton DE. Leaks in the pipeline: separating demographic inertia from ongoing gender differences in academia. Proceedings of the Royal Society of London B. 2012;272: 3736–3741. 10.1098/rspb.2012.0822 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 2. Larivière V, Ni C, Gingras Y, Cronin B, Sugimoto CR. Bibliometrics: global gender disparities in science. Nature. 2013;504: 211–213. 10.1038/504211a [DOI] [PubMed] [Google Scholar]
- 3. West JD, Jacquet J, King MM, Correll SJ, Bergstrom CT. The role of gender in scholarly authorship. PLoS ONE. 2013;8: e66212 10.1371/journal.pone.0066212 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 4.Elsevier Report. Gender in the global research landscape. elseviercom/research-intelligence/resource-library/gender-report. 2017.
- 5. Holman L, Stuart Fox D, Hauser CE. The gender gap in science: How long until women are equally represented? PLoS Biology. 2018;16: e2004956 10.1371/journal.pbio.2004956 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 6. Wutte M. Closing the gender gap. Nature. 2007;448: NJ101–NJ102. 10.1038/nj7149-101a [DOI] [Google Scholar]
- 7. Reuben E, Sapienza P, Zingales L. How stereotypes impair women’s careers in science. Proceedings of the National Academy of Sciences. 2014;111: 4403–4408. 10.1073/pnas.1314788111 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 8. Trower CA, Chait RP. Faculty diversity: Why women and minorities are underrepresented in the professoriate, and fresh ideas to induce needed reform. Harvard Magazine. 2002;104: 33–37. [Google Scholar]
- 9. Umbach PD. Gender equity in the academic labor market: An analysis of academic disciplines. Research in Higher Education. 2007;48: 169–192. 10.1007/s11162-006-9043-2 [DOI] [Google Scholar]
- 10. Hosek S, Cox AG, Ghosh-Dastidar B, Kofner A, Ramphal N, Scott J, et al. Gender differences in major federal external grant programs. RAND Corporation; 2005. [Google Scholar]
- 11. Pohlhaus JR, Jiang H, Wagner RM, Schaffer WT, Pinn VW. Sex differences in application, success, and funding rates for NIH extramural programs. Academic Medicine. 2011;86: 759 10.1097/ACM.0b013e31821836ff [DOI] [PMC free article] [PubMed] [Google Scholar]
- 12. Zuckerman H. Persistence and change in the careers of men and women scientists and engineers. National Academy Press. 1987; 127–156. [Google Scholar]
- 13.Rosenfeld RA. Outcome analysis of academic careers. Review prepared for the Office of Scientific and Engineering Personnel, National Research Council. 1991.
- 14. Long JS, Paul DA, Robert M. Rank advancement in academic careers: Sex differences and the effects of productivity. American Sociological Review. 1993; 703–722. 10.2307/2096282 [DOI] [Google Scholar]
- 15. Hopkins AL, Jawitz JW, McCarty C, Goldman A, Basu NB. Disparities in publication patterns by gender, race and ethnicity based on a survey of a random sample of authors. Scientometrics. 2013;96: 515–534. 10.1007/s11192-012-0893-4 [DOI] [Google Scholar]
- 16.O’Dorchai S, Meulders D, Crippa F, Margherita A. She figures 2009–Statistics and indicators on gender equality in science. Publications Office of the European Union. 2009.
- 17.Feldt B. The faculty cohort study: School of medicine. Ann Arbor, MI: Office of Affirmative Action. 1986.
- 18. Stack S. Gender, children and research productivity. Scientometrics. 2004;45: 891–920. [Google Scholar]
- 19. Larivière V, Vignola-Gagné E, Villeneuve C, Gélinas P, Gingras Y. Sex differences in research funding, productivity and impact: an analysis of Québec university professors. Scientometrics. 2011;87: 483–498. 10.1007/s11192-011-0369-y [DOI] [Google Scholar]
- 20. Moss-Racusin CA, Dovidio JF, Brescoll VL, Graham MJ, Handelsman J. Science faculty’s subtle gender biases favor male students. Proceedings of the National Academy of Sciences. 2012;109: 16474–16479. 10.1073/pnas.1211286109 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 21. Knobloch-Westerwick S, Glynn CJ, Huge M. Science faculty’s subtle gender biases favor male students. Science Communication. 2013;35: 603–625. [Google Scholar]
- 22. Lee S, Bozeman B. The impact of research collaboration on scientific productivity. Social Studies of Science. 2005;35: 673–702. 10.1177/0306312705052359 [DOI] [Google Scholar]
- 23. Wuchty S, Jones BF, Uzzi B. The increasing dominance of teams in production of knowledge. Science. 2007;316: 1036–1039. 10.1126/science.1136099 [DOI] [PubMed] [Google Scholar]
- 24. Abramo G, D’Angelo CA, Di Costa F. Research collaboration and productivity: is there correlation? Higher Education. 2009;57: 155–171. 10.1007/s10734-008-9139-z [DOI] [Google Scholar]
- 25. Larivière V, Gingras Y, Sugimoto CR, Tsou A. Team size matters: Collaboration and scientific impact since 1900. Journal of the Association for Information Science and Technology. 2015;66: 1323–1332. 10.1002/asi.23266 [DOI] [Google Scholar]
- 26. Long JS. Measures of sex differences in scientific productivity. Social Forces. 1992;71: 159–178. 10.2307/2579971 [DOI] [Google Scholar]
- 27. Bozeman B, Monica G. How do men and women differ in research collaborations? An analysis of the collaborative motives and strategies of academic researchers. Research Policy. 2011;40: 1393–1402. 10.1016/j.respol.2011.07.002 [DOI] [Google Scholar]
- 28. Abramo G, D’Angelo CA, Di Costa F. Gender differences in research collaboration. Journal of Informetrics. 2013;7: 811–822. 10.1016/j.joi.2013.07.002 [DOI] [Google Scholar]
- 29. Badar K, Hite JM, Badir YF. Examining the relationship of co-authorship network centrality and gender on academic research performance: The case of chemistry researchers in pakistan. Scientometrics. 2013;94: 755–775. 10.1007/s11192-012-0764-z [DOI] [Google Scholar]
- 30. Lewison G. The quantity and quality of female researchers: A bibliometric study of Iceland. Scientometrics. 2001;52: 29–43. 10.1023/A:1012794810883 [DOI] [Google Scholar]
- 31. Webster BM. Polish women in science: A bibliometric analysis of Polish science and its publications. Research Evaluation. 2001;10: 185–194. 10.3152/147154401781776999 [DOI] [Google Scholar]
- 32. Bozeman B, Corley E. Scientists’ collaboration strategies: implications for scientific and technical human capital. Research Policy. 2004;33: 599–616. 10.1016/j.respol.2004.01.008 [DOI] [Google Scholar]
- 33. Long JS. The origins of sex differences in science. Social Forces. 1990;68: 1297–1316. 10.1093/sf/68.4.1297 [DOI] [Google Scholar]
- 34. Fuchs S, Von Stebut J, Allmendinger J. Gender, science, and scientific organizations in Germany. Minerva. 2001;39: 175–201. 10.1023/A:1010380510013 [DOI] [PubMed] [Google Scholar]
- 35. Reskin BF. Scientific productivity, sex, and location in the institution of science. American Journal of Sociology. 1978;83: 1235–1243. 10.1086/226681 [DOI] [PubMed] [Google Scholar]
- 36. Wright AL, Schwindt LA, Bassford TL, Reyna VF, Shisslak Catherine M amd Germain PAS, Reed KL. Gender differences in academic advancement: Patterns, causes, and potential solutions in one U.S. college of medicine. Social Forces. 2003;68: 1297–1316. [DOI] [PubMed] [Google Scholar]
- 37. Bleidorn W, Arslan RC, Denissen JJ, Rentfrow PJ, Gebauer JE, Potter J, et al. Age and gender differences in self-esteem—a cross-cultural window. Journal of Personality and Social Psychology. 2016;111: 396 10.1037/pspp0000078 [DOI] [PubMed] [Google Scholar]
- 38. Jagsi R, Griffith KA, Jones R, Perumalswami CR, Ubel P, Stewart A. Sexual harassment and discrimination experiences of academic medical faculty. JAMA. 2016;315: 2120–2121. 10.1001/jama.2016.2188 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 39. Martin JL. Ten simple rules to achieve conference speaker gender balance. PLoS computational biology. 2014;10: e1003903 10.1371/journal.pcbi.1003903 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 40. Tower G, Julie P, Brenda R. A multidisciplinary study of gender-based research productivity in the world’s best journals. Journal of Diversity Management. 2007;2: 23–32. 10.19030/jdm.v2i4.5020 [DOI] [Google Scholar]
- 41. Jordan CE, Clark SJ, Vann CE. Do gender differences exist in the publication productivity of accounting faculty?. Journal of Applied Business Research. 2008;24: 77–85. [Google Scholar]
- 42. Britton DM. The epistemology of the gendered organization. Gender and Society. 2000;14: 418–434. 10.1177/089124300014003004 [DOI] [Google Scholar]
- 43. Reagans R, Zuckerman EW. Networks, diversity, and productivity: The social capital of corporate R&D teams. Organization Science. 2001;12: 502–517. 10.1287/orsc.12.4.502.10637 [DOI] [Google Scholar]
- 44. Hong L, Page SE. Groups of diverse problem solvers can outperform groups of high-ability problem solvers. Proceedings of the National Academy of Sciences. 2004;101: 16385–16389. 10.1073/pnas.0403723101 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 45. Whittington KB, Smith-Doerr L. Women inventors in context: Disparities in patenting across academia and industry. Gender & Society. 2008;22: 194–218. 10.1177/0891243207313928 [DOI] [Google Scholar]
- 46. Bear JB, Woolley AW. The role of gender in team collaboration and performance. Interdisciplinary Science Reviews. 2011;36: 46–153. 10.1179/030801811X13013181961473 [DOI] [Google Scholar]
- 47. Herrera R, Duncan PA, Green MT, Skaggs SL. The effect of gender on leadership and culture. Global Business and Organizational Excellence. 2012;31: 37–48. 10.1002/joe.21413 [DOI] [Google Scholar]
- 48. Campbell LG, Mehtani S, Dozier ME, Rinehart J. Gender-heterogeneous working groups produce higher quality science. PloS ONE. 2013; e79147 10.1371/journal.pone.0079147 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 49. Ferber MA, Teiman M. Are women economists at a disadvantage in publishing journal articles? Eastern Economic Journal. 1980;6: 1189–193. [Google Scholar]
- 50. McDowell JM, Smith JK. The effect of gender-sorting on propensity to coauthor: Implications for academic promotion. Economic Inquiry. 1992;30: 68–82. 10.1111/j.1465-7295.1992.tb01536.x [DOI] [Google Scholar]
- 51. Ghiasi G, Larivière V, Sugimoto CR. On the compliance of women engineers with a gendered scientific system. PloS ONE. 2015;10: e0145931 10.1371/journal.pone.0145931 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 52. Crow MS, Smykla JO. An examination of author characteristics in national and regional criminology and criminal justice journals, 2008-2010: Are female scholars changing the nature of publishing in criminology and criminal justice? American Journal of Criminal Justice. 2015;40: 441–455. 10.1007/s12103-014-9250-x [DOI] [Google Scholar]
- 53. Fahmy C, Young JT. Gender inequality and knowledge production in criminology and criminal justice. Journal of Criminal Justice Education. 2017;28: 285–305. 10.1080/10511253.2016.1233346 [DOI] [Google Scholar]
- 54. Zettler HR, Cardwell Stephanie M, Jessica MC. The gendering effects of co-authorship in criminology & criminal justice research. Criminal Justice Studies. 2017;30: 30–44. 10.1080/1478601X.2016.1265958 [DOI] [Google Scholar]
- 55. Jadidi M, Karimi F, Lietz H, Wagner C. Gender disparities in science? Dropout, productivity, collaborations and success of male and female computer scientists. Advances in Complex Systems. 2017; 1750011. [Google Scholar]
- 56. Teele DL, Kathleen T. Gender in the journals: Publication patterns in political science. PS: Political Science & Politics. 2017;50: 433–447. [Google Scholar]
- 57. Araújo T, Elsa F. The specific shapes of gender imbalance in scientific authorships: a network approach. Journal of Informetrics. 2017;11: 88–102. 10.1016/j.joi.2016.11.002 [DOI] [Google Scholar]
- 58.Araújo T, Elsa F. Big Missing Data: are scientific memes inherited differently from gendered authorship? arXiv preprint arXiv. 2017; 1706.05156.
- 59. Wahlund S. Zusammensetzung von populationen und korrelationserscheinungen vom standpunkt der vererbungslehre aus betrachtet. Hereditas. 1928;11: 65–106. 10.1111/j.1601-5223.1928.tb02483.x [DOI] [Google Scholar]
- 60.Bergstrom T, Bergstrom C, King M, Jacquet J, West J, Correll S. A note on measuring gender homophily among scholarly authors. 2016.
- 61. Macaluso B, Larivière V, Sugimoto T, Sugimoto CR. Is science built on the shoulders of women? A study of gender differences in contributorship. Academic Medicine. 2016;91: 1136–1142. 10.1097/ACM.0000000000001261 [DOI] [PubMed] [Google Scholar]
- 62.Bentley JT, Adamson R. Gender differences in the careers of academic scientists and engineers: A literature review. Special Report. 2003.
- 63. Long MT, Leszczynski A, Thompson KD, Wasan SK, Calderwood AH. Female authorship in major academic gastroenterology journals: A look over 20 years. Gastrointestinal Endoscopy. 2015;81: 1440–1447. 10.1016/j.gie.2015.01.032 [DOI] [PubMed] [Google Scholar]
- 64. Bendels MH, Bauer J, Schöffel N, Groneberg DA. The gender gap in schizophrenia research. Schizophrenia Research. 2018;193: 445–446. 10.1016/j.schres.2017.06.019 [DOI] [PubMed] [Google Scholar]
- 65. McKenzie K, Ramonas M, Patlas M, Katz DS. Assessing the gap in female authorship in the journal emergency radiology: Trends over a 20-year period. Emergency Radiology. 2017;24: 641–644. 10.1007/s10140-017-1510-x [DOI] [PubMed] [Google Scholar]
- 66. Sheltzer JM, Smith JC. Elite male faculty in the life sciences employ fewer women. Proceedings of the National Academy of Sciences. 2014;111: 10107–10112. 10.1073/pnas.1403334111 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 67. Garfield E. The history and meaning of the journal impact factor. JAMA. 2006;295: 90–93. 10.1001/jama.295.1.90 [DOI] [PubMed] [Google Scholar]
- 68. Nittrouer CL, Hebl MR, Ashburn-Nardo L, Trump-Steele RC, Lane DM, Valian V. Gender disparities in colloquium speakers at top universities. Proceedings of the National Academy of Sciences. 2018;115: 104–108. 10.1073/pnas.1708414115 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 69. Débarre F, Rode N, Ugelvig L. Gender equity at scientific events. Evolution Letters. 2018;in press. 10.1002/evl3.49 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 70. Wright S. The genetical structure of populations. Annals of Human Genetics. 1949;15: 323–354. [DOI] [PubMed] [Google Scholar]
- 71.Wang YS, Erosheva EA. On the relationship between set-based and network-based measures of gender homophily in scholarly publications. arXiv preprint arXiv:161009026. 2016.
- 72. Benjamini Y, Hochberg Y. Controlling the false discovery rate: a practical and powerful approach to multiple testing. Journal of the Royal Statistical Society: Series B. 1995; 289–300. [Google Scholar]
- 73. Bonham KS, Stefan MI. Women are underrepresented in computational biology: An analysis of the scholarly literature in biology, computer science and computational biology. PLoS Computational Biology. 2017;13: e1005134 10.1371/journal.pcbi.1005134 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 74. Wren JD, Kozak KZ, Johnson KR, Deakyne SJ, Schilling LM, Dellavalle RP. The write position: A survey of perceived contributions to papers based on byline position and number of authors. EMBO reports. 2007;8: 988–991. 10.1038/sj.embor.7401095 [DOI] [PMC free article] [PubMed] [Google Scholar]
- 75. Bürkner P-C. brms: An R package for Bayesian multilevel models using Stan. Journal of Statistical Software. 2016;80: 1–28. [Google Scholar]
Associated Data
This section collects any data citations, data availability statements, or supplementary materials included in this article.
Supplementary Materials
Data Availability Statement
The raw input data from Holman et al. [5] is archived at https://osf.io/bt9ya/, and all the derived data are contained within the paper and its Supporting Information files. The R scripts used to produce all results, figures and tables are freely available at https://github.com/lukeholman/genderHomophily, and a report explaining this R code and its outputs can be viewed online at https://lukeholman.github.io/genderHomophily/.