We first focus on research resource requirements. As mentioned earlier, the typical annual research expenditures per faculty member differ substantially across the seven disciplines. For example, industrial engineering faculty tend, for the most part, to train a small number of students at a time. Additionally, much of the research in industrial engineering is theoretical or computational in nature. These two characteristics suggest that, for industrial engineering, researchers do not need to compete against each other for limited resources, and institutional support may not be as important a factor in faculty productivity.
In contrast, most faculty in molecular biology conduct experimental research, and many require significant lab space and expensive specialized equipment. Moreover, faculty in molecular biology are able to compete for funding supporting the creation of large centers or the acquisition of major equipment. Thus, availability of resources, especially institutionally granted resources or institutional support for securing large grants, can be crucial components of academic success in molecular biology 
. Furthermore, consistent with the Matthew effect 
, researchers who have already received more institutional support are able to secure even more research resources.
Since historically female faculty members have received less institutional support and have had less access to research resources 
, these considerations prompt a question with significant policy implications: Could the differences in resource requirements lead to distinct gender-specific publication patterns across disciplines? In order to answer this question, we systematically investigated gender-specific publication rates for the seven disciplines. Even though several studies report greater publication rates by male authors 
, we hypothesize that only in disciplines where resource requirements are high and institutional support is vital will female faculty members typically publish fewer papers than their male peers. Thus, we predict that gender differences in publication rate in disciplines such as industrial engineering are going to be quite low. In contrast, we predict that gender differences in publication rate are going to be very significant in molecular biology and similar disciplines.
We define the publication rate of a faculty member
years into her/his career as the number of scientific articles published by the individual
years after her/his first publication. We cannot simply compare the raw publication numbers per year, because these numbers depend strongly on publication year
and career stage
denote the number of publications published by author
, and let
be the total number of authors that have started their careers no later than year
. We calculate author
’s z-score (standard score) in year
is the average number of publications per author from discipline
published in year
is the standard deviation of the number of papers per author published in year
Average number of annual publications per author.
In order to account for the effect of career stage, we consider
, which is the z-score of author
as a function of the career stage
is the year of the first publication of author
(, S10). Please note that by considering the z-score we are not making any assumption about normality of
, but merely making the results easier to compare across disciplines and time periods.
Gender difference in publication rate.
Our analysis fully confirms our hypothesis (, , ). As predicted, for disciplines where research expenditures are high, such as molecular biology, we found that females consistently publish at a rate significantly lower than males, whereas for industrial engineering we do not observe a significant difference between genders. More importantly, as shown in , we found that the gender difference in publication rate, measured as the average z-score of females, has a significant negative correlation with magnitude of typical research expenditures. Our results thus support the hypothesis that gender differences in institutional support have had a crucial effect on the publication rates of females.
Lower publication rates of female faculty is correlated with higher requirements for research resources.
It is important to point out that in our analysis we did not consider human and social capital such as collaboration level and leadership position, which may also have critical roles for a productive career 
, as research resources. Whether and how the gender difference in the ability to acquire these resources harder to quantify affects career productivity is a matter worth of further investigation.
We next investigated gender-specific and discipline-specific effects of career relative risk profile of an academic career on publication patterns. The risk to pursue a faculty position after obtaining a Ph.D. varies across disciplines. A graduate student considering an academic career in chemistry faces a small risk if unsuccessful. Within about six years from publication of their first paper, successful individuals will move into independent positions (, S11, S12 and Methods). Doctoral degree holders in chemistry unable or uninterested in obtaining academic positions can chose from among a number of high-paying careers in industry and government.
In contrast, an individual considering an academic career in ecology faces a much more uncertain future. Instead of waiting six years post publication of the first paper to learn whether it will be possible to secure a faculty position, an ecologist has to wait an average of eight years (, S11, S12, ). Perhaps even more challenging, doctoral degree holders in ecology who are not able or not interested in obtaining academic positions may have to settle for jobs that do not pay a significant premium over academic positions.
These observations raise a critical question: Could the different risk profiles of STEM disciplines lead to distinct gender-specific selective pressures? Because pursuing an academic career is a risky undertaking and because propensity towards risk-taking 
, self-motivation towards career development 
, social expectations 
, perception of gender stereotypes 
and biological constraints 
are different for females and males, we surmise that a female will choose to pursue an academic career in “high-risk” disciplines, such as ecology, only if she is so highly qualified that she will be quite confident of success. This biased self-selection for outstanding individuals among females likely happens prior to embarking on an academic career 
, leading to females’ advantage in career performance that would be magnified in later stages of career due to the Matthew effect 
. In contrast, because of the low risk profile of chemistry, we expect that female faculty members in chemistry will incur no extra burden when compared to their male colleagues. It is worth mentioning that an alternative hypothesis is that high career risk induces selection for individuals with greater propensity to risk-taking among females. However, this is consistent with our hypothesis, since risk-taking might be a necessary ingredient, among other intellectual abilities, towards success, and individuals may augment their competence through risk-taking. Therefore, females who enter disciplines with high career risks may be not only risk-takers but in fact also highly qualified.
We further hypothesize that the higher qualification of females in high-risk disciplines will become apparent through higher impact per publication. In order to uncover gender differences in publication impact, we studied a commonly used metric of academic performance, the
. We studied the
-index instead of the total number or average number of citations because the distributions of these numbers can be dramatically biased by a single highly-cited publication 
-index avoids this bias by identifying the number of publications of an author that have at least that number of citations. Moreover, because the
-index was introduced after the time period considered for the data, it will not be affected by behaviors of the authors aimed at deliberately increasing their
An identified weakness of the
-index is its dependence on the number of publications. In order to compare the publication impact of authors with different number of publications, we determined the dependence of the
-index on the number of publications for the faculty cohorts in the seven disciplines considered. We found that for these seven disciplines the
-index grows with the number of publications as a power law 
is the number of publications ( and Methods). For
-index would grow linearly with number of publications. Importantly, since we find
, one cannot explain the observed values of
through self-citations alone (Methods).
Relation between impact and number of publications.
We next measured the deviations of h
-indices from the trend predicted by Eq. (4) for individual faculty members to obtain the z-scores (standard score) of their publication impact (). Let
denote the h
-index of author
her/his total number of publication. The z-score of h
-index of author is
Comparison of publication impact for authors with different numbers of publications.
We then calculated the average z-scores of this publication adjusted
-index of females (, S4
and Methods). Our analysis unambiguously shows that for all ranges of number of publications, female faculty members in ecology published research with higher impact than their male counterparts, whereas for faculty in chemistry we found no significant gender-specific differences in impact.
The data in suggest that the difference
in publication impact may be an increasing function of the discipline-specific risk profile
associated with an academic career. That is,
While we lack a theory for the true definition of career risk,
, it is plausible that it will be a function of factors such as the time
to reach career independence, the fraction
of Ph.D. graduates that go on to careers in academia, and the reciprocal of the salary premium of non-academic careers (, 
), which we define as
Even though we do not know its functional form, we can expand
as a multivariate polynomial,
and it follows that we can expand
Because we only have
data points, we must fit our data to combinations of at most
terms in the expansion. Ordinary least squares regression indicates that the difference in publication impact across the seven disciplines is positively correlated with several combinations of the factors in Eq. (9), thus confirming the existence of the relative risk associated with academic careers and its gender-specific role on publication impact (). In we show the correlation between the gender difference in publication impact and the academic career risk, quantified as
Linear models predicting the gender difference in publication impact.
Higher publication impact of female faculty is correlated with higher relative risk of academic career choice.
This model suggests that in disciplines where there are few non-academic career options available and the time to reach career independence is long, and where it is difficulty to recover salary loss due to unsuccessful academic career, pursuing an academic position is highly risky.