Changing the balance of males and females in biology


In most universities, undergraduate biology is a female dominated subject. At graduate school, roughly half of PhD students are men and half are women. But further on in the academic career the proportion of females starts to drop off. In biology-related fields, 38% of postdocs are women, dropping to 26% at assistant professor and 18% for full professors. Where does this change come from?


A recent study by Sheltzer & Smith identified recruitment at postdoc level to be a major factor in the decline. Male lab leaders were more likely than female lab leaders to have other men working in their labs. Specifically, male lab leaders had around 36% female postdocs in their labs, compared to 46% for female lab leaders. There was also a small, but significant difference between ‘elite’ and ‘normal’ labs. Elite labs are those where the leader has won a prestigious prize or funding, or become a member of the National Academy of Sciences. The researchers found that in male elite labs only 31% of Postdocs were female, compared to 37% in normal labs. These statistics are shown below.

Gender composition of biology laboratories in the United States. Data adapted from figure 1 of Sheltzer & Smith (2014)


The difference between elite and normal labs may seem small, and there are over 3 times as many non-elite labs in the USA than elite labs. However, once we take in to account the power of an elite lab's name on a CV this difference is enhanced. Sheltzer & Smith found that elite labs produced 4 to 6 times as many faculty members as normal labs. So the next generation of professors is disproportionally selected from elite labs, which in turn are male dominated. Since these male postdocs then go on to recruit their own postdocs, a feedback is generated whereby male elite labs heavily influence the gender balance in Universities. The question is what the consequence of that feedback will be for the gender balance in biology departments?


To quantify the importance of male elite labs we created a simulation of the Postdoc-Professor demography, using the data collected by Sheltzer & Smith. We started with an equal balance of males and females across all labs, with 3.4 times as many normal labs than elite labs (again taken from their data). We assumed that elite labs were able to offer 3 times as many postdoc positions as normal labs, due to better availability of funding. Then on each ‘generation’ (5 year period) we assigned finishing PhD students to Postdoc positions, using the frequencies given above. For example, the probability that a female is recruited to an elite lab with a male leader is 31%, while the probability a male is recruited is 69%. We then took the postdocs from the previous generation and hired them to professor positions that became available through retirement (one in six of the current professors retired each generation). We assumed that individual men and women were equally likely to be recruited to these positions, but success depended strongly on where they had done their postdoc. Those who had done their postdoc in an elite lab had 4 times the chance of being recruited. Both elite and normal universities used the same recruitment policy.

Change in gender ratio in the model

Running this simulation and displaying the results above, we can see how the current ratio of males to females in biology professor positions in the USA should change over time. First the good news. If the postdoc stage is the only point at which women drop out of an academic career, i.e. there is no discrimination in the hiring process at professor level, then we expect the gender balance to go from its current level of 4:1 (in elite groups) to 1.67:1. This will take about 100 years, but the trend is in the right direction.


The rest is just bad news. The ratio of 1.67:1 is stable. This means that even if we started with a 1:1 gender ratio today then we would expect 63% men and 37% women to be employed as biology professors in the future. Since the model assumes that the only place at which females drop off is at the postdoc level, this estimate is very conservative. Sheltzer & Smith have already shown that elite male labs employ fewer female PhD students. Other studies have shown that the path in to a PhD is harder for women. Less is known about how the path to elite status is helped by being a male professor, but it is hard to see how the sort of closed circles of decision-making within national science academies and prize committees can favour gender equality. 1.67:1 is a best case scenario.


What can we do to reduce inequality? We can think about this with use of the following equation, derived from our model, for the Male:Female ratio
R = \frac{(1-0.46)(1+E)}{0.37+0.31E}
The numbers here, 0.46, 0.37 and 0.31 come from the postdoc recruitment frequencies discussed above. The only unknown parameter here is $E$, which we call the elite factor. It is the total contribution that elite labs make to professor positions. It can be calculated by multiplying the average number of postdoc positions available in elite labs (3) by the increased chance of being recruited if you worked in an elite lab (4) and dividing by the ratio of normal to elite labs (3.4). The numbers in brackets are those we used in the simulation above, and give

R=\frac{(1-0.46)(1+3.52)}{0.37+0.31 \times 3.52}=1.67

which is the ratio we found in the simulation. 67% more males the females at professor level.


Our equation now allows us to investigate how certain policies might change the male:female ratio. For example, if we could somehow change recruitment policy at elite male labs so that 50% of recruits are female then,

R=\frac{(1-0.46)(1+3.52)}{0.37+0.5 \times 3.52}=1.14

making a dramatic difference to the male:female ratio. On the other hand, if we changed the policy only at non-elite labs, then we would have

R=\frac{(1-0.46)(1+3.52)}{0.5+0.31 \times 3.52}=1.53

Much the same as the original value of 1.67. In conclusion, if we want to radically change the gender balance in biology faculties, we should focus on postdocs at elite groups. Elite groups are smaller in number, and only marginally more prone to recruiting males over females compared to non-elites, but disproportionally important in creating gender differences later on.


We should always be sceptical about parameter values in a model like this. While the recruitment proportions are measured in the Sheltzer & Smith study, our calculation of the elite factor is more open to question. Sheltzer & Smith did not report how many more postdoc positions are available in elite labs, nor could they provide completely reliable estimates of how much more likely a postdoc from an elite lab is to be recruited. The figure below shows how elite factor effects the ratio of male:female professors. This effect is rather small, indicating that the gender bias is not caused simply by the existence of elite research groups. The division of research in to elite and non-elite environments does not in itself lead to biased gender ratios.

Role of elite factor on male:female ratio

In summary, reducing the gap between elite and normal labs will not in itself greatly alter the gender bias. Instead, the male:female ratio at professor level can be reduced by focussing efforts on equality at postdoc level in elite research labs. We should ensure that women postdocs are equally recruited and supported in elite labs. Since elite labs feed the majority of professor positions then, assuming there is no gender bias in the professorial recruitment process, this can produce a more rapid change toward gender equality.


Reference: Sheltzer, J. M., & Smith, J. C. (2014). Elite male faculty in the life sciences employ fewer women. Proceedings of the National Academy of Sciences, 111(28), 10107-10112.


Matlab Code: simulation and analysis