Cumulative Advantage of Brokerage in Academia

Abstract

Science is a collaborative endeavor in which "who collaborates with whom" profoundly influences scientists' career trajectories and success. Despite its relevance, little is known about how scholars facilitate new collaborations among their peers. In this study, we quantify brokerage in academia and study its effect on the careers of physicists worldwide. We find that early-career participation in brokerage increases later-stage involvement for all researchers, with increasing participation rates and greater career impact among more successful scientists. This cumulative advantage process suggests that brokerage contributes to the unequal distribution of success in academia. Surprisingly, this affects both women and men equally, despite women being more junior in all brokerage roles and lagging behind men's participation due to their late and slow arrival to physics. Because of its cumulative nature, promoting brokerage opportunities to early career scientists might help reduce the inequalities in academic success.

Figures (18)

• Figure 1: Brokerage in academic collaborations. Joint publications among three authors $a$, $b$ and $c$ create links in the collaboration network at the time of their first publication (solid, curved arcs with an aggregated view at the bottom). We consider the collaboration between $a$ and $c$ at time $t_{ac}$, with or without $b$, as the tertius iungensobstfeld_socialnetworkstertius_2005 brokerage event between $a$, $b$ and $c$. At this point, the broker $b$ has collaborated separately with $a$ at $t_{ab}$ and $c$ at $t_{bc}$ before this joint publication. Repeated collaborations (dashed gray arcs) are disregarded in determining the brokerage event between the three co-authors.
• Figure 2: Skewed career lengths and academic impact. (A) The distribution of career lengths, as measured by the years between the first and last publication. To account for variations in career lengths, we partition this distribution into five percentile-based bins of decreasing size which we refer to as career stages $s_0$ to $s_4$ (color shades, sizes on top). (B) Throughout these stages, scientists publish papers and may participate in brokerage multiple times in varying roles (as $a$, $b$, or $c$; see \ref{['fig:01-01_fig1']}). We count their brokerage participation at each completed stage $s_i$ as $B(s_i)$. For example, both Alice and Bob participated once in their first career stage, $B(s_0) = 1$. (C--D) The distribution of academic impact by the end of a career is measured by the total number of received citations and publications. To compare scientists by their career impact, we place them in an impact group $Q_0$ to $Q_4$. As with the career stages, we partition the impact distributions using the same five percentile-based bins (color shades). For example, Alice achieved $Q_2$ in productivity (D) with a total of seven articles (circles in her timeline in B), while Bob achieved $Q_3$ with eleven publications. Overall, the vast majority of scientists leave academia early and achieve a lower impact in their scientific careers. A small fraction, however, stay longer and achieve significant success. Citation counts were increased by 1 only for the logarithmic scale visualization without affecting the actual percentile binning.
• Figure 3: Brokerage frequency and academic impact. We measure academic impact separately for two metrics: (A) the total number of received citations and (B) the total number of publications. We compare the brokerage participation $B_m(s_i)$ of scientists in impact group $Q_m$ to those that achieve the next impact level $Q_{m+1}$ (increasing color intensity) along career stages $s_i$ (x-axis). The cumulative distributions of brokerage for two different impact groups at stage $s_3$ are shown on the right. Each marker on the left shows the probability $P(B_{m+1} > B_m)$ that a scientist from group $Q_{m+1}$ has a higher brokerage frequency than a scientist from group $Q_m$. Error bars indicate bootstrapped $95\%$-confidence intervals, and all visible results are statistically significant ($p<0.05$, see \ref{['sec:methods']}). Almost all comparisons are above the neutral line, showing a positive relation between participation in brokerage and eventual success across all career stages. Scientists who eventually reach higher success levels engage in brokerage more frequently across all career stages. While this effect remains positive but roughly constant for the least successful scientists, it increases for the most successful ones over their careers. Comparing the two most successful groups ($Q_3 \leftrightarrow Q_4$), small differences in early careers ($s_0$) snowball later on ($s_3$), hinting at a cumulative nature of brokerage.
• Figure 4: Cumulative advantage in brokerage. (A) Brokerage rate changes across consecutive career stages. Each marker shows the probability $P(R_{s+1} > R_s)$ that a scientist of impact group $Q_m$ has a higher brokerage count per year at stage $s+1$ compared to the earlier stage $s$. Statistical test and uncertainty estimations are the same as in \ref{['fig:03_bf_success']}. We find that the rates increase with each career stage for the most successful scientists, indicating that they not only accumulate more brokerage but also do so at increasing rates. A consistent speed-up is also unique to them, given that less successful groups show a significant slow-down of brokerage throughout many career stages, especially in productivity. The cumulative distributions of brokerage rates for $Q_4$ at stage $s_1$ and $s_2$ are shown on the right. (B) The cumulative nature of brokerage rates, as measured by a positive correlation of individuals' rates between two consecutive career stages $s_i$ and $s_{i+1}$. Scientists with a higher brokerage rate in one stage tend to have a higher rate in the next stage and vice versa. This correlation is also stronger for more successful researchers, indicating that the cumulative nature of brokerage is more pronounced for them. The rank correlation between brokerage rates at stages $s_2$ and $s_3$ of scientists in productivity $Q_4$ is shown by the joint PDF on the right.
• Figure 5: Gender disparities in brokerage participation. (A) The number of active female and male authors per year shows the under-representation of women in physics. (B) Blue dots represent all-men brokerage event counts, and red dots represent all-women events. Light blue dots indicate events with two men and one woman, and light red dots indicate events with two women and one man. Stars mark the first-ever occasion of a given type of gendered brokerage. We see that all-women brokerage started appearing roughly 80 years after the first women joined physics. (C) The probability of a broker being a woman (w) or a man (m) given the gender of co-authors $a$ and $c$ (columns). Men are much more likely to be brokers. Women are less likely to be brokers if $a$ or $c$ are men. (D) Women usually serve as brokers earlier in their careers, while men typically do so at more senior levels. (E) Comparison of joint career stage distributions of authors $c$ (x-axis) and $a$ (y-axis). We divide the distribution of a given gender composition (columns) by the distribution over all brokerage events, regardless of gender (the case where both are female is shown in the left inset). Values over 1 (green) indicate an over-representation of the respective gender-seniority combination. Values below 1 (purple) mean under-representation. We find that the differences in representation depend on the roles in which women participate. Whenever $a$ or $c$ are female, there is an under-representation in the respective senior career stages (rows for $a$ and columns for $c$ in the three left-most panels). When both $c$ and $a$ are male, their distribution is similar to the overall distribution, as they contribute the highest group size (the right-most panel in E).