The role of mentorship in protégé performance

Abstract

The role of mentorship in protégé performance is a matter of importance to academic, business and governmental organizations. Although the benefits of mentorship for protégés, mentors and their organizations are apparent, the extent to which protégés mimic their mentors' career choices and acquire their mentorship skills is unclear. The importance of a science, technology, engineering and mathematics workforce to economic growth and the role of effective mentorship in maintaining a 'healthy' such workforce demand the study of the role of mentorship in academia. Here we investigate one aspect of mentor emulation by studying mentorship fecundity-the number of protégés a mentor trains-using data from the Mathematics Genealogy Project, which tracks the mentorship record of thousands of mathematicians over several centuries. We demonstrate that fecundity among academic mathematicians is correlated with other measures of academic success. We also find that the average fecundity of mentors remains stable over 60 years of recorded mentorship. We further discover three significant correlations in mentorship fecundity. First, mentors with low mentorship fecundities train protégés that go on to have mentorship fecundities 37% higher than expected. Second, in the first third of their careers, mentors with high fecundities train protégés that go on to have fecundities 29% higher than expected. Finally, in the last third of their careers, mentors with high fecundities train protégés that go on to have fecundities 31% lower than expected.

Figure 1 |. Relationship between mentorship fecundity and other performance metrics.

a, Cumulative distribution of the mentorship fecundity for NAS members (red) and non-NAS members (black). NAS members have an average fecundity of ${\langle k\rangle }_{\text{NAS}}=14$, which is far greater than the average fecundity of non-NAS members, ${\langle k\rangle }_{\text{non-NAS}}=3.1$, indicating that fecundity is closely related to academic recognition. Not all mathematicians in the non-NAS group were eligible for NAS membership, owing to citizenship and other circumstances. This fact makes the result in the figure all the more striking. b, Average number of publications as a function of the mentorship fecundity, for NAS members (red) and non-NAS members (black). NAS members have nearly twice as many publications on average as non-NAS members for all fecundity levels. Error bars, 1 s.e.

Figure 2 |. Evolution of the fecundity distribution.

A–c, Cumulative distribution of the fecundity of mathematicians that graduated during 1910 (a), 1930 (b) and 1950 (c) (symbols), compared with the best-estimate predictions of a mixture of two discrete exponentials (lines). Monte Carlo hypothesis testing confirms that this model can not be rejected as a model of the fecundity distribution during every year from 1900–1960, as denoted by the P values above the α = 0.05 significance level (Methods). d–f, Best-estimate parameters as functions of time, calculated by maximum likelihood for a mixture of two discrete exponentials. Dashed lines denote average parameter values between 1900 and 1960 and coloured circles indicate the years displayed in panels a–c. The probability, π_h, of being a ‘have’ changes over time, generally in relation to historic events (hashed grey shading indicates the First and Second World Wars). In contrast, the average fecundities remain stable, with time-average values of ${\overline{\kappa }}_{\text{h}}=9.8\pm 0.4$ and ${\overline{\kappa }}_{\text{hn}}=0.47\pm 0.03$, until 1960, the time at which mentorship records become incomplete (Methods), and then steadily decrease (grey shaded region).

Figure 3 |. Branching process null models.

a, Subset of the mathematician genealogy network. Mentors/parents (black circles) are connected to each of their protégés/children (white circles). The horizontal positions of mathematicians represent their graduation/birth dates, t. The bottom two parents were born in 1924, the top two parents were born in 1937, and all four parents have a child born in 1958. From a parent’s perspective, three essential features of the empirical network must be preserved in random networks generated from the two branching process null models: the birth date, t_p, the fecundity, k_p, and the chronology of child births, {t_c}. b, Random networks from ensemble I preserve these three essential features. Solid red lines highlight the links in the empirical network whose end points can be randomized. Dashed red lines illustrate one of the possible randomization moves after switching the corresponding pair of links. We note that the age difference between parent and child is not preserved. c, Random networks from ensemble II preserve the three essential features as well as the age difference between parent and child. Solid blue lines of the same colour highlight the links in the empirical network whose end points can be randomized. Dashed blue lines illustrate one of the possible randomization moves after switching the corresponding pair of links. Random networks for each ensemble are generated by attempting 100 switches per link (Methods).

Figure 4 |. Effect of age difference between mentor and protégé, t_c − t_p, on protégé fecundity.

a, Fecundity distribution of children born during the 1910s (for which the average fecundity was 1.4) to parents with k_p < 3, 3 ≤ k_p < 10 and k_p ≥ 10, compared with the expectation from ensemble I (grey line). We separate children into terciles (early, middle, late) according to t_c − t_p, and denote the average fecundities of the children born early, middle and late in their parents’ lives as $\langle k_{\text{E}}\rangle$, $\langle k_{\text{M}}\rangle$ and $\langle k_{\text{L}}\rangle$, respectively. The average fecundity of children born to parents with k_p < 3 is higher than expected, regardless of whether they were born during the early, middle or later part of their parents’ lives. We also note that the average fecundity of children born to parents with k_p ≥ 10 decreases throughout their parents’ lives. b, We quantify the significance of these trends during each decade (coloured symbols) by computing the z-score of the average child fecundity, $\langle k_c\rangle$, compared with the average child fecundity in networks from ensemble I. This information is summarized by identifying the linear regression (solid black line; slope and intercept as shown). The regression lines for networks from our null model (grey lines) vary around the expectation of our null model (dashed black line). c, Significance of linear regressions in b. We compare the slope and intercept of the empirical regression (black circle) with the distribution of the slope and intercept of the same quantities computed from the null model. Because these quantities are approximately distributed as a multivariate Gaussian, we compute the equivalent of a two-tailed P value by finding the fraction of synthetically generated slope–intercept pairs that lie outside the equiprobability surface of the multivariate Gaussian (dashed ellipse). The slopes and intercepts of the regressions for children of parents with low (P = 0.009) and high (P < 0.001) fecundities are significantly different from the expectations for the null model, consistent with the data displayed in a. Comparisons with expectations from random networks from ensemble II yield the same conclusions (Supplementary Fig. 4).