Blute Blog

As described previously, Malgrem et. al. (gated) found that mentors with low fecundity (< 3) train protégés that go on to have fecundities 37% higher than expected throughout their careers – what I interpreted as a trade-off of quantity for quality of protégés, with the latter yielding more grand-offspring.

The fecundity of the protégés of these low fecundity mentors appears to increase across their careers (while always remaining higher than expected) while that of high fecundity mentors (> 10) decreases (crossing from above to below expected). In the first third of their careers, the high fecundity mentors go on to have protégés with fecundities 29% higher than expected, while in the last third of their careers, these mentors go on to have protégés with fecundities 31% lower than expected.

Some such shifts might be explained by different initial conditions combined with adaptive phenotypic plasticity. The low fecundity mentors might be so because they are working in a crowded field and so produce high quality protégés. These protégés too then are born in a crowded field and so are initially somewhat low fecundity themselves, but as their career progresses, this combination of low fecundities causes the number of competitors to shrink, and if the protégés are adaptively plastic, they increase the number of their protégés as time goes on. By contrast, high fecundity mentors might be so because they are working in an uncrowded field and so produce many protégés. These protégés too then are born in an uncrowded field and so are initially high fecundity themselves, but as their career progresses, this combination of high fecundities causes the number of competitors to grow, and if the protégés are adaptively plastic, they switch to quality decreasing their numbers of protégés as time goes on.

In any event, for mentors apparently it is not necessarily good to be highly fecund because there is a cost in quality and therefore in grand-offspring. However, given that one is going to be highly fecund, it is better to be so earlier rather than later in one’s career. On the other hand, if one’s goal is the quality of mentorship provided, perhaps later is O.K. There are lessons for graduate students here as well (if the results are generalizable beyond mathematics). You could be well served by not hooking your fate to a star, but if you do hook it to a star, you had better get on board early. On the other hand, if the quality of the mentorship you receive is the goal even at the risk of not getting on board at all, then perhaps later is O.K.