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.

I have been away from this blog for awhile – spring is travel time for many academics and I recently had interesting visits to Paris and Montreal. I came home, among other things, to a couple of issues of Nature. One interesting article by Malmgren et. al. (June 3, gated) on the role of mentorship in science related to a question I had been asked while away .

I had been asked why I talk about offspring “production” and “re-production” rather than the more common replication (for asexuals) or reproduction (for sexuals). The reason I use the term “offspring production” is that reproduction or replication has not taken place until the complete life-cycle has been repeated. Consider for example a semelparous (“big bang”) life cycle in which individuals grow and then produce offspring all at the end of the life cycle. Such an individual grows and produces offspring, but its life cycle has not actually been repeated until those offspring have grown and produced offspring in turn – i.e. until grand-offspring have been born. Until then, it is more logical to say the parents have “produced” offspring rather than saying they have replicated or reproduced.

As for the term “re-production”, it obviously means something like ‘producing again’. Much of the literature in evolutionary ecology uses the term “offspring quality” vaguely without specifying what is meant, e.g. see the discussion in an article by Wilson et. al. in TREE in April on “What is individual quality? (gated). I am saying what I mean (and commonly what others implicitly mean) that by making fewer larger as opposed to more numerous smaller spores, gametes, offspring etc. (and more generally engaging in parental care), parents are assisting their offspring with producing their own offspring in turn. But if I said “reproduce” it would be confused with the conventional meaning i.e. what I mean by produce. So I emphasize the ‘again’ by calling it “re-produce”. Specifically, just as the low-density in size relative to resources favouring consumption can be contrasted with the high-density favouring digestion (deriving more breakdown products from each unit of food consumed), the low-density in numbers favouring offspring production can be contrasted with the high-density favouring re-production (deriving more grand-offspring from each offspring produced).

What has all this to do with mentorship in science? Well using data from some 7,259 mathematicians who graduated between 1900 and 1960, Malmgren et. al. showed not only that success in science (number of publications, USNAS membership) is correlated with mentorship fecundity, but that the same trade-off discussed above between production and re-production obtains there. Mentors with low fecundity (< 3) train protégés that go on to have fecundities 37% higher than expected throughout their careers. “Somewhat counter-intuitive”? Not at all. All other things being equal, as all evolutionists know there is a trade-off between quantity and quality of offspring and, it should be emphasized, high quality offspring go on to produce more grand-offspring. The meaning of their other findings is less obvious however and will be the topic of a later post.