  The role of mentorship on protege performance is a matter of importance to
academic, business, and governmental organizations. While the benefits of
mentorship for proteges, mentors and their organizations are apparent, the
extent to which proteges mimic their mentors' career choices and acquire their
mentorship skills is unclear. Here, we investigate one aspect of mentor
emulation by studying mentorship fecundity---the number of proteges a mentor
trains---with 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 uncover
three significant correlations in mentorship fecundity. First, mentors with
small mentorship fecundity train proteges that go on to have a 37% larger than
expected mentorship fecundity. Second, in the first third of their career,
mentors with large fecundity train proteges that go on to have a 29% larger
than expected fecundity. Finally, in the last third of their career, mentors
with large fecundity train proteges that go on to have a 31% smaller than
expected fecundity.
