  Understanding how institutional changes within academia may affect the
overall potential of science requires a better quantitative representation of
how careers evolve over time. Since knowledge spillovers, cumulative advantage,
competition, and collaboration are distinctive features of the academic
profession, both the employment relationship and the procedures for assigning
recognition and allocating funding should be designed to account for these
factors. We study the annual production n_{i}(t) of a given scientist i by
analyzing longitudinal career data for 200 leading scientists and 100 assistant
professors from the physics community. We compare our results with 21,156
sports careers. Our empirical analysis of individual productivity dynamics
shows that (i) there are increasing returns for the top individuals within the
competitive cohort, and that (ii) the distribution of production growth is a
leptokurtic "tent-shaped" distribution that is remarkably symmetric. Our
methodology is general, and we speculate that similar features appear in other
disciplines where academic publication is essential and collaboration is a key
feature. We introduce a model of proportional growth which reproduces these two
observations, and additionally accounts for the significantly right-skewed
distributions of career longevity and achievement in science. Using this
theoretical model, we show that short-term contracts can amplify the effects of
competition and uncertainty making careers more vulnerable to early
termination, not necessarily due to lack of individual talent and persistence,
but because of random negative production shocks. We show that fluctuations in
scientific production are quantitatively related to a scientist's collaboration
radius and team efficiency.
