Reputation and impact in academic careers

Abstract

Reputation is an important social construct in science, which enables informed quality assessments of both publications and careers of scientists in the absence of complete systemic information. However, the relation between reputation and career growth of an individual remains poorly understood, despite recent proliferation of quantitative research evaluation methods. Here, we develop an original framework for measuring how a publication's citation rate Δc depends on the reputation of its central author i, in addition to its net citation count c. To estimate the strength of the reputation effect, we perform a longitudinal analysis on the careers of 450 highly cited scientists, using the total citations Ci of each scientist as his/her reputation measure. We find a citation crossover c×, which distinguishes the strength of the reputation effect. For publications with c < c×, the author's reputation is found to dominate the annual citation rate. Hence, a new publication may gain a significant early advantage corresponding to roughly a 66% increase in the citation rate for each tenfold increase in Ci. However, the reputation effect becomes negligible for highly cited publications meaning that, for c ≥ c×, the citation rate measures scientific impact more transparently. In addition, we have developed a stochastic reputation model, which is found to reproduce numerous statistical observations for real careers, thus providing insight into the microscopic mechanisms underlying cumulative advantage in science.

Keywords: Matthew effect; computational sociology; networks of networks; science of science; sociophysics.

Fig. 1.

Quantifying cumulative reputation measures and citation dynamics. (A and B) Growth trajectories of the cumulative publications $N\prime \left(t\right)$ and citations $C\prime \left(t\right)$, appropriately rescaled to start from unity in each ordinate. The characteristic $\overline{\alpha }$ and $\overline{\zeta }$ exponents shown in each legend are calculated over the growth phase of the career. The mathematicians [E] have distinct career trajectories, with $\overline{\alpha }\approx 1$ because collaboration spillovers via division of labor likely play a smaller role in publication rate growth. See SI Appendix, Tables S1–S9, for ${\alpha }_i$ and ${\zeta }_i$ values calculated for individual careers. (C) Relation between ${\tau }_{1/2}$ and cumulative citations $c_p$. (D) PA dynamics with $\pi \approx 1$ break down for $c<c_{\times }$. The reputation effect provides a citation boost above the baseline PA citation rate attributable to $c_p\left(t\right)$ only.

Fig. 2.

Quantitative patterns in the growth and size-distribution of the publication portfolio for scientists from 3 disciplines. (Left) $c_{i,p}\left(t\right)$ for each author’s most cited papers (colored according to net citations in 2010) along with $C_i\left(t\right)\sim t^{{\zeta }_i}$ (dashed black curve). (Right) The evolution of each author’s rank-citation profile using snapshots taken at 5-y intervals. The darkest blue data points represent the most recent $c_i\left(r,t\right)$, and the subset of red data points indicate the logarithmically spaced data values used to fit the empirical data to our benchmark DGBD rank-citation distribution model (4) (solid black curve; SI Appendix). The intersection of $c_i\left(r,t\right)$ with the dashed black line corresponds to the author’s h-index $h_i\left(t\right)$.

Fig. 3.

The citation life cycle reflects both the intrinsic pace of discovery and the obsolescence rate of new knowledge, two features that are discipline dependent. (Left) For each of three disciplines, the averaged citation trajectory $\langle \mathrm{\Delta }{c}^{\prime }\left(\tau \right)\rangle$ is calculated for papers in the nth quintile with the corresponding citation range indicated in each legend. For example, for physicists in dataset [A], the top 20% of papers have between 74 and 17,032 citations, and the papers in percentile 21–40 have between 31 and 73 citations. (Right) $\langle \mathrm{\Delta }{c}^{\prime }\left(\tau \right)\rangle$ calculated for rank-ordered groups of papers (listed in each legend) for three authors chosen from each discipline.

Fig. 4.

Comparison of three MC career models against empirical benchmarks demonstrated in Figs. 1–3 and SI Appendix, Figs. S1–S3. For each model, we show $\langle \mathrm{\Delta }{c}^{\prime }\left(\tau \right)\rangle$ for the top four groups of ranked papers, the evolution of $c_{i,p}\left(\tau \right)$ and $C_i\left(t\right)$ (dashed black curve), and the evolution of the rank-citation profile $c_i\left(r\right)$ at 5-period intervals. The best-fit DGBD β and γ parameters are also useful as quantitative benchmarks. For each model, we evolve the system over $T\equiv 40$ periods, each period representative of a year. See SI Appendix for further elaboration of the model parameters used in the MC simulation.