Quantifying the distribution of editorial power and manuscript decision bias at the mega-journal PLOS ONE

We analyzed the longitudinal activity of nearly 7,000 editors at the mega-journal PLOS ONE over the 10-year period 2006-2015. Using the article-editor associations, we develop editor-specific measures of power, activity, article acceptance time, citation impact, and editorial renumeration (an analogue to self-citation). We observe remarkably high levels of power inequality among the PLOS ONE editors, with the top-10 editors responsible for 3,366 articles -- corresponding to 2.4% of the 141,986 articles we analyzed. Such high inequality levels suggest the presence of unintended incentives, which may reinforce unethical behavior in the form of decision-level biases at the editorial level. Our results indicate that editors may become apathetic in judging the quality of articles and susceptible to modes of power-driven misconduct. We used the longitudinal dimension of editor activity to develop two panel regression models which test and verify the presence of editor-level bias. In the first model we analyzed the citation impact of articles, and in the second model we modeled the decision time between an article being submitted and ultimately accepted by the editor. We focused on two variables that represent social factors that capture potential conflicts-of-interest: (i) we accounted for the social ties between editors and authors by developing a measure of repeat authorship among an editor's article set, and (ii) we accounted for the rate of citations directed towards the editor's own publications in the reference list of each article he/she oversaw. Our results indicate that these two factors play a significant role in the editorial decision process. Moreover, these two effects appear to increase with editor age, which is consistent with behavioral studies concerning the evolution of misbehavior and response to temptation in power-driven environments.

The emergence and rapid growth of megajournals a in the last decade represents a drastic industrial paradigm shift in the production of scientific knowledge [1,2,3,4,5,6]. This transition places pressure on several fundamental aspects of the scientific endeavor. First, the personnel resources required to referee the 60,000+ megajournal articles each year is quite substantial [3,6]. Second, the publication volume stresses the individual cognitive capacity of scientists as well as the technological knowledge-storing capacity which is fundamental to the long-term need to be able to search, retrieve, and classify literature. By way of example, over its first 6 years, PLOS ONE grew at an annual rate of 58%, roughly 18 times larger than the net growth rate of scientific publication over the last half-century; in 2012, the 23,468 articles published by PLOS ONE alone represented approximately 1 in every 1000 science publications indexed by the Web of Science [6]. And third, megajournals rely on a highly scalable model for managing the scientific publication process. In particular, PLOS ONE relies on thousands of acting scientists comprising its editorial board, who simultaneously continue their role as research leaders. This dichotomy, being both a producer and gatekeeper of knowledge, creates the conditions for conflict of interest, because scientists must balance conflicting incentives arising from their duties as both authors and editors.
Oversight of the editorial board is a formidable challenge in megajournals, calling for strategic management policies to document editor activities and address unintended incentives. a Megajournals are typically online-only e-journals, the largest of which publish upwards of 500 articles per month and serve a multi-disciplinary audience. Consequently, the production process is primed for growth, in particular international growth [1]. The top 5 megajournals, ranked by the number of articles published in 2016 (in parenthesis) according to Scimago Journal & Country Rank, are PLOS ONE (22,159), Scientific Reports (20,883), Royal Society of Chemistry Advances (13,025), Oncotarget (6,391), and Physical Review B (5,483).
However, our fundamental understanding of this problem is hindered by the lack of transparency -both during the review process and also post-publication. b Ironically, while this lack of transparency -e.g. blinding of authors, reviewers, and editors -is justified as facilitating unbiased peer review, it makes external monitoring of operational misconduct difficult. This tradeoff is an important consideration for the management of the scientific practice, not least because research shows that misconduct may organically arise from the basic pursuit of internal (and external) power [7] and the innate difficulty of avoiding temptation in decision-heavy endeavors [8] -conditions characteristic of science.
For these reasons, the oversight of editor activity is necessary in order to address social and cognitive biases that can enter into the manuscript decision process. For example, the multi-disciplinary journal Proceedings of the National Academy of Sciences (PNAS) has a two-tiered editorial board system in which National Academy of Science members serve as editors of individual submissions, and a smaller rotating Editorial Board provides an additional oversight layer for approving final decisions. Similarly, Management Science also employs a two-tier system comprised of a rotating Editor-in-Chief which serves above a second layer of "Department Edi- b We chose to study the megajournal PLOS ONE primarily because the full article text are readily available and in a stable format, because it has a single review and publication process, because it is not affiliated with a society (in which case we would likely be missing significant information capturing significant author-editor social relations), and because the sample size of publications and editors is large enough to be amenable to methods of statistical inference. Unlike most journals, PLOS ONE does provide the name of the editor overseeing each article, a crucial aspect which we leverage in this study. Two other multidisciplinary journals with a distributed editor management system that also provide the editorial board member name on each article are the weekly journal Proceedings of the National Academy of Sciences of the United States of America and the monthly journal Management Science.
tors" who oversee the review and manuscript decision process for individual submissions. As we shall explore in more detail, there is substantial variation in editor activity, even within the same journal (see Fig. 1). Thus, in addition to standard editor policies [9], a two-tiered editorial board system helps establish accountability on the part of the manuscript-level editors. But megajournals developed around principles of scalability, and so one might expect high editor activity levels -but how high is reasonable? Against this background, we performed an in-depth analysis of PLOS ONE, the largest journal in the world, over its first 10-years of publishing (2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015). Not surprisingly it also has the largest editorial board of any journal, and reports for each article the particular handling editor that accepted the publication. By combining editor, author, article and citation level data for each publication, we constructed a large multi-variable dataset centered around the 6,934 PLOS ONE editors. The longitudinal nature of this dataset facilitates identifying the role of social factors underlying editor manuscript decisions, thereby providing insight into a domain of science that has traditionally been undocumented, since most journals do not reveal editor-article associations. As such, we contribute to recent efforts [10,11] aimed at measuring biases in the editor manuscript decision process.
The results of our descriptive analysis and panel regression modeling indicate that a small but prolific set of PLOS ONE editors are exceeding reasonable activity levels -e.g. roughly 1 in 100 PLOS ONE editors are more active than the most active PNAS editor. Moreover, within this group of extremely active editors, we establish significant editor-level decision bias and high levels of citations directed at the editors, consistent with an unethical citation remuneration strategy on the part of manuscript authors that could include calculated coordination with the particular manuscript editor. On that note, it is important to clarify that identifying, with certainty, cases of author and/or editor misconduct would require case-by-case internal investigation, which is beyond the capacity of our data and methods. Instead, we focus on defining outliers in the editor activity distribution and identifying shifts in editor bias over time that are consistent with poor oversight in megajournals, unintended incentives associated with active academics serving a dual role as gatekeeper, and overall a cause for concern.
It is of course possible that anomalous editor activity is more widespread in science than currently appreciated, and would be evident for other journals if their editor data were also available. c  the proliferation of an entirely new layer of megajournals. Addressing the problem may require implementing editor activity quotas, as well as following the example of PLOS journals in making editor data available. Steps in this direction will increase the transparency of the publication process, and foster the development of data sources, methods and protocols for rigorously assessing the integrity of the scientific peer review system [9]. In light of this issue, our contribution to the literature is to develop methods to quantitatively assess the distribution of editor activity in large distributed boards, to measure the editor-author relationship, and to correlate these social factors with editor decisions and outcomes.
In what follows, we provide motivation for our framework in Section 1 and specify our data sources and statistical measures in Section 2. We analyze sample descriptive statistics in Sections 3 3.1-3 3.2, which develops intuition for typical editor activity levels and manuscript decision times at PLOS ONE. Comparing with editor activity levels at PNAS and Management Science, two journals that also employ distributed editorial boards comprised of academic editors, identifies anomalous activity levels among the most prolific PLOS ONE editors.
In Section 3 3.3 we further explore the hypothesis that the observed anomalous activity is related to "scientific gaming" by modeling two types of cooperative "back-scratching": (i) editors making biased decisions in the review process towards their close scientific peers, and (ii) authors enticing favorable decisions by providing remuneration in the form of citations directed towards the editor's research. More specifically, we leverage the longitudinal aspects of available PLOS ONE editor data using panel regression with editor fixed effects to demonstrate robust statistical support for these hypothetical mechanisms -the emergence of power-driven bias supported by subtle citation remuneration. Based upon these empirical findings, we conclude in Section 3 3.4 by estimating a lowerbounds for how many citations an engaged editor could garner by leveraging the high-throughput capacity of a megajournal with little editorial oversight. We provide additional evidence of concerted citation gaming by analyzing the complete career publication records for three PLOS ONE editors who display anomalous editor activity levels.

Background and Motivation
This work contributes to several research streams focused on understanding the economics of science [12], the persistent growth of scientific production and its implications for knowledge accumulation and research evaluation [6], and a variety of ethics issues related to the growth and densification of social networks in science [13]. Our work also draws on the scientific community's efforts to develop data-driven models Physical Review D. Instead, here we address the need for transparent and centralized oversight of the editor team megajournals; The two-tiered editor Board and Manuscript Editor system used by PNAS is a good example, thereby providing a more robust three-tiered manuscript review process.

FIG. 1:
The distribution of editor activity in three multidisciplinary journals. (A) Comparison of the distribution P (nE) of annual activity nE (per editor) for three journals with distributed editorial boards comprised of acting academics. Plotted is the cumulative distribution, i.e. the fraction of all editors that oversee nE or more articles per year, showing that there is a small but significant subset of PLOS ONE editors with extremely high activity levels. (B) Comparison of the distribution P (SE) of normalized annual activity SE (per editor per year), which measures the annual activity relative to the median activity across all journal editors in a given year, thus better accounting for variation in journal size. In both panels we report the kernel density estimate of the probability density functions, P (nE) and P (SE); vertical dashed lines indicate the activity level corresponding to the top-5% of all editors for a specific journal.
for understanding the social factors underlying the scientific process [14,15,16]. To this end, we employ an empirical approach that leverages the vast amounts of available publication metadata in order to expand our knowledge about science itself [17]. In particular, our effort to capture the obscure yet fundamental interactions between individuals -here the editor-author relation -leverages social science methods paired with recent advances in computing and the availability of unstructured yet rich data sources captured in vast online repositories [18].
It is important to frame science of science analysis [16] around important science policy challenges [12,15,19] -e.g. how to increase the efficiency of scientific discovery [20], how to improve sustainability of scientific careers [21] in an increasingly metrics-oriented system [6,22], and how to reconfigure the scientific funding system [23]. Indeed, maintaining high quality standards and addressing social and cognitive biases in science is crucial, especially in light of disinformation campaigns aimed at discrediting science itself [24,25].
With this in mind, we focus on the intersection of megajournals, distributed academic editorial boards, and the fidelity of the manuscript decision process. It is well-known that the peer review process is not perfect [26], as demonstrated by recent work on editor and referee bias in the review of positive scientific results [27], and editor gender bias in the selection of reviewers [28]. Against this background, we also contribute to recent efforts quantifying the role of social factors on manuscript decisions and decision timescales [10,11,29,30]. In particular, our results demonstrate the value of transparency in the editorial process, and provide guidance for establishing oversight of editorial boards, which serve as the gatekeepers of vetted and accepted knowledge.

PLOS ONE article data
We gathered the citation information for all PLOS ONE articles, indexed by A, from the Web of Science (WOS) Core Collection. From this data we obtained a master list of the unique digital object identifier, DOI A , as well as the number of authors, k A , a list of their surnames and first-middle name initials, and the number of citations, c A , at the time of the data download (census) date on December 3, 2016. We then used each DOI A to access the corresponding online XML version of each article at PLOS ONE by visiting the unique web address "http://journals.plos.org/plosone/article?id=" + "DOI A ". Because the full-text XML files have common and relatively stable structure over the 10-year period of analysis, we were able to collect the same metadata for each PLOS ONE article. As such, we parsed each article's reference list, resulting in a dataset of more than 6.7 million outgoing citations. We used the list of coauthor names for each citation to estimate the rate of citations directed at handling editors. Based upon a string match between the full last name and first initial of the coauthor and handling editor, we estimate that 0.3% of citations are directed at the handling editor, and roughly 8% of PLOS ONE articles have at least one such handling-editor citation [see Fig. S1].
Given the fact that most journals do not make the editorpublication association data available, while also considering the magnitude of the data collection, it is beyond the scope of our analysis to perform a comprehensive comparison of editor patterns at all megajournals. Thus, our study is primarily a case study of PLOS ONE. Nevertheless, in order to provide an initial comparison of editorial board size and activity, we collected, processed and analyzed editor-publication data for two other journals with a distributed editor manage-

Article and editor measures
In our study, the principal unit of analysis is a PLOS ONE editor, which we denote by the index E. For each E we collected the corresponding group of N E articles over which he/she has served as editor. This editor-article (A, E) association is publicly available in both the published electronic article as well as on the article webpage, appearing in the article abstract and author information byline. To maintain context among the variables we define in our analysis, quantities that are mostly article-specific are denoted by the index A, those that are mostly editor specific are denoted by the index E, and quantities that are properties of both are indexed as x A,E .
Embedded in the XML file for each article are various editor, coauthor, and article metadata which we extracted from the webpage of each A and then aggregated for each E. All together, the entire dataset for the 10-year period 2006-2015 is comprised of 141,986 articles and 6,934 editors. In both of our panel regression models we refine this dataset to the 3749 editors with N E ≥ 10 articles to reduce small sample noise at the editor level, resulting in 128,734 articles. From these articles and their editors we define the following quantities: 1. The net editor activity, N E , is the number of articles overseen by editor E over the total editor service period, L E , which is the number of days between an editor's first and last article through the end of 2015.
2. The article acceptance time, ∆ A , is the number of days between the submission and acceptance of article A. Note that this duration does not include the time interval between acceptance and publication, as factors external to the editor process could affect this process, its timeline, and thus its ultimate duration.
3. The annual activity, n E , is the mean number of articles edited per year while serving as editor at a particular journal, i.e. n E = 365N E /L E . The inverse measures the editor turnover time d E = L E /N E , which is the mean number of days between two articles published in PLOS ONE, a proxy for the intensity of the time commitment required of a given editor. 6. The "citation remuneration" C A is the total number of references that cite the editor's research among the articles he/she edited. This number is calculated by going through the reference list of each article, and identifying publications that include the editor's last name and firstname initial among the authors. Likewise, the editor citation rate, f A , is the fraction of the total references on a given article that cite his/her work.
7. The editor's PLOS ONE service age, τ ≡ τ A,E , is the time difference between the acceptance date of the first accepted article of editor E and the acceptance date of a given article A, measured in years. Figure 2 shows the statistical distribution of several important quantities, with article-level statistics shown in blue, and editor-level statistics shown in red throughout the remainder of the analysis; Figure S2 shows additional distributions for less important measures.

Normalization to account for citation inflation and research subject area
PLOS ONE is a multi-disciplinary journal, accepting submissions from all research domains. The disciplinary diversity among accepted papers introduces a significant measurement challenge, because we seek to explain meaningful variations in citation impact for articles, net of publication year (indexed by t) and discipline-specific subject areas (indexed by s). To address the latter, we use the classification system defined and maintained by PLOS ONE to assign each article to one of six primary subject areas: (i) Biology and life sciences, (ii) Medicine and health sciences, (iii) Physical sciences, (iv) Social sciences, People and places, (v) Engineering and technology, Computer and information sciences, (vi) Ecology and environmental sciences, Earth sciences. For more details see Supplemental Material (SM) Section 1.
We must also standardize the citation impact measure to address three principal statistical biases: variation in publication rates across discipline, censoring bias and citation inflation. The first refers to the fact that larger disciplines, e.g. "Biology and life sciences", produce more publications, and hence, more citations than other disciplines such as "Earth sciences". The second bias reflects the fact that older publications have had more time to accrue citations than newer ones. And the third bias refers to the fact that more citations are produced over time as a product of increasing publication rates and reference list lengths, leading to a significant inflation in the relative value of citations. By way of example, a recent study demonstrated that the total number of references produced by all scientific articles is growing by 5.6% annually, and hence doubling every 12.4 years [6].
To address these three measurement problems, we map the raw citation count c s A,t of a given article -measured at the WOS census date Y = 12/03/2016 -to a normalized or "detrended" value . (1) The mean, ln(1 + c s t ) , and the standard deviation, σ[ln(1 + c s t )], are calculated only over publications from the same year t and refined subject area s. The constant 1 is added to each citation count in order to avoid the divergence (ln 0) associated with uncited articles, and does not affect the results.
By analyzing the logarithm of the citation count, this normalization leverages the universal log-normal statistics of citation distributions [31]. Moreover, by rescaling the logarithm by the standard deviation, the underlying inflationary bias has been removed, and so the distribution of P (z) is stationary, thereby permitting cross-temporal comparison. As such, z is particularly well-suited for regression analysis, as recently demonstrated in longitudinal analyses of cumulative advantage [32] and collaboration [33] within researcher careers. Figure S3 demonstrates that the probability distributions P (z|s, t) are all approximately normally distributed, and thus sufficiently time invariant for the purposes of our analysis, for each subject area and year -with the exception of 2015 publications, which did not have enough time to converge to the log-normal distribution, and so we omit these data from our first regression analysis where z is the dependent variable. Figure S4 provides a correspondence chart relating z s A and c s t values to provide a estimate of effect sizes in our regression analyses. For example, in 2008, a publication with the baseline value z = 0 (meaning that ln c A is equal to the logarithmic mean value for publications from that year, ln c A,t = ln c t ) corresponds to roughly 26 citations; in 2010 it corresponds to 17 citations; and in 2012 to 10 citations.

Repeated editor-author associations
We investigate whether editor-author associations correlate with publication outcomes by tabulating the set of N k authors appearing within the article set of a given editor. That is, for each article we recorded the last name and first initial of each of the k A coauthors. Then, for each editor we tallied the number of articles (A E,k ) he/she edited for a given author (proxied by the individual surname + first-initial combinations, e.g. "J"+"Smith"). Because of the name disambiguation problem, it is difficult to distinguish authors with the same name, especially for authors with extremely common surnames. Thus, we removed from our analysis those authors with common surnames (e.g. Xie, Yang, Adams, Johnson), using the PLOS ONE editor name list to determine which surnames appear with significant frequency that might significantly contribute to false-positive union of coauthor counts. We describe this procedure in the Supplemental Material Section 2, where we also provide the full list of surnames which we ignored in our author analysis. After tallying the author names for each E, we then ranked the list of those coauthors. d Two recent studies have also operationalized the "social tie" between editor and author using two similar methods, either by using prior department, coauthorship, and mentorship histories [10] or by measuring the distance within the collaboration network [11]. Ideally, one would be able to capture the union of all three methods for estimating the strength of the social relation between editor and author. Due to data limitations this is not feasible, and so we use a simple heuristic: independent of the precise combination of A E,k attributed to the k A coauthors of a given article, we estimate the presence of a social ties between the authors and editor based on whether or not any of the authors have A E,k ≥ 2 articles with a given editor -i.e. "repeat authors".
Because of its large publication volume, senior coauthors may have lengthy experience publishing with PLOS ONE. As such, it is not unreasonable that the corresponding authors of new submissions would elect editor(s) that previously oversaw their accepted publications. Along the same lines, it is also unlikely that submitting authors would be assigned the same editor as in previously accepted articles just by chance. Thus, to test for spurious relations, we use a shuffling method to show that this repeat author criteria indeed identifies a subset of articles that are rather distinct, pointing to the accuracy of this method in identifying editor-author ties.
Applying this method, for each editor we tagged the articles featuring at least one repeat author using the indicator variable R A,E = 1; the remaining articles are denoted by R A,E = 0. In total, the articles with R A,E = 1 represent 13.9% of all articles. We denote the number of repeat authors per editor by K2 E , and Fig. S2(B) shows that each editor has on average 5.2 repeat authors. Likewise, on a per-article basis, Fig.  S2(C) shows that on average 11% of an editor's articles have R A,E = 1. However the distribution of the fraction ρ E is skewed with 10% of editors having 26% or more of their articles with R A,E = 1; the median ρ E value is 0.1. In conclusion, our "repeat author" method identifies a sufficiently large number of articles with R A,E = 1 that we can use this binary classification to estimate the impact that social factors have on editor decisions by comparing an editor's article set with R A,E = 1 to the counterfactual set with R A,E = 0.

Distribution of editor activity
Compared to MS and PNAS, the editors at PLOS ONE demonstrate an extremely wide range of annual activity as measured by n E , the mean number of articles edited per year d We investigated the distribution of the rank-coauthor profile within an editor's article set, and found that the distribution P (A E,k ) decays like a binomial distribution, but with deviations in the tail. The maximum value Max[A E,k ] depends to a large degree on N E . Thus, unlike the rankcoauthor distribution within a given researcher's publication profile, which is well-fit by a discrete exponential distribution and characterized by a subset of "super-ties" representing extremely strong career partners [33], the editor-author distribution is not characterized by extremely strong social ties. To illustrate the broad range of activity, Fig. 1(A) shows the cumulative distribution P (≥ n E ), which conveys the fraction of editors with activity larger than a given n E level. The activity distributions are generically right skewed -most editors oversee a few articles a year, whereas the most active editors (e.g. top 5%) are significantly more active than the average editor within each journal. However, the upper limits of editor activity allude to the distinct differences between journals. Comparing the larger journals PLOS ONE and PNAS directly, we count 85 editors at PLOS ONE that are more active than the most active PNAS editor who averages 22 articles per year. For a comparison at the distribution level, we calculate the Gini index, which is a useful sample-size independent measure of dispersion or "inequality" across the units of analysis. This standardized measure quantifies the mean difference between all pairs in the population, with larger values indicating higher levels of inequality: the Gini index values are: 0.47 (PLOS ONE), 0.36 (PNAS), 0.40 (MS). Nevertheless, these comparisons do not account for differences in size, publication standards, and acceptance rates between the journals.
To further highlight the anomalous activity of extremely active PLOS ONE editors, we calculated the normalized annual activity, S E , which controls for journal-specific volume, acceptance criteria and acceptance rates. Figure 1(B) shows the kernel density estimate of the distribution P (S E ), which demonstrates data collapse across the three journals, indicating a common bulk distribution of editor activity net of extrinsic factors -except for the distinct truncation scale for extreme values. To be specific, the truncation of the upper tails of P (S E ), corresponding to the most extreme editor activity, is roughly 4 times the median activity for MS, 10 times for PNAS, and nearly 20 times the median activity level for PLOS ONE editors.
To demonstrate the extent to which editorial power could be scaled over time, we also analyzed the total articles per editor, N E . Figure 2(A) shows the 100 most-prolific editors, who collectively oversaw 17,000 (12.2%) of the total 141,986 articles; and Fig. 2(B) shows the full distribution P (N E ), which is again extremely right-skewed. The full distribution shows that while most editors have overseen just a few articles, 50% have served on 11 or less articles; meanwhile the most prolific editor, Vladimir Uversky, has served on roughly 27 times (557/20.5) as many articles as the average editor. In terms of the cumulative fraction of all articles edited by a given percentile: the bottom 25% of editors oversaw just 3% of the total 141,986 articles; the middle 65% of editors oversaw 55%; the top 10% of editors (693 editors) oversaw 42%; and the top 10 editors together oversaw 3,408 articles, corresponding to 2.4% of the total articles.
Together, these numbers illustrate the remarkable upper limits of editor power facilitated by a high-throughput megajournal lacking policy management of editor activity.

Distribution of editor acceptance times
An additional factor that could explain the skewed activity distribution at PLOS ONE is the skewed distribution of the number of days between receiving an article and accepting the article, ∆ A , as shown in Fig. 2(C). Similarly, we measure the mean acceptance time for articles handled by a given editor, ∆ E , finding that variation at the level of individual articles manifests in significant variation at the level of editors. Figure 2(D) shows a correspondence in mean values, ∆ E ≈ ∆ A = 126 days or roughly 4 months; however, the standard deviation in ∆ E across editors is roughly a month, meaning that some editors are significantly faster (slower) than others.
Even among the 100 most active editors there is a wide variation in ∆ E , as demonstrated by the color coding of individual editors in Fig. 2(A). Indeed, the extremely high activity levels of the 10 most active editors is largely explained by their rapid acceptance times, with several editors averaging just around 2 months per article from submission to acceptance. Moreover, the variation in article acceptance times means that the number of articles being handled at any given time can also vary widely across editors. On average, the time between articles accepted by a given editor, d E , is about half as long as the time for an article to be accepted (2 d E ≈ ∆ A = 126 days), meaning that even the average editor is handling roughly two articles at a time. This estimate does not include the additional effort associated with articles that are not ultimately accepted. Because keeping track of multiple tasks requires marginally more effort per task, the effort required to maintain activity at extreme levels would likely be daunting -if one were to maintain reasonable manuscript evaluation standards.

Modeling shifts in editor behavior -panel regression with editor fixed effects
Do shifts in editor behavior reflect adjustments required to offset the increasing marginal effort associated with such high activity levels? If so, could this adjustment be facilitated by social coordination? And at what cost? In what follows, we provide evidence in support of our hypothesis that the extremely active editors at PLOS ONE are gaming the system by leveraging the scalability of the megajournal platform.
To test this hypothesis we model two article-level outcomes using editor and article-level controls: (i) what is the article's citation impact, z A , and (ii) how long was the article under review before being accepted, ∆ A . In principle, both variables reflect on editors' responsibility to oversee the peerreview process and to assess the scientific merit of submissions -without bias. As such, a diminishing ability to assess research quality and a tendency to favor repeat authors -with some remuneration in the form of citations to the editor's work (solicited or not) -would be consistent with the adjustment to the demands of extreme activity and possibly a harbinger of coordinated misconduct. To this extent, of principal interest among the covariates are those representing social aspects of the editor-author review process.
Namely, we shall focus on the variation within each editor's profile associated with repeat authors, R A,E , and the rate of references directed at the editor's publications, f A . For example, Fig. 2(G) shows the distribution P (f A ), which indicates that 92% of articles do not have any references that cite the handling editor; calculated across all articles, the mean value f A = 0.003 [see Fig. S1]. However, among the remaining 8% of articles with f A > 0, there is a wide range, with the average value f A |f A > 0 = 0.036 corresponding to roughly one in every 28 references citing the editor's work. The longitudinal feature of our data is crucial, as trends across each editor's service career, captured by τ E , would be consistent with behavioral changes reflecting increased workload, apathy, and possibly a hitherto under-appreciated form of coordinated scientific misconduct -editor-author citation remuneration.
1. Model I: Trends in citation impact of accepted articles, z A . Recent studies show a negative trend in the scientific impact of a researcher's publications across the career [32,33]. In our first model, we ask a similar question: does the scientific   p-values in parentheses * p < 0.05, * * p < 0.01, * * * p < 0.001 quality of the article's overseen by a given editor change over time?
The dependent variable is the normalized citation impact of an article z s A relative to the subject area s. By matching each article to its editor E, we capture the longitudinal dimension quantified by τ A,E , the number of years into his/her editorship at PLOS ONE. We proceed with a panel regression framework including editor fixed-effects (β E,0 ) to control for time-invariant individual-level characteristics, which facilitates identifying causal pathways since R A,E captures two opposite scenarios. For this panel analysis we exclude articles from 2015, since our analysis of z s A in the bottom row of Fig. S3(B) indicates that these articles have not had enough time to sufficiently converged to the baseline Normal N (0, 1) distribution. Thus, by considering only those editors with N A ≥ 10, this additional threshold reduces the dataset from 128,734 to 102,741 articles (observations).
The specification of our linear fixed-effects model is given by The results of this basic model estimates are shown in the first two columns of Table I, where the second column corresponds to the standardized (beta coefficient) coefficients The article-level variable k A controls for team-size effects, and is incorporated in logarithm since the distribution of authors per publication is right-skewed and approximately lognormal in various team-oriented disciplines [13]. Along these lines, we also include subject area as well as publication year dummies variables to further control for cross-disciplinary and temporal variation in the explanatory variables.
The first covariate of interest is ∆ A , the amount of time it took for the article to be accepted. The model indicates that publications that are under review for a longer time tend to have lower citation impact (β ∆ = −0.127; p < 0.001). This is consistent with the assumption that articles that fail to signal their novelty and/or scientific contribution may require more deliberation time between the authors, the reviewers, and the editor.
The principal explanatory variable of interest is τ A,E , the duration of editor service at PLOS ONE at the time of acceptance of the article, is the strongest variable in explaining z E , with standardized coefficientβ τ = −0.143 (p < 0.001). This result is consistent with two other studies of longitudinal citation patterns within careers [32,33], and suggests that an editor's discrimination power decreases across his/her career. In terms of the magnitude of the effect, this means that in the first seven years (≈ e 2 ) of the editor's service, the mean impact decreases from z = 0 to z = −0.36 (assuming the editor starts out on par, i.e. z = 0); this change corresponds to a decrease in citation impact from 26 citations to 18 citations, or a 31% decrease (using 2008 citation values, see Fig. S4).
The repeat author indicator variable, R A,E , shows a significant positive coefficient β R > 0.09 (p < 0.001), possibly due to repeat coauthors likely being more experienced and more prominent within their scientific community. In order to identify additional signatures of bias among the extremely active editors, we estimated two additional models, the first including an additional interaction term R A,E × ln τ E and the second including an additional triple-interaction term The marginal effect of editor longevity (ln τE) on the normalized citation impact (zA) of the articles he/she accepts, including an interaction term R × ln τ to distinguish between those articles with R = 1 (with repeat authors) and R = 0 (no repeat authors). Both interaction coefficients are negative and significant at the p < 0.001 level; the difference in the coefficients is significant at the p ≤ 0.005 level. (B) The marginal effect of citing the editor's publications (fA) on the time the editor takes to accept an article ∆A, including an interaction term R × f to distinguish between the articles with R = 1 and R = 0. Both interaction coefficients are negative, however due to small sample size for the R = 1 cases, only β f ×R(0) (p < 0.001) is significant, with β f ×R(1) only significant at the p = 0.096 level. Shaded interval indicates the 95% confidence interval calculated using the delta method with all covariates evaluated at their mean values.
T 10,E × R A,E × ln τ E , where T 10,E = 1 if the editor is ranked in the top-10 according to N E and 0 otherwise. The former double-interaction term captures the potential combined effect of editor age and social ties while the latter triple-interaction term captures the additional effect of being extremely prominent editor at PLOS ONE. The model estimates for the tripleinteraction are shown in the fourth column of Table I, and indicate that articles with R A,E = 1 have decreasing impact for larger τ (β T ×ln τ = −0.025; p = 0.028). Moreover, we observe an additional negative effect related to the combination of top-10 editors who accept articles with R A,E = 1 for larger τ (β T ×R×ln τ = −0.103; p = 0.017).

Figure 3(A)
shows the decline in z over time, and also illustrates the marginal effect of editor service age τ on z A for R A,E = 0, 1. Both trends are negative, however the marginal effect for R A,E = 1 is more so, such that by ln τ = 1 (corresponding to roughly 3 years of service), the characteristic article citation impact is below average, with no significant difference from the articles with R A,E = 0 by ln τ = 2 corresponding to roughly 7 years.
It is possible that the significance of the estimated coefficient β R could arise by chance due to a spurious correlation. In order to rule out this scenario, we implemented a randomization scheme in which we shuffled the values of R A,E across the dataset, without replacement, thereby conserving the total number of observations with R A,E = 1, corresponding to 16,242 observations or 15.81% of the sample. We implemented this "placebo" regression model by shuffling the dataset 1,000 times, each time recording the value of β R . Figure 4(A) shows the distribution P (β R ) of the 1,000 placebo estimates; indeed, none of the placebo estimates are larger than the real estimate, thereby ruling out the possibility that β R is significant due to chance alone. We tested the tripleinteraction term β T ×R×ln τ using the same placebo method. Figure 4(B) shows that the significance of this additional specification is also not due to spurious correlations.

Model II: Trends in acceptance time, ∆ E .
The average PLOS One article takes 126 days from being officially received and processed by the editor, reviewed (possibly over several rounds), and finally accepted. This characteristic timescale is higher than the global average across journals which was recently estimated to be roughly 100 days, with only slight variation observed when disaggregating journals by their impact factors [29]. However, within PLOS ONE we observe great variation in the acceptance time of individual articles, demonstrated by the distribution P (∆ A ) in Fig. 2(D). This variation is highlighted by two remarkable extremes -we observed one publication with ∆ A = 0 days (DOI:10.1371/journal.pone.0031292) and one publication (DOI:10.1371/journal.pone.0028904) with ∆ A = 1927 days, or more than 5 years to finally be accepted. Moreover, we find that 0.43% of articles are received and accepted within 7 days, possibly following the rapid transfer of a submission between PLOS journals. e  Table I) and the decision time model (panel B, see Table  II), we ran each of these models using a randomized repeat author variable, implemented by shuffling just the variable across the observations without replacement (i.e., conserving the total number of observations of a given value). Thus, this second model aims to explain the wide range of acceptance times observed across all articles, and in particular, within editor profiles. To this end, we test wether editor decisions times are correlated with variation in the number of references citing the editor's work. For this panel analysis we use data for editors with N A ≥ 10, corresponding to 128,734 articles (observations). The specification of our linear fixedeffects model is given by The results from our model parameter estimates are shown in Table II along with their standardized (beta coefficient) counterparts. f In addition to the covariates used in the citation impact model, we include an extra variable -the fraction of the article's references that cite the editor's work, f A . As in the first model, higher impact articles tend to get accepted more quickly (β z = −0.0343; p < 0.001), likely because higher quality research is more easy to identify, and so there is a faster consensus towards a decision to accept. Also, the more coauthors on the article, the longer the articles tended to take in order to be accepted, in line with expected increasing coordination costs in assembling and submitting referee revisions in large team endeavors (β k = 0.0297; p < 0.001). We observe a significant positive relation between editor service age and the acceptance time, in line with the increasing time demands as an editor becomes busier within the journal f We ran both model I and II without including subject area (SA) fixed effects, and did not observe a significant difference in the estimates of either model. This surprising result can be explained as a combination of the citation rates between SA being rather uniform (see Fig. S4) in addition to the fact that the editor fixed-effects approximately control for the variation in subject areas across individual articles if one assumes that editors do not oversee articles from outside their principal research area. compounded by additional external activities (β τ = 0.137; p < 0.001).
More importantly, we find a negative relation between editor citations and acceptance time (β f < 0), albeit the weaker in relative magnitude as indicated by its standardized coefficient (β f = −0.009; p < 0.001). Nevertheless, this significant negative relation is consistent with author-editor remuneration.
Consistent with the aforementioned social feature, the model indicates a significant reduction in ∆ A for repeat authors (β R = −0.0878; p < 0.001), corresponding to a 100β R = 9% reduction in acceptance time relative to other articles by the same editor with R = 0. In real terms, for the average article, this effect corresponds to roughly a  In order to illustrate the differences in ∆ A associated with the combination of these two covariates of interest, we added an interaction term f A ×R A,E to the model specified in Eq. 3, thereby distinguishing the relation of f between articles with R = 1 and R = 0. Figure 3(B) shows the marginal effect of f on ∆ A , with articles with R A,E = 0 showing a statistically significant negative relation (β f ×R=0 = −0.75; p < 0.001)consistent with "paying more the first time." Similar to the previous model, we again tested for spurious relationships that may yield a positive coefficient β R > 0 by shuffling the indicator variable R A,E without replacement (corresponding to 19,319 observations or 15% of the sample with R A,E = 1). We then implemented the regression model 1,000 times, and show the distribution P (β R ) of the 1,000 placebo estimates in Fig. 4(C). None of the placebo estimates are larger in magnitude than the real estimate, thereby ruling out the possibility that β R is significant due to chance alone.

Is citation remuneration scalable?
In previous sections we provide evidence that PLOS ONE editors -especially the extremely active ones -may treat repeat authors differently, by lowering their standards of quality judgement and providing faster decision times. In this section we estimate the potential net inducement that these repeat authors could provide, whether by coordinated or uncoordinated remuneration. It is important to reiterate that knowledge of the editor's identity is not known at the point of submission; however it is not impossible that authors and the handling editor could communicate externally. Indeed, this is a generic possibility present with any journal, and not specific to any particular aspect of the review process at PLOS ONE.
To this extent, it is impossible to use the data at hand to know the exact context of each of the references citing a PLOS ONE handling editors' work. Thus, it is best to assume that the majority of the citations directed at the handling editor's research follow the same intent purposes of any other reference. Nevertheless, it is well-documented that citation attribution is susceptible to factors that undermine the credit system in science, such as unjustified self-citation [34,35] and reciprocal-citation [36]. Motivated by the results of the second regression model, it is clear that citing the editor -either an unsolicited nudge or a coordinated remuneration -could entice a faster and more positive decision. But if coordinated, what could be the net gain from leveraging the scalability of a megajournal?
To address this question, we leverage the size of the PLOS ONE dataset to identify measurable differences in the citation rate to editors conditional on the article including or not including repeat authors (R A,E = 1, 0, respectively). To be specific, for each editor we collected the set of N E,R=1 articles with R A,E = 1 and counted the total number of references C R=1 made by this set of articles, and also the number of those references citing the editor's work, C E,R=1 . Similarly, for the set of N E,R=0 = N E − N E,R=1 articles with R A,E = 0, we also calculated C R=0 and C E,R=0 . Thus, the total number of references from all articles overseen by an editor is simply T E = C R=0 + C R=1 , and the total number of citation received by the editor, independent of R, is We then define the conditional editor citation rates f E,1 = C E,R=1 /C R=1 and f E,0 = C E,R=0 /C R=0 and plot their distributions P (f E |R A,E = 0, 1) in Fig. 5(A). The mean value for repeat authors f E,R=1 = 0.0041 is 46% larger than f E,R=0 = 0.0028, and the probability distribution P (f E |R A,E = 1) shows a prominent excess in the right tail, suggesting that a sufficiently large f may be an enticing nudge. Statistical tests for the difference in means (T-test), difference in median (Mann-Whitney test), and difference in distribution (Kolmogorov-Smirnov test) all reject the null hypothesis that the mean, median, and distributions are equal at the p < 10 −9 level.
We also calculated the expected number of citations that an editor might gain due to the differences in citing behavior of repeat versus non-repeat authors. We measure this difference as which should be equal to 0 for those editors who are completely unbiased with respect to R. Of course, there are fluctuations due to the finite sample size N E . Figure 5(B) shows the probability distribution P (∆C E ) with mean value ∆C E = 3.1 and standard deviation σ ∆C = 15.2. However, the distribution is leptokurtic and significantly right-skewed (skewness = 3.5) as compared to the normal distribution with the same mean and standard deviation. In particular, the skew points to an excess number of editors with relatively large and positive number of citations attributable to differences in the citation rates for R = 1 versus R = 0. Remarkably, we count 34 editors with ∆C E > ∆C E + 3σ ∆C , representing 2% of the 1595 editors we analyzed with N E ≥ 20; however, we count only 2 editors with ∆C E < ∆C E − 3σ ∆C . The positive outlier ∆C E values are on the order of 100 citations, which is a lower bound estimate for the possible net gains from coordinated remuneration with repeat authors, C remun. , i.e. ∆C E ≤ C remun. ≤ C E,R=1 . While it is possible that statistical outliers could arise for reasons aside from social factors (i.e. repeat authorship and remuneration), it is unlikely that an editor would simultaneously be an outlier in various categories. As further evidence of anomalous editor behavior, Fig. 5(C) combines three editor service measures in a single scatter-plot visualization: editor activity, n E , the average citation impact of articles overseen by each editor, z E , and the total citations directed at the handling editor's research, C E . We restrict this analysis to articles published prior to 2014 and analyze the subset of 1071 editors who still have N E ≥ 20 after this refinement. First, we use the T-statistic to test whether the mean citation impact of an editor's article set is significantly different from 0; the color of each data point shows whether the T-test indicates that z E is significantly above 0 (cyan), below 0 (orange), or not significantly different (grey). This test returns 210 editors with z E > 0.1 and 173 editors with z E < −0.1 that have corresponding T-test p-value less than 0.1. Second, we find no significant relation between the C E and n E variables. However, as the scatter plot indicates, there are three striking outliers when all three variables are considered together, and two of these three editors are top-10 editors -Vladimir Uversky (rank r = 1) and Matjaz Perc (r = 7) -and the third, Andrzej Slominski, is the 41st most-active PLOS ONE editor. These anomalous outliers obtained several hundred citations each from the article's they oversaw (C E ), more than 10 times greater than the average C E = 8.6 citations.
Are these levels of editor citation remuneration unreasonable or just the result of untiring service? To address this question we analyzed the complete career publication records for each of these 3 outlier editors using data from the Web of Science. Differing citation rates for articles under the influence of each editor compared to articles not under their influence should signify an underlying self-citation strategy cloaked as editorial service. To this end, we separated the citations received by each anomalous editor into three groups -citations derived from: (i) the set of PLOS ONE articles handled by a given editor (indicated by red); (ii) the editor's own articles (i.e. traditional self-citations, indicated by yellow); (iii) the set of citing articles not belonging to group (i) or (ii), denoted as "other" (grey). Figure 5(D-F) shows the mean citation rate for articles in each group for each anomalous editor. For each anomalous editor we also selected a second active PLOS ONE editor from the same research area and calculated the corresponding citation rates from their complete publication records. By way of example, V. Uversky cites his own work on average 12.4 times in each of his publications, while "other" researchers typically cite his work 1.7 times per article. Using the citation rate by "other" researchers as his baseline, then V. Uversky self-cites 643% more than the average article that cites his work; this excessive self-citation rate is also observed for the other two anomalous editors. Within the set of PLOS ONE articles overseen by V. Uversky, we calculate an average rate of 2.3 citations per article, which is 39% more than his baseline citation rate; this was the smallest percentage excess for PLOS ONE edited articles observed among the three anomalous editors.
To assess whether these excess citation rates are abnormal for PLOS ONE editors, we compared each anomalous editor with a comparable editor from the same discipline and with relatively high total editor activity: Y. Moreno (N E =93 articles), J. Brandner (N E =74), and D. Borchelt (N E =73). For each comparison editor, the citation rate for "other" articles and PLOS ONE edited articles are quite similar, whereas this is not the case for the anomalous editors. As further evidence of a self-citation end strategy, the PLOS ONE citation rate for the anomalous editors is on par with the self-citation rate of their corresponding comparison editor.
All together, it is rather clear that the scalability of editor citation remuneration within this megajournal can yield significant returns when the excess citations for edited articles are compounded by excessive editorial activity. This advantage could compound into even more citations due to the effects of reputation and cumulative advantage across the career [32,37,38]. Moreover, this analysis of editor remuneration only compares articles handled at PLOS ONE and does not include editor activity, not to mention referee service, at other journals. Upon manual inspection, we confirm that several of the extremely active editors simultaneously served on the editor or academic advisory board for various other megajournals such as PeerJ, Palgrave Communications, Royal Society Open Science, Frontiers and Scientific Reports, which is further cause for concern.

Discussion
We analyzed the largest journal in the world, whose transparent policy of listing the particular academic editor who accepted each individual article facilitates a large-scale analysis of editor bias in the manuscript peer-review process. Quite unexpectedly, our preliminary descriptive analysis revealed anomalous editor activity levels that cannot be explained by the distributed makeup of the editorial board, as comparison with two other distributed academic editorial boards (MS and PNAS) did not reveal such extreme outliers. It is quite possible that such variation in editorial activity and decision biases documented here occur in nearly every journal at hitherto imperceptible rates. Moreover, it is not uncommon for journals to have a single editor or small team of editors who are themselves academics. Rather, the principle cause for concern raised here is that megajournals that lack editorial board oversight thereby harbor an environment in which individuals could in principle scale efforts to extreme levels with significant net effects.
Because PLOS ONE employs acting academics, the double role as gatekeepers and producers of knowledge is primed for conflicts of interest. As such, there are two clear incentives for coordinated editor-author activity -power and citation remuneration. Research shows that when the acceptability of misconduct increases gradually in power-driven environments, that a "slippery-slope effect" [7,8,39] may facilitate the spread of misconduct, which may be inevitable even among individuals who initially had good intentions. Scientific actors in gatekeeper positions may be particularly susceptible to subtle forces of misconduct, because in addition to being a process mediated by negotiation, the information concerning the review process is tightly concealed. Ironically, instead of protecting the system, this lack of transparency may harbor the emergence of author-editor strategies for "gaming the scientific system".
Against this background, we developed various methods for detecting editor anomalies by analyzing the longitudinal development of the entire editorial board comprised of nearly 7,000 editors. We started with a descriptive approach, focusing on the most active editors, ranked according to the total number of articles N E . Among this prominent set we ob-served a wide range of mean acceptance times, ranging from ∆ E = 175 to as short as ∆ E = 56 days. Not surprisingly, and not upstanding to their service, several of the editors with the shortest ∆ E were among the 10 most active editors. For example, on average, new articles edited by the most active editor, Vladimir Uversky, appear every 3.2 days in PLOS ONE. This extreme activity is attributable to the the relatively short acceptance time of ∆ E = 77 days for his articles, whereas the editor average is 130 days. The variability in acceptance time within each editor's profile was also high (see Fig. S3). One potential explanation for the prevalence of such short review times is the transferability of reviews from other PLOS journals, which can then be used in the PLOS ONE editor decision process [5]. Journals that have similar transferability policies should monitor its use, in particular the frequency in which it results in extremely short acceptance times; by way of example, roughly 1 out of every 200 articles accepted by PLOS ONE were received and accepted within 7 days.
We also compared the annual activity, defined as the average number of articles overseen per year n E for a given editor, between 3 journals: Management Science, PNAS, and PLOS ONE. Our analysis of the distribution of n E and the standardized variant S E shown in Figure 1 points to unreasonably high activity among the most active editors at PLOS ONE. For example, the most active PNAS editor oversees 22 articles per year on average, and we count 85 editors at PLOS ONE that exceed this activity level.
Because editors have fixed time resources, it is likely that higher editor activity correlates to less time spent evaluating each article. Indeed, our data does not measure the actual attention given by the editor and referees to each article. Nevertheless, due to inefficiencies in handling multiple tasks at once, it is reasonable to expect that editors require increasing marginal effort per additional article being overseen at any given time. Thus, trends in editor quality judgement and acceptance times are attributable to the overload associated with excessive activity. To this end, we leveraged the longitudinal aspect of editor careers using model specifications with editor fixed-effects to control for unobserved time-independent factors. Our goal was to explain variation in editor behaviori.e. manuscript quality judgement and decision time -with respect to a plausible mechanism -coordination with repeat authors in lieu of citation remuneration -which we hypothesize to be stronger among the extremely active editors.
In the first model we analyzed trends in the citation impact of articles overseen by editors -answering the questions: does quality judgement change over time, does it depend on social relations, and is it more extreme among the 10 most active editors? First, a significant trend across the career would indicate that editors' ability to evaluate article quality changes over time. A positive trend would be consistent with increased quality assessment, i.e. learning how to identify high-quality research and reject low quality research. And a negative trend would be consistent with lower commitment to editorial service, e.g. being overwhelmed by increasing workload, becoming apathetic, or possibly an increased susceptibility to social pressure. Our results indicate that citation impact decreases over time, meaning that the negative factors outweigh the pos-itive factors. By way of example, consider an editor starting at PLOS ONE in 2008 whose accepted articles were initially of average citation impact - Figure 3(A) illustrates how in year 7, his/her accepted articles are likely to be 31% less-cited than those from his/her first year of service. Moreover, we found that this negative trend was pronounced if there was a significant social tie between the editor and authors, or if the editor was one of the 10 most active editors. Together, these results point to the diminishing quality of research entering the literature as a result of poor editorial board management.
At this point it is worth discussing alternative explanations and limitations of our data and methods. First, we lack information concerning the quality of the referee reports, which could manifest in editor's receiving poorer advice over time. Second, establishing social ties between author and editor was based on statistical arguments, since it is unfeasible to account for all possible social relations and the variation in their strengths. For sake of simplicity, we indicated social ties using an indicator variable R A,E = 1 that tags articles containing at least one author that published two or more times with a given editor. In small research areas, with lower citation rates and lower representation among the editorial board, it is possible that there would only be a single editor with expertise in the area, making repeat interactions more likely. However, with an editorial board size of nearly 7,000, it is hard to imagine this scenario being the rule rather than the exception. Nevertheless, it is possible that other spurious correlations of this nature could explain the significance of our regression results with respect to the variable R. We investigated this possibility using a "placebo" randomization scheme, the results of which demonstrate the robustness of our method of identifying "repeat authors", as they do not represent a spurious configuration (see Fig. 4).
In the second model we investigated variation in article acceptance times and its relation to author citing behavior towards the editor and repeat authorship. We found that articles having a larger fraction of citations citing the editor's research were likely to be accepted faster. Figure 3(B) indicates a 1 week difference in mean article acceptance time between an article citing none of the editor's research and an article with 10% of its references citing the editor's research. Moreover, articles exhibiting social tie between editor and author were found to be accepted 9% faster, corresponding to roughly 10 days for the average article. The most plausible reason that an author would cite the editor's work is because editors are, in principal, appointed due to their prestige within the community. Moreover, as the editor continues to publish research, then the number of possible publications to cite also increases over time. Nevertheless, we provide several lines of evidence that editors' behavior correlates with citation remuneration, an analog to the more common "self-citation" [34,35]. The literature on self-citations offers various explanations for the observed frequency which ranges between 20 to 40% of references [35], such as signaling prestige in cross-disciplinary mobility [40], as well as bias towards citing one's past collaborators. To the same extent, an additional explanation for the negative relation between citing the editor's work and acceptance time, aside from strategic nudging, is the possibility that editors are better able to assess research quality, as well as obtain reliable reviewers, if the article is closer to their field of expertise. However, unlike traditional forms of self or reciprocal citation rigging, the incentives to sway the editor decision are significantly larger. The difference in acceptance times for repeat authors provides further evidence that citations are indeed an effective form of remuneration [34].
If some editor's are truly privy -and responsive -to such nudges, the follow-up question is how much could one really gain by playing this market? Because it is extremely difficult to measure and interpret the context behind individual citations, we appealed to the dataset size to look for evidence of variation in editor citation rates (f E ) depending on whether the citations arise from repeat authors or not -in principle, there should be no observable difference. Figure 5 summarizes multiple lines of evidence that indicate that the anomalously extremely active PLOS ONE editors have leveraged the high-throughput volume and weak PLOS ONE editorial board oversight to their own benefit. For example, by comparing the citation rate for articles with and without repeat authors, we arrive at a lower bound for the impact of citation remuneration in the hundreds of citations. To some this may seem like a small amount, but this represents revenue from just one source, not including editorial board service at other journals as well as gains from referee service.
We provide additional evidence of citation remuneration on the part of three editors with anomalous activity levels identified in Fig. 5(C). By analyzing their complete publication records we are able to compare the self-citation rates for the articles in PLOS ONE they oversaw to the baseline citation rate for articles that they did not oversee. Comparing their self-citation rates with other PLOS ONE editors from the same research area, we provide several lines of evidence that the anomalously active editors are pursuing strategic selfcitation strategies that include leveraging their editorial power.
PLOS ONE has an enormous impact on the production of scientific literature and the connectivity of the science citation network [6]. Given the implicit constraints in monitoring and managing such a large and distributed organization, it is not unlikely that a small set of individuals would take advantage of the system. Along these lines, several of our findings have plausible explanations that range from editor apathy to misconduct on the part of authors, editors or even both in coordination. Thus, our study demonstrates why large megajournals should record, monitor, and embrace transparency, and to make sure the incentives for editor service do not introduce unintended conflicts-of-interest. As science continues to grow, these conflicts-of-interest may become more difficult to avoid, e.g. in large teams or a large journal, due to the difficulty in monitoring individual activities and managing incentives in distributed operations [13]. As such, it is important to develop methods for identifying anomalous behaviour, and to sanction these cases after thorough internal review. While manuscript editors certainly deserve credit for their service to science, it is important to address the possibility that some editors may have more covert intentions underlying their excess editor activity. We conclude with some policy recommendations.

Conclusions
Megajournals represent a rapidly expanding market, and much attention has been paid to the potential impact of the article processing charge (APC) "pay-to-publish" model, as well as the strain on the available pool of referees due to high article throughput [3]. However, less attention has been paid to the management of their editorial boards. Our study shows that megajournals should implement additional levels of oversight in an effort to reduce the decline in editor quality judgement and to prevent editor-level misconduct. A good starting point may be the two-tiered editorial board system implemented by the journals Proceedings of the National Academy of Sciences and Management Science, in which a rotating body of managing editors oversees the board of article editors.
Also, despite the plethora of researcher metrics being developed and refined in order to evaluate individual scientific achievement [22], much less attention has been paid to the scientific actors at the other end of the negotiation table -the editors who serve as scientific gatekeepers. Holding the power to accept or reject a scientific article has obvious ramifications for the authors of the manuscript. Even more, this decision has the profound effect of determining whether or not their conclusions enter in to the corpora of scientific literature, and thus, the cannon of scientific knowledge. As such, in addition to maintaining high standards for the sake of impact factors and the like, it is crucial that journals maintain high standards for the sake of science. If not least because the advancement of knowledge is cumulative -building and relying on what has been previously published. By allowing publication standards to diminish, the deluge of newly published research may clog the system with faulty results, if not fraudulent misinformation [24,25]. With the democratization of online publication in the general sense, it is not implausible that the same prevalence and ease of misinformation spreading in the digi-tal publication world [41], where the role of editors has been largely diminished or eliminated, could also emerge within science. Thus, it is important to highlight the value and responsibility that editors have in maintaining the integrity of science. Accelerated forward by the era of high throughput megajournals, it is important to establish transparency standards for both sides of the review process, e.g. by making openly available Peer Review Evaluation metadata.
To this end, all journals should follow the lead of PLOS journals by publicly recording the specific editor overseeing the review of accepted articles, e.g. printing this information on the article cover page. This will facilitate the transparent evaluation of editors activities and can readily be justified on account of transparency, sanctioning, quality management, and responsible science. As gatekeepers to our knowledge base, science editors have a pronounced responsibility to remain unbiased. Our results, however, indicate that social biases are nevertheless predominant features despite best efforts. The thought of being held accountable by digital fingerprints may be an effective nudge in the right direction.
And finally, electronic-only journals which do not have volume restrictions should nevertheless consider placing restrictions on the number of articles an editor can oversee at a time and per year. In addition to discouraging editors from taking advantage of their power, it would also encourage higher quality standards for accepting articles. By implementing such editor policy changes at PLOS ONE, it would certainly make for an interesting policy experiment, providing an additional opportunity to observe shifts in editor behavior, and possibly strengthening the case for linking the observed behavioral trends to editorial board mismanagement and serial misconduct.

Article subject area classification
It is well known that citation rates are affected by discipline-dependent factors. Indeed PLOS ONE is comprised of articles from a range of disciplines, and is classified by WOS as a "Multidisciplinary" journal. Thus, we were careful not to blindly pool the citation impact measures from all articles together. Instead, we methodically separated the articles into subsets, so that the relative citation difference between two articles is less biased by disciplinary and even sub-disciplinary factors, such as research community size and innovation level. As a result, we are able to more accurately estimate differences in citation impact, used here as a proxy for scientific impact.
We grouped the articles by subject area (SA) based on the internal PLOS ONE classification subject area classification system derived from a controlled thesaurus of nearly 8,000 keywords. To be specific, we started with the keywords appearing on the webpage of each article A. Nearly all articles have 8 keywords per article, with only a handful of articles containing less than 8. PLOS ONE also has an article-classification scheme which is used to group articles for comparing article visibility.
While these keywords are helpful for classifying articles, they are not fully sufficient. Instead, PLOS ONE implements a 2level classification system which is evident using the "page-views" applet on each article's "Metrics" page. By way of example, the article with DOI 10.1371/journal.pone.0000112 is classified primarily as "Biology and life sciences", with 3 subclassifications (Evolutionary Biology, Genetics, and Population Biology). At the core of this classification system are 10 top-level groups: ranked according to their empirical frequency, they are: (i) Biology and life sciences, (ii) Medicine and health sciences, (iii) Physical sciences, (iv) People and places, (v) Social sciences, (vi) Engineering and technology, (vii) Computer and information sciences, (viii) Ecology and environmental sciences, (ix) Earth sciences, (x) Science policy.
Thus, a fundamental problem is the fact that articles have multiple subclassifications, and so there is no 1-1 correspondence between a given article and a single top-level classification. A second problem is that not all articles have the classification data, despite the fact that all articles do have keywords. Thus, we developed a algorithmic method to classify articles into a small set of refined subject areas using only their keywords as classifier inputs. To be specific, we calculated the weighted bipartite network associating keywords and top-level classifications by aggregating the statistics for all publications with top-level classifications and keywords. In this way, we calculated a vector of 10 weights for each keyword corresponding to the 10 top-level classifications. Then, we identified the principal SA of each article by combining the weight vectors for each of the individual keywords, and choosing the SA with the largest weight. Take again the article DOI:10.1371/journal.pone.0000112 with the 8 keywords "Chromosome 4", "Genetic loci", "Centromeres", "X chromosomes", "Population genetics", "Chromosomes", "Sex chromosomes", "Alleles". As one might expect, these article keywords give the largest weight to SAs (i)"Biology and life sciences" and (ii)"Medicine and health sciences".
Applying this method to all articles, we found that the biomedical classifications (i) and (ii) are the most common first and second ranked classifications. Figure S3(A) shows the SA count histogram for all PLOS ONE articles, with 123,750 (87.1% of all articles) having "Biology and life sciences" as the principal classification, and none having "Science policy" as the principal classification. Contrariwise, only 17 articles had "Earth sciences" as the principal classification. To account for the fact that the majority of the keywords in the PLOS ONE thesaurus are related to (i) and (ii), leading to the disparity in the principal classification, we created an exception rule in order to better account for the second-ranked classification. First, if the principal classification was (i), then we instead used the second-ranked classification as the principle classification. This rule helped to classify more publications for SA (iii)-(ix), as demonstrated by the second count histogram shown in Fig. S3(B). As one final step to condense the SA classifications, we joined the groups (iv) and (v), (vi) and (vii), and (viii) and (ix), since intuitively, there is considerable overlap between these SAs. Thus, Fig. S3(C) shows the final refined distribution of articles across the 6 refined SA used in our analysis: the smallest refined SA is 6/7 with 533 articles and the second-smallest is 4/5 with 1839 articles over (1), shown for publications from 3 annual cohorts. Surprisingly, there is less substantial variation between the refined subject areas than expected. Nevertheless, for the sake of methodological completeness and robustness, we maintain the classification by refined subject areas throughout the analysis.