Step 1: Development of Basic Manuscript Element Allocation Matrix
The first step in using the proposed method is to divide the efforts invested for developing a scientific manuscript into the four basic elements: ideas, work, writing and stewardship. We will use a hypothetical example to illustrate this step. The example considered is roughly based on a journal article that our group recently developed (a few details are modified and fictitious names are used). The objective of the project was to characterize Deepwater Horizon oil spill (BP spill) related wastes collected from several beaches in Alabama. The team consisted of five members: a second year graduate student (Jim Johnson), a lab technician (Jack Norman), a post-doctoral fellow (Jill Jones), an associate professor (Janet Fonda), and a full professor (Clem Peter). Professors Peter and Fonda jointly developed the grant proposal that funded the effort. The project involved collection of field samples, analysis of the samples to quantify polycyclic aromatic hydrocarbons, analysis of the data, preparation of figures, and writing the manuscript. The lab work primarily employed standard techniques, but a new instrument, which required considerable tuning and calibration, was used to characterize several unique samples collected by the field team. After completing the first draft of the manuscript, the group discussed and divided the overall effort into: 0.2, 0.3, 0.35, 0.15 (or 20, 30, 35, 15 %) for the four basic elements ideas, work, writing and stewardship, respectively. These values were recorded in a spreadsheet tool (EXCEL) as weight fractions, instead of percentages, purely for computational convenience (see Table 1).
Table 1 Basic manuscript element matrix
It is important to note that these weight fractions are not fixed estimates; they can be dynamic and can vary for different projects. As the manuscript evolves, one could potentially revisit these numbers and adjust them, if the group felt it is needed. However, in practice, one would quickly realize that there is not much room for adjustments since the four element fractions should add to unity, an extremely useful mathematical constraint. Keeping track of such simple mathematical constraints is an incredibly powerful way to manage this problem and we will illustrate its unique power in the next section. Also, one could impose several other meaningful constraints (discussed below) on the relative weights of various elements that would thwart any serious revisions.
First, it is important to carefully assess the weight assigned to the first element “ideas.” Several ideas, especially the ones suggested in open forums such as group meetings or seminars, are primarily shared as technical suggestions; and no one really knows whether these suggestions are feasible ahead of time. Even great ideas require considerable amount of work and writing to bring to fruition. Therefore, in most cases, the weight assigned to ideas should be less than the weight assigned to work and writing which are the two most important elements. However, this is not a rule; it is just an empirical suggestion.
Secondly, the fourth element “stewardship” should always get the lowest weight since it only makes indirect contributions. This, perhaps, should be considered as a rule. It is important to note that most guidelines, including the original ICMJE (2010) method, do not give any credit for resources, funding, and research management. The proposed approach is flexible to accommodate these conventional guidelines; if one chooses to follow them, they should simply assign zero to the stewardship element.
With some of these constraints in mind, good initial estimates for the four basic elements are: 0.25, 0.30, 0.30, and 0.15. These are fairly realistic estimates for any standard article where data and writing will be the two most important elements. With these initial estimates, any team can discuss and calibrate the values to fit the needs of their own manuscript. It is important to include all potential authors in these discussions. Also, it is important to communicate with others in the team why they will not be recognized as co-authors. When we exclude potential co-authors we have an obligation to let them know about our decision well ahead of time. This is an excellent approach to avoid authorship conflicts.
Step 2: Development of a Draft Authorship Matrix
The second step is to develop a draft version of the authorship matrix. This step is an iterative process where the goal of the first iteration is to tease out all underlying problems related to authorship sharing. Step-2 should be started as an individual assessment process. The senior author (person who is willing to be the steward or guarantor of the work, it was Peter in this case study) should communicate with all potential authors and ask them to estimate their contribution levels. Jim Johnson (graduate student) is the youngest author in our group who did most of the field work, analyzed various samples, and also contributed to writing. When Peter informally asked him to estimate his contributions, Jim was quick to say that he appreciated others help, but he did most of the work and hence should get at least 50 % of credits for this paper. Note he automatically focused on credits, a natural instinct. As a second step, Peter sent a follow-up email reminding him about his estimate of 50 % and asked him whether he could itemize his contributions to each of the four basic elements. Jim replied quickly and his estimates were 30, 80, 60, and 10 % for ideas, work, writing and stewardship, respectively. These numbers were entered into the draft matrix and was weighted based on respective element fractions and the net contribution made by Johnson was estimated to be 52.5 % (the actual computation is: 30 %*0.2 + 80 %*0.3 + 60 %*0.35 + 10 %*0.15 = 52.5 %). Interestingly, the itemized estimates yielded a value fairly close to his rough estimate of 50 %. The above process was repeated for all five researchers and the estimates are summarized in Table 2.
Table 2 Draft authorship matrix
The first observation to be made from these data is that the three active contributors (Johnson, Jones and Peter), who were fully engaged in the project, felt that they contributed to about 50 % of the project. The other two passive contributors (Norman and Fonda) felt that they contributed about 25 %. Based on several such surveys we have found that these are typical estimates most researchers (both young and experienced) would assign when their names appear on a multi-author article with about five to six co-authors. The problem is that these estimates violate “mathematical balance” constraints! Note, in Table 2, the sum for each column is well over 100 %, with a net total of 206 %; this implies that the group has contributed to two articles! This sort of overestimation routinely occurs in the current model when each author claims his/her own share of credit on their CV, annual review, or promotion application. We just do not have an unbiased approach to document this overestimation problem. This problem occurs because we currently do not have a process to evaluate the relative worthiness of our contribution in light of other’s contributions. For example, after reviewing Table 2, graduate student Johnson quickly realized that when he claimed that he did 80 % of work he also implicitly judged that his four colleagues, who were also equally engaged in the project, did only 20 % of the work, which was not true in this project effort. One of the useful outcomes of the proposed method is that it will help demonstrate such inconsistencies, which can be used to discuss the importance of team work and compromise. Having this information on paper will help educate the team to develop a sense of mutual respect and camaraderie.
Step-3: Finalizing the Authorship Matrix
The next step is to discuss these draft estimates and negotiate as a group to balance all four elements. The best approach is to adjust each element (or column) to satisfy the associated mathematical balance constraint. If required, one could complete a more detailed assessment by further dividing the element of interest into sub elements. Such divisions could be particularly useful for complex elements such as “work,” which might involve multiple tasks. The power of the proposed framework is that it can be refined into a cascading set of sub-matrices to analyze such complex elements. To demonstrate this process, first we will divide “work” into three sub-elements. Note one could use any number of sub-elements; here we divided work into the following three sub-elements: field work, lab work, and data-analysis work. We then followed a step similar to Step-1 to estimate the fractional weight for each of these work elements and these estimates are summarized in Table 3. The next step is to create a work-load allocation matrix (which is similar to Step 2) where each individual researcher was asked to estimate his/her own contribution to all three work elements. These estimates were agreed upon as a group and weighted with appropriate fractions to develop a balanced work allocation matrix shown in Table 4. We can now use these balanced estimates to revise the work element in the authorship matrix.
Table 3 Basic work element matrix
Table 4 Work load allocation matrix
Note that the development of sub-matrices (shown in Tables 3, 4) is an optional step, which can be skipped if one can directly formulate the final version of the responsibility matrix by negotiating the numbers as a team to satisfy all the balance constraints. In this case study, we adjusted the “work” element using the cascading sub-matrix method, whereas the other three elements (ideas, writing and stewardship) were adjusted by direct negotiations. The final version of the full authorship matrix is shown in Table 5.
Table 5 Final authorship matrix
The authorship matrix provides all necessary information for deciding the rank of an author. Based on these data, Johnson will be the first author, Jones the second author, and the senior author Peter will be the third author or he could invoke the practice of noblesse oblige and serve as last author, depending on his personal preference. If there is a tie, we believe senior personnel (in this case Fonda) should be placed behind the junior author. This matrix methodology solves the author order problem without any ambiguity. The person who has contributed to all four elements and has considerable responsibility for the element “stewardship” (Peter, in this case) should serve as the guarantor for the article. He/she should also oversee the construction of authorship matrix and communicate with all potential authors about their respective responsibility levels.
The final issue to be addressed is what should be the minimum total contribution (MTC) below which one would not qualify for recognition as a co-author. A good rule of thumb to guide this process is every co-author should contribute a minimum of 50 % of the average contribution. This rule can be defined using the mathematical formula:
$$ {\text{Minimum}}\,{\text{Total}}\,{\text{Contribution}}\,\left( {\text{MTC}} \right) = \left( {0.5*100\% } \right)/{\text{n}} $$
where n is the total number of qualified co-authors who have contributed for three or more basic elements. The important point here is that the cut-off level should depend on the total number of authors; for example, while it is reasonable to contribute 5 % on a large collaborative ten author article, the same 5 % might not be adequate if it is a focused article with just two authors. The proposed rule of thumb helps capture this relationship. Using the above formula, MTC cut-off level will be 16.7 % for three authors (n = 3); 10 % for five authors (n = 5), and 5 % for 10 authors (n = 10). Since these are rules of thumb estimates, some level of personal judgment should be exercised when using these estimates. The cut-off MTC level for the current case study is 10 %; both Norman and Fonda have contributed 9.3 %, which is quite close to the cut-off level and hence should qualify for co-authorship (note, one of the senior author’s numbers can be adjusted to maintain the overall balance). The final authorship data can be presented in journals either in the detailed matrix format shown in Table 5, or can be rounded off and condensed into a concise summary format shown in Table 6.
Table 6 Authorship contributions