Resolving a dispute for first authorship where the value and demarcations of individual contributions are hard to identify

Question

My co-author and I (both PhD students in a university) have been working on a large-scale simulation project for the last 1.5 years. This is what we agree upon.

1. I came up with the idea.
2. We took an existing open-source code (under MIT license), forked it, modified it suitably according to our needs, fixed some bugs improving and enhancing it in many ways. The split of contribution to this aspect is fuzzy here. We gave our contributions back to that project which has been accepted and our names acknowledged as contributors in the readme.MD file in the project's github repository. My co-author is listed first among the 2 contributors and I did not have any objection to that.
3. Having made the existing code good enough for our purposes, we started the stage of adding new codes. Set up of the simulation infrastructure was mostly done by me. Say 65% to 35% split with my co-author. I explored a lot of possibilites and techniques.
4. I came up with the idea of application of an existing method into this project to speed-up the code. This worked and was successful. 100% my contribution as both agreed. It provided the speed, but was not "strictly" necessary. But is a practical addition, otherwise results would not arrive in reasonable time.
5. I derived 80% of the equations in the paper, including a few critical ones.

At this stage, we had a written (email) agreement on the authorship, and I was agreed as the first author with my colleague as the second author.

Now, some problems happened.

• Due to a set of official circumstances (pre-planned mobility for another project at another university), I had to temporarily leave the project for 40 days. I required visas for this country, whose paperwork set me back by another 15 days or so. It was not explicitly agreed with the co-author what that would mean to the authorship or the work split or any other aspects of the work. The mobility money would have expired if I did not take it and our common (and sole) supervisor knew this, and still approved my trip.

• My colleague continued to work on the project, which already had a definite framework in place prior to my temporary absence.

• Hoewever, the colleague started facing several numerical issues and convergence failures. Although the code infrastructure and numerical methods remained the same, they had to tweak a lot of numerical parameters to obtain the result. This took a considerable time.
• My colleague started writing the draft of the paper. I typed all the new equations in the main text of the paper (about 25). My colleague typed standard equations that go into the appendix.
• Now, this is where it gets more confusing. My colleague typed 80% of the text of the paper.
• They also interpreted the results.
• For figures in the paper, I did 2 illustrations (artwork), one of them a full-page flow diagram of the entire methodology. The other is the graphical abstract of the paper.

A dispute came about just before submission. However, we decided to retain the status quo of the authorship order as agreed originally. The submission got rejected.

I put in the groundwork for an alternate journal suitable for the manuscript, which was reviewed by this co-author. I did a complete re-factoring of the manuscript over a period of two weeks. We submitted this refactored version to the second journal keeping authorship order intact.

The second submission underwent peer-review, and came back with "major revision requested", one of which involved simulation of the model with a major change in a critical parameter (that changes the results substantially).

Our supervisor allocated this task to me, which took exactly 2 weeks to complete. One of the comments by the peer-reviewers was to shorten the length of the paper drastically. This time, our supervisor did all the refactoring, and now we have the revised manuscript with updated results and rebuttal statement.

However, my co-author stepped in on Friday (8 days before re-submission deadline) and claimed that he should be the first author.

Our supervisor is caught in a dilemma, as there is no clear way to demarcate and judge this. Our supervisor requested both of us to go through our university's arbiter who will interview us independently for 1 hour each.

It should also be mentioned that I gave up first authorship to the co-author to a couple of small conferences and poster presentation. Without my express verbal or written permission, my co-author presented two posters (which they created themselves) with their name as the first name and mine as second, and they had the travel money for the same. I was silently okay with this, as our work gets more publicity.

Clearly, I feel entitled to first authorship for this journal. I wonder if the community agrees and if so, how may I present the case?

Answer 1

Simply, add a footnote above your names, or above the paper's title, and in the footnote write something like: the first two authors have equal contributions. Yes, it is something that I have seen before. It is also not really a big deal. People are judged by their skills and understanding in the interviews and thesis examinations.