publications - Why do people sometimes put authors with equal contribution in non-alphabetical order?

I've seen papers (e.g., in Science) where the first two authors are listed in non-alphabetical order, and yet there are asterisks behind their names to say that they contributed equally.

It seems strange to me, because if the two authors are in alphabetical order, then it could be that the first author contributed more or the two contributed equally, and this can be made clear with asterisks in the paper if it's the latter case. When they're in non-alphabetical order, however, if someone only sees the author list without seeing the paper, he/she will likely assume that the first author contributed most.

So my question is: Are there particular reasons why people do that? (This question is related, but I don't think the answers there get to my question.)

Answer

There are some requirements for funding¹², a degree³, tenure and similar for which literal first authorship counts. If one of the equally contributing authors gains an advantage from being the first author due to this while the other one doesn’t or has a smaller advantage, it can make sense to have the order deviate from the alphabetic one.

Another conceivable scenario would be that the first authors is well-known in the respective field and was made first author to attract a little bit more attention to the paper.

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^{¹ For example several faculties in Germany have schemes for evaluation and publication-based funding that assign special value to first-author publications. Some of those do not mention joined first authorships and do not make sense with multiple first authors, which indicates that first authorship is meant literal (example in German, search for Erstautor).}

^{² This journal, e.g., lists a handful of funding organisations that will pay the publication costs, if the first author is funded by the respective organisation. Joined first authorship is not mentioned. Even if this may be dealt with on a per-case basis, just flipping the first authors may be easier.}

^{³ For example, for a publication-based PhD thesis, it may required that the included publications be first-author publications (example, again in German) without the case of joined first authors being considered. While the latter may be allowed on a per-case basis, flipping the authors may be much easier and avoid a lot of bureaucracy.}