Are there any publications that explain the origin of conventions of authorship order by field?
I have found two works that I think are interesting and relevant.  

First, there is a sequence of three papers by Beaver and Rosen from 1978-79 on the history of scientific collaboration: "Studies of Scientific Collaboration" (Part I, Part II, Part III, unfortunately all paywalled by Springer).  These articles document a relationship between co-authorship and "professionalization" of science, noting that although co-authorship has a long history of equal relationships, it surges when it becomes tied to access to facilities, money, and power particularly as judged by peers within the scientific community.  

Ubiquitous co-authorship only emerged in the mid-20th century, and given the scientific economic environment in the US and Western Europe, there seems to be a plausible relationship to the three main authorship traditions that have been observed:


Biomedical research is very dependent on judgement of scientific peers, and thus would be natural to have the highest co-authorship and most complex and hierarchy-driven interpretation of author order, distinguishing "primary contributor" (protege) from "senior author" (patron).
Mathematical research, on the opposite end of the spectrum, requires little in the way of funding or access to resources, and thus has the shortest co-author lists and most egalitarian traditions for interpreting authorship.
Engineering research, although heavily funded and often strongly dependent on access to facilities and equipment, is less dependent on peers and more dependent on providing near-term results to government or industrial patrons, and thus it is unsurprising that it ends up in the middle state.


For comparison, then, we may consider the second paper, "What is authorship, and what should it be? A survey of prominent guidelines for determining authorship in scientific publications", a 2009 comparison of 10 different society authorship policies, which range from NIH setting forth a biomedical canon in which only the "corresponding" author really counts to the American Statistical Association, which says that the convention chosen for author order should be explicitly explained (no mathematical society is included, unfortunately).

Now all of this might be snapshots and "just-so stories" that are not the actual causality and history, but it's at least an interesting starting point for interpretation and investigation.