Authorship for multidisciplinary collaborations
First, the collaborators should be commended for discussing co-authorship and authorship order issues early in the research project. As a practical matter, these discussions can prevent bitter disputes later. These discussions are necessary in multidisciplinary collaborations because different disciplines have different authorship practices. I like the collaborators’ agreement, to follow the standard authorship conventions of the discipline of the journal in which a manuscript is submitted. I assume that the project will result in several manuscripts, which could be submitted to journals in different disciplines.
One alternative expectation is to choose the conventions that would benefit the most junior members of the research team.
For further advice about co-authorship and authorship order, see any standard reference on responsible conduct of research.