Do note however that many times the first author is not the principal investigator (ie the person that has the funding for the study and is often tenure track faculty) but is often a graduate student or a post-doc. The principal investigator may be in the middle or even at the end of the author list. Thus just excluding first author self-citations is probably inadequate. The chances are high that a grad student or post-doc is going to cite their adviser's previous papers.
That’s only true in some areas (e.g. some biological fields). In other areas (e.g astronomy or much of physics), it’s decreasing order of contribution. In mathematics, the author list is usually alphabetical.
It is also traditional that the first author, in addition to doing the most of the scientific work, takes on most of the writing He/She also edits together the various other authors contributions.
