It is important to note that "Communicated by" can mean a direct submission of a paper by a scientist who is not (in most cases) directly involved in the paper itself. It was designed as a way for established scientists to give a "leg up" to their younger colleagues by allowing them to circumvent the normal review process. This means you may have to give these types of papers a bit more scrutiny as a reader.
PNAS is the publication where I have most commonly seen "Communicated by" publications, but this feature was phased out in 2010:
Until July 1, 2010, members were allowed to communicate up to 2 papers
from non-members to PNAS every year. The review process for these
papers was anonymous in that the identities of the referees were not
revealed to the authors. Referees were selected by the NAS member.
PNAS eliminated communicated submissions through NAS members as of
July 1, 2010, while continuing to make the final decision on all PNAS
papers. (wikipedia)