Hi Dale,
I am not a lawyer, and the following is not legal advice.
It's kind of complicated, and depends on what you really mean by
"compatible". In the sense described here:
https://en.wikipedia.org/wiki/License_compatibility then the
licenses are compatible.
As for the packages, pbdDMAT (and possibly pbdDEMO; I don't
remember) contain small amounts of modified code from R itself,
and so they retain the GPL >= 2 licensing.
pbdNCDF4 is a derivative work (in the copyright sense) of a GPL
>= 3 package, and so is licensed under GPL >= 3.
pbdSLAP, pbdBASE, pbdMPI, pbdPROF, and pbdADIOS are licensed under
MPL 2.0.
pbdPAPI is licensed under the 3-clause BSD license.
All of these licenses are compatible in the sense that they may
legally be combined into a single work. The license of the
combined work, as I understand, still depends on who you ask. The
FSF would probably say it would be GPL, but I suspect they would
make that argument for almost any R extension, and certainly any
which uses compiled code (see their opinion on interpreted
languages
https://www.gnu.org/licenses/gpl-faq.html#IfInterpreterIsGPL). I
have read opinions of other lawyers who have broader
interpretations; and indeed, I believe that commercial enterprises
such as Revolution Analytics could not exist if the FSF's opinion
were completely accurate. But as I understand, this issue has
never been taken to court, so I don't think anyone really knows.
Best
-Drew