Tubulin should be present in spirochaetes, and should not have got
there by horizontal gene transfer. Some defects in cytoskeletal
function should probably form a circular gene linkage group.
Monophyletic groups contain all the descendents of a single common
ancestor. The prokaryotes are paraphyletic, because they exclude
eukaryotes, which are related to the Archaea more closely than Archaea
are to Bacteria.
Most of the genes from the proto-mitochondria of eukaryotes have
been lost. Sometimes this is complete, but in the case of several
essential genes, the genes have migrated into the host nucleus. Even if
the mitochondria are lost (if the organism becomes entirely anaerobic
and no longer requires them), it may retain the genes it gained from
its endosymbiotic partner. This is indeed the case for
Pelomyxa. Giardia does actually possess mitochondria,
but they have become so small and modified that it was not at all clear
that that was what they were. Other organisms possess hydrogenosomes,
which have the same sort of biochemistry and import mechanisms as
mitochondria, but have lost the genetic machinery (all the necessary
bits have been transferred to the nucleus).