Gary writes:
Are there any known organisms for whom their ancestries in the fossil record are largely incomplete? ...
Yes. It is very common to have simply enormous gaps in the record.
For example, the fossil record for bats is very poor. They are delicate, and do not fossilize easily. See
Chiroptera: Fossil Record at the excellent Museum of Paleontology (UC Berkeley). Extract:
Although bats are one of the most diverse groups of mammals today, they are one of the least common groups in the fossil record. Bats have small, light skeletons that do not preserve well. Also, many live in tropical forests, where conditions are usually unfavorable for the formation of fossils. Thus we know little about the early evolution of bats.
There are some fossils, and the page goes on to describe them.
An even more extreme example (for obvious reasons) is the fossil record of jellyfish. See
Scyphozoa: Fossil Record, also at UCMP. Extract:
Scyphozoans are extremely rare as fossils; their soft bodies, which are composed mostly of water, can only be preserved under very unusual conditions. A few possible but poorly known scyphozoans have been described from the Vendian (Late Precambrian), and scattered scyphozoan fossils are known throughout the Phanerozoic. Shown here, from the collections of the Senckenberg Museum in Frankfurt, Germany, is a specimen of Rhizostomites from the Late Jurassic Solnhofen Limestone of Bavaria, Germany, a body of rock which has yielded many fossils of exceptional preservation.
There are many other similar examples, and also cases of fossils in the record for which we have little idea of what they might be related to, either before or after. I don't have any examples immediately.
Cheers -- Sylas