The stereotype is that the deep ocean is where species go when competition in shallow-water environments is too intense. When extinction events happen, those in the deep ocean disappear, to be replaced by the next band of losers. Perhaps this entire paradigm is wrong.
The evidence frequently cited to support the traditional view is that fossil sites formed in shallow waters contain animals extinct in shallow waters, but which persist in the depths. But, what has been happening in the depths? It is hard to tell because fossil sites are rare that are reflective of life over time in the depths.
Recently fossils found in the Austrian Alps have helped illuminate this issue. Approximately 180 million years ago a segment of the deep sea was apparently teaming with life. This area was smothered by an undersea landslide, which preserved the contents. Plate tectonics did the rest and now the fossils are to be found in the Austrian Alps. How convenient. Several thousand fossils representing 68 species of animals have been excavated.
Many of the animals in the rocks still exist in the deep. This contradicts the accepted paradigm that the extinction in the deep sea is common, and species are replaced by refuges from the shallow-sea regions. Further, many of those found in the fossils represent the oldest known relatives of those in today's deep seas. [The study so far has focused on echinoderms (e.g., startfish, sea urchins, sea lilies) and brachiopods (animals similar in shape to bivalve mollusks, though unrelated).] This indicates that the animals went from the depths to the shallows, not vice versa. This conclusion is further supported by the finding that many of the extinct echinoderm and brachiopod families were known previously only from fossils in more recent shallow-water sediments.
Thus, the deep seas may be the nursery for those ultimately successful (at least for a time) in the shallow-sea environment, not the last hurrah for those species about to disappear.
The report can be found at: http://rspb.royalsocietypublishing.org/content/281/1786/20132624.abstract
A summary by the University faculty that undertook the study can be found at http://www.port.ac.uk/uopnews/2014/05/29/deep-sea-findings-overturn-previous-research/.