First things first, a little backstory:
Sometime between the Paleocene and Eocene epochs, there was a mysterious, sudden, dramatic rise in global temperature. This moment in time was known as the "Paleocene-Eocene Thermal Maximum", shortened into "PETM". In just 20 to 50 millennia, the temperature rose by five to eight degrees Celsius, and this heatweave persisted for another 200 millennia (that's just the mean estimate.)
While its impact on terrestrial plant and animal life is well-known, the focus of the question is on how the PETM impacted the marine ecosystems. The warmer the water's temperature, the less oxygen it can hold, so the equatorial waters--which may have been 36 degrees Celsius--were absent of the plankton vital for oceanic food webs. And since water has a low albedo, it absorbs carbon dioxide rather than reflects it. And in an episode as CO2-rich as the PETM, the oceans absorbed so much of the greenhouse gas that they had become acidifed. That, in turn, depleted the supply of carbonates, which many animals relied on to build shells and other structures. Indeed, fossil remains of coral reefs dating from the PETM to several million years afterwards were rare, and anywhere between one-third and half of all the deep-sea species of foraminifera (tiny, planktonic lifeforms) went extinct. Finally, the warmer waters also affected the arrangement of a particular layer called the lysocline:
The lysocline marks the depth at which carbonate starts to dissolve (above the lysocline, carbonate is oversaturated): today, this is at about 4 km, comparable to the median depth of the oceans. This depth depends on (among other things) temperature and the amount of CO2 dissolved in the ocean. Adding CO2 initially raises the lysocline, resulting in the dissolution of deep water carbonates. This deep-water acidification can be observed in ocean cores, which show (where bioturbation has not destroyed the signal) an abrupt change from grey carbonate ooze to red clays (followed by a gradual grading back to grey). It is far more pronounced in north Atlantic cores than elsewhere, suggesting that acidification was more concentrated here, related to a greater rise in the level of the lysocline. In parts of the southeast Atlantic, the lysocline rose by 2 km in just a few thousand years.
So here are the points of departure:
- The Paleocene-Eocene Thermal Maximum did happen at the same time as OTL and at the same speed, but it lasted three to four times longer, which lifted the lysocline to a depth of one mile and wiped out the coral reef ecosystem as well as 25% of other marine species.
- An additional element is the development of the forest walls of fully marine trees or "megamangroves", trees so tall that they support themselves on buttress roots rather than the familiar stilts. These walls are currently cosmopolitan at tropical and temperate latitudes and stop at a maximum depth of 250 feet. Even though they did debut during the PETM, they did not become this formidable barrier until later in the Eocene (41-37 ma).
And now, using our knowledge of shark genera or species that were around to witness the PETM, could they survive a longer PETM coupled afterwards by the natural building of walls of exclusively marine trees?