The mass appearance of ammonite fossils in lower Jurassic strata suggests that, like the nautiluses, the ammonites were superbly designed to extract maximum oxygen from minimal dissolved volumes of the oh-so precious gas. They do so because of a powerful pump gill system that was capable of moving sufficient volumes of low-oxygen water across the gill surface to yield the necessary number of oxygen molecules from seawater to live. To formalize this:

What support is there for this hypothesis that basal Jurassic ammonites were low-oxygen specialists? We know that early Jurassic ammonites are found in great numbers in otherwise animal-free strata, and we know their body chamber length increased at this time. Unfortunately, ammonite soft parts are still unknown, and we do not know if they had four gills (like Nautilus) or two (like modern-day squid and octopus). But from the very unstreamlined shells of the majority of early Jurassic forms, it is clear that these animals were not fast swimmers. It is far more likely that they floated slowly or swam gently near the surface, using their air-filled shell like a zeppelin. Their pump gill forced huge volumes of water across their lungs in short periods of time, allowing them to live where most animals could not.

The ammonites went on to stay very common right up to the end of the Cretaceous. My work in Spain and France in the late 1980s showed that they were killed off, very suddenly, as a consequence of the Cretaceous Chicxulub asteroid. But by the end they were living in higher-oxygen waters and their shapes changed subtly, allowing a more active and vigorous life style.