Most ancient species exists?

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In aquaria they may live for a long time but they have buoyancy problems (they tend to float at the top) and problems producing new shell (the new shell is discolored, black and malformed). There are no known solutions to these problems. Only two places have ever had fertile eggs laid successfully in captivity; Waikiki Aquarium and an aquarium in Japan. A third aquarium in Austria may have also succeeded but I have not been able to validate this report. Nautilus eggs have never been found in the wild, no one has ever raised a hatchling to maturity in captivity. For these reasons they are not, in my opinion, a good pet choice for home aquarists. This is one of the reasons that I have chose to not write a popular article on their care in captivity.

taken from here
 
An LFS down the street from me has a Nautilus. They are so cool.
 
The nautilus is an interesting ancient creature with predecessors reaching 30+ft long and/or 10ft+ in diameter. These were the ammonites, baculites, and belemnites. Interesting topic that should have it's own thread instead of derailing this FISH thread.
 
sharks hands down

Not even close. Sharks actually have advanced evolutionary traits (like advanced eyesight, endothermic capabilities, electrical field sensitivity, advanced olfactory senses, moveable mandibles, etc). They come from an ancient order. But, even those fore-runners were more advanced than amphioxus, chemarae, hagfish, lampreys, and the like.
 
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