Hi, okay, I literally created an account, because I could not leave this thread like this.
First of all: don't use Zootierliste for fish. It's the one thing that is actually bad. If you want to determine, whether there is an elasmobranch species present, fine. But not for numbers, breeding events or exchanges. First of all the teleost species are not accurate, don't get changed often enough and since most of the records are created by people visiting, are fairly inaccurate. Fish mainly have activity periods throughout the day and there are never all species seen when a person goes by one time. Tanks are also very complex these days and its so easy to just overlook an individual. Also, with aquariums backstage holding is so much more important. You can't raise the fish in the display tanks, so they basically don't know of any offspring, if it didn't have a press release.
I can only speak for European aquariums, but corals are well oragnised and are never sourced from the wild by now. Same goes for anemones and almost all jelly species. There are two species that are fairly new in European collections generally and I'm unsure where they got their founders.
Freshwater fish are by now almost exclusively bred. What you need to understand here is that the hobby aquarists are well-organised in unions and interest groups and so on throughout Europe. The center of that is actually Germany/Netherlands/Austria, but most countries have some sort of organisation. It's not difficult to get most species to breed and hobbyists have so much pride in the upbringing that they do a really good job. Since it's also easier then with salt-water fish, it's good business and a handful of professional dealers offer many tank bred animals (often declared as ENZ (eigene Nachzucht, the German term for self-bred, which is just the established way.)) There is quiet the healthy exchange between public aquariums and hobbyists, especially through citizen conservation projects. For example all Zoogoneticus tequila (extinct in the wild) that are in aquariums came through a privately organized studbook of sorts.
Now for elasmobranchs, thats a different story. Many species are already successfully bred and raised, like zebra sharks, eagly rays, blacktip reef sharks, and especially the smaller species (bamboo shark, masked rays, etc.) Some species still pose a challenge, because either the breeding cue wasn't identififed yet or raising the offspring poses a challenge. So it is possible that aquariums actively decide to catch new animals once they figure that out to increase the number of founders and genetic diversity.
Now for the most difficult part: The reef fish. This is a big issue, but it's completely different than what you might expect. Many species actually reproduce, but are never raised. First of all, it's very difficult to obtain the spawn from the big display tanks, since the life support systems (filtration) are designed to remove organic matter before it spoils the water. And gametes and larvae are organic matter. Most of these larvae are also planctonic. It's incredibly difficult and time consuming and unpleasent to look at. I once worked for a public aquarium, where we really wanted to do that because the species that spawned was super in demand, but we would have had to raise the ticket prices by 200%. For something people can't see and don't care about.
There are a few companies that are successful in breeding and raising these species. In Europe DeJong Marinelife is the very best example. They offer many tank bred species, while also catching individuals sustainably. The tank bred animals often cost about three times the price. But and here is the literal catch: it is possible to catch ornamental fish sustainably in the wild. It depends on skills, populations that you catch from and acclimatisation. But DeJong's philisophy is to offer only tank bred individuals within the next few decades. And they are getting close to it. They are also starting to breed groupers, elasmobranchs and so on.
Some marine teleost species are actually easy to breed and raise and are bred within the aquariums, but those are always the ones with some form of brood care, where the larvae then won't enter the filtration system.
I can of course not account for every aquarium within Europe, but the ones that are lead by scientific principles do a really good job. And just because they buy some species wild caught, doesn't mean it's unsustainable or harmful.
I will also take a wild guess how this question came up: there is a new "revelation documentary" out from the producers that also produced blackfish. The basic premise is that anyone that buys fish destroys the coral reefs.
