The arrival of hard parts and the increase of oxygen would have opened up host of unexploited niches, something that usually leads to evolutionary booms.
Hard parts require calcification. calcium is required for certain cellular functions so some of it was always in the environment. Storing it in a structural form (like our bones) is actually not a bad way of ensuring that the organism always has a readliy available supply, in addition to its protective properties. Calcium got in the water the same way sodium did, it washed in from dissolving and weathering of rocks that contained it. A few billion years of accumulation put enough in the water that organisms could utilize it.
I wonder if oxygen and hard parts were connected (I'm sure this isn't my own idea but I don't know where I got it
). Hard shells can cover much of an animal's body surface, so less surface is available for gas exchange. That would mean things like a clam's or a trilobite's shell (and the accompanying ecological opportunities) aren't possible till there's a minimum level of oxygen in the water (and/or the animal has a gill to absorb it more efficiently). Though this hypothesis doesn't cover small hard parts such as spines and stings.
Another postulate I've heard for the cambrian explosion is sex. As soon as you have sexual reproduction, the fact that each new DNA host is actually carrying a combination of alleles from two different DNA hosts (with a few mutations) rather than merely reproducing a complete set of alleles (with a few mutations) from one DNA host means that variation, and thus evolution, can work a lot quicker. That's also a reason why no such period of rapid speciation has occurred since - you only get to invent sex once.
My problem with sex is that AFAIK the Cambrian explosion is an explosion of (multicellular)
animal life. I don't know if there was a similar radiation in other eukaryotes at the same time but I've never heard of any. And clearly sex
predates animals because most eukaryotes have it. (It
could be that sex evolved more than once, though*. Then the question would be whether it caused similar explosions every time it appeared in a group of creatures.)
My favourite idea is a combination of ecology and development (which also allows a role for oxygen and hard parts). The boom in diversity could be due to a boom in complexity; once a threshold level of genetic complexity was present in development (eg. a number of front-to-back "compartments" of gene expression), all sorts of features - heads, sense organs, muscles, appendages etc. - could evolve relatively easily (this sort of compartmentation means that one compartment or group of compartments can be modified independently of the others. You could develop legs near the bottom of your sides without sprouting random legs all over your body).
Of course with more available body parts you have more ecological options. You could be a better burrower, an active predator, a sophisticated filter feeder etc. You could also get into massive arms races. More diversity --> more ecological interactions --> more pressure to evolve, and there's your positive feedback loop until the ecospace is full to bursting.
Development could also help explain why no (or few**) phyla appeared after the CE. When relatively complex bodies first originated there would be little competition in the realm of big, complex and motile things. You could tweak your basic developmental program, be not-so-great and still get along until you evolved a better version.
Once, however, a few lineages hit on a good program and radiated into the available niches, new (and likely not-so-great) experiments would've found it much harder to survive. After each mass extinction, there still would be complex survivors with a head start. Furthermore, these survivors would've built additional complexity on their basic phylum-specific developmental plans since the Cambrian, so it would've been even more difficult for
them to evolve a new body plan that actually works (try to rebuild a foundation with a house on top of it).
I would have to know more about development and body plans and stuff to know if this is really a good idea or just sounds fancy but at the moment I rather like it. All this, of course, assuming "phyla" represent something real about animals and aren't just random lineages like all others.
These authors seem to think they do (and they say it's the developmental genetic "compartment maps", rather than the "body plan" per se, that's phylum-specific. I took their word for it.)
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*I honestly don't know what the evidence says about that. I don't know how conserved the process of meiosis is, for example, and whether the differences between various creatures indicate descent with modification or convergent evolution. (And I'm damn lazy and won't do the reading right now)
**IIRC there's at least one phylum that's thought to have originated after the Cambrian but I can't recall which one it was.