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The Cambrian Explosion refers to the sudden appearance of complex life on the planet Earth during the Cambrian Period.
Cambrian Explosion is verifiable all over the world.

How does that fit into the Evolution Theory?

If we all evolved from the same single cell organism, how does all those Filos appeared at the same time?
As I understand, Evolution would suggest a gradual mutation of the organisms and the constant creation of new Filos over time. Does the Cambrian Explosion discredits the Evolution?
Not really my field of expertise, but some papers support the idea that the Cambrian explosion is compatible with Darwinian theory of evolution. Here is an example.
Creationists don't seem to like this ;)
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There is no paradox whatsoever, all the contrary, the simpler the organism, the greater the chances to mutate, so under Darwinism, the Cambrian Explosion was bound to happen.
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the simpler the organism, the greater the chances to mutate
Where did you get it?
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Simpler organisms tend to have shorter life-spans, thus higher rates of mutation accumulation. And you can see that in action in real life: the greatest diversity exists among the simplest organisms.
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