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Since they do not show up fully formed, can you explain to me how half a lung (or claw, or flipper) could present a clear advantage for natural selection to act upon.
Yes, but only because I read Darwin, and he did it for me. Swim bladders hold air for floating. Living tissue has the marvelous ability to be able to absorb nutrients from the substances it is in contact with. Some fishes can use their swim bladders to collect oxygen. This confers an obvious survival benefit.
Other fishes have tubes (I'm sure there's a more technical term, but I can't seem to think of it right now) in their swim bladders. This provides more surface area and makes the swim bladder a better organ for the intake of oxygen from the air in it.
Oh, I forgot to mention the first step, which is an opening to the outside of the fish, which allows it to intake air into the swim bladder. Some fishes have to provide their own air, pulled from the water, and this obviously is pretty useless for breathing. Many fishes do have an outlet for their swim bladder to take in it's own air.
Obviously, at this point, we don't need much else. The tubes multiply, the surface area multiplies, and the swim bladder becomes quite efficient at absorbing oxygen, allowing the fish to survive in situations where it can't breathe water. At that point, it may still occasionally be used as a swim bladder, but it's a lung, too.
The claw works like this, as Darwin also explained. The second segment of the front leg develops a ridge. This allows the first segment, furthest from the lobster, to press things against the ridge. This is a grasping mechanism, and it confers obvious benefit, and it needs no more than a bump.
Believe it or not, now all that has happened is that ridge/bump has grown so large that it meets the first segment of the leg along the entire length of the segment, allowing it to work very well for grasping. As that happened, shape changes made the grasping effects even better, as the end part of the limb and the ridge gained the correct shape to be an efficient claw.
All the steps I've outlined above are seen in nature, are small enough that even you would allow such mutations, and they lead to the claw and lung.
I'll let someone else take a shot at the hand to flipper lineage, but I suspect even you could find the intermediate steps with a little thought.
Funny, it turns out you can line up those kind of steps even with something as complex as an eye, and show the steps in living creatures today!
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A good starting point is this English translation of an early Chinese article: http://dawning.iist.unu.edu/...a/bjreview/97Apr/97-13-7.html
The time frame in that article is 3-5 million years, not 2-3. That still makes it very rapid, but it is nearly double the time frame you gave.
It seems to me, as a real amateur at all this, that with every niche of life open to the evolving species of the Pre-Cambrian and Cambrian era, it's no wonder evolution was so rapid. Even after the extinction of the dinosaurs, mammals filled most of the niches of life in 10-20 million years, which is an extremely rapid explosion of evolution due to lack of competition. Many avenues of development were open to the new organisms.
The Cambrian explosion was a perfect period for the same sort of development, and it's not real surprising, due to the way we label things and the way life tends to "fill the niches" that no new phyla have developed since. There was a discussion on a different thread about the way we classify life forms, and we would not be prone to creating a new phyla in which to put some new life form we found today.
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