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the whole point though. We DON'T have access to ancestral DNA so we can't deduce what you have deduced above.
We don’t have access to the ancestral DNA, no, but we do have access to the DNA of living animals, and this is how the family trees of life are constructed (or, more accurately, how they are refined). Let’s say we have three animals — A, B and C — and we look at their genomes. The genomes of A and B turn out to be much more similar to each other than either is to the genome of C. We assume, then, that A and B share a common ancestor with each other more recently than either does with C. If A and B shared a common ancestor more recently than A and C, then A and B's genome should be more similar, having had less time to diverge from each other. Now imagine that A is a rabbit, B is a lungfish and C is a tuna, and you see why the tree of life is constructed as it is.
It's not just genetic evidence, by the way. Lungfish and coelacanths were grouped with land vertebrates long before there was DNA evidence for it, based on morphological evidence.
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My point is that an ancestral fish was a fish and will have DNA to match this. It will also be more closely related to a modern fish than say a rabbit in terms of its DNA. So it would be safe to assume that an ancient fish was an ancestor of the modern fish.
The ancient fish will probably not have DNA significantly more similar to the modern fish than to rabbits. The DNA of fish has gone through hundreds of millions of years of mutations - just like those of rabbits, and the fish wouldn't be very much alike. The DNA of different fish is very different - a noted above, lungfish are more genetically similar to monkeys than to tuna, while tuna are more genetically similar to elephants than to sharks.
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Now, if you are suggesting that the DNA of some modern fish is more closely related to a rabbits than it is to other fish then dare I say it.....fishy pun.....this would be a red herring. Because these fish are NOT the ancestors of rabbits. They are infact modern fish.
I'm not sure why you think this is relevant. The significant fact about these fish being lumped in with rabbits and monkey's genetically is that their ancestors diverged from those of other fish before they diverged from land vertebrates. This means that the common ancestor of all fish is also an ancestor of land vertebrates. So, even without any fossil evidence, we'd assume that land vertebrates eventually trace their ancestry to fish. This is the simpler explanation, because it just requires a creature that looks like a fish, one of whose descendent lines lost thi distincitve fishiness to become tetrapods. The other possibility, that the common ancestor was not a fish, would require the distinctive features of fishiness to have arisen at least three times independently in different lineages of fish ancestors. Monkeys evolving from fish is the simpler explanation (and, once fossil evidence is taken into account, the only sensible explanation).