Edit: Wow a lot of bs going on in the comments. First of all, there's an immense number of ways a DNA strand can degrade, and only one of them splits the strand in two. The relative importance of all these pathways depend on the environment of the DNA, which obviously changes for each and every fossil you have. The global kinetics of "DNA degradation" are supposedly first-order, which implies constant half-life.
What zbyte64 said. Once the animal dies, the enzymes that constantly fix and error-check DNA are no longer around. DNA then degrades over time, cleaving in half every ~521 years on average. So past a million years or two, the fragments are so small, meaningfully putting them back together would be an impossible task, like reconstructing a porcelain bowl you had ground into dust.
Not if this really is well-described by independent probabilities, i.e., a chance of being preserved that falls exponentially in time. Even if after 1 million years only half of the strands of DNA have had all their info destroyed, and even if (very unrealistically), the ones that haven't been destroyed are completely intact, then after 100 million years you would need to start with 2^100 = 10^30 DNA strands to have a single one last. And there are < 10^18 cells in a land animal.
No, the only way for something to survive is if the half life model breaks down and the chance of decay during different time periods isn't independent. This would be the case if one of the strands was somehow preserved accidentally.
Why would this be an exponential process? The error is per base pair per unit time. If a DNA fragment is split cleanly in half, each half should have double the expected time to failure as the whole, because there is half the number of base pairs each with the same likelihood of error as before.
It's just like nuclear atomic decay. For each base pair, there is a small chance of decay each small time step. The chance of any given base pair remaining undecayed through some time T is the product of all those probabilities, which fall exponentially in T. The expected number of total surviving base pair is also exponentially falling.
People are talking about two different things in this thread, and that's why people are talking past each other. Some people think halving means "half the number of base pairs remain" which would be an exponential process, yes. The other group thinks that "halving" means literally cut in half -- a failed base pair cuts the DNA strand into two pieces. That would be a linear decay process. As someone with no understanding of the underlying decay processes it's not obvious to me which one is right.
Yes, but you need fragments of only about 50 basepairs to assemble a genome (or a big part of it) back. A typical DNA strand has on the order of hundreds of millions of basepairs.
So, after 1042 years, only a quarter of the bonds will be intact. After 100 million years, only 1 in every 2^190000 bonds will be expected to still be intact. Taking 2^10 = 1000, that's 1 in every 10^57000. I think that's quite a bit higher than our estimate for the number of particles in the universe (https://www.quora.com/How-many-particles-are-there-in-the-un...)
So, if we assume that the dinosaur has 1 billion base pairs in its genome (huge assumption, see my other comment), it has degraded over 110 million years with a half life of 512 years, there is functionally 0 base pairs left[1] in each dna helix. Even statics can't help much there! I'm wide open to the possibility that I am incredibly wrong in any one of these assumptions however
I didn't actually look into this or any of the references but I suspect the half-life model is not appropriate in the extreme case. That is, it's an approximation that works on a certain non pathological scale like newtonian physics. Probably need the quantum mechanics version for this.
