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I expect very large error bars on any serious answer, but what's the number of generations between the very first life form (that can be described as evolving in generations) and humans? Is it closer to a quadrillion or a trillion?

A related answer says there are 300,000 generations between us and the chimp/human common ancestor.

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The generations that preceded multicellular life will so vastly dominate the answer that the last 500,000,000 years don't even matter. So life is 3.5 billion years old, and for most of this time, life was prokaryotic, dividing every 20 minutes or so. Thats 26,000 generations per year. Multiply that by 3.5 billion and you get 9 trillion generations. That is likely an overestimate, based on optimal growing conditions of bacterial in exponential growth. But it is unlikely to be orders of magnitude off.

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    $\begingroup$ eukaryotes have been around for ~2.7 billion years so this should be taken with a large margin of error. Also we don't know how fast the earliest life reproduced, but it is probably accurate within one or two orders of magnitude. $\endgroup$ – John Nov 17 '17 at 0:40
  • $\begingroup$ I agree. It is difficult to know how fast the division time was. My original estimate came from my experience with bacteria in exponential growth in optimal media. I am going to edit my answer. $\endgroup$ – Karl Kjer Nov 17 '17 at 10:56
  • $\begingroup$ prokaryotes often make clones, so their generations are of a different kind. $\endgroup$ – com.prehensible Nov 17 '17 at 11:45
  • $\begingroup$ We cannot be sure that the earliest life forms had well defined generations. It must have taken eons to learn replicating regularly. It is not even given that the life emerged just once and that we descend directly from the earliest organisms. $\endgroup$ – jmster Nov 17 '17 at 18:05
  • $\begingroup$ There may have been some failed first attempts. The optimized codon table is evidence of this. But all life on Earth today is evolved from a single common ancestor. There is no doubt about that. The evidence comes from conserved molecules like rRNA, tRNAs and the codon table. $\endgroup$ – Karl Kjer Nov 18 '17 at 3:35

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