I think one important thing that needs to be recognized is that if there was a world wide flood 4000 years ago, then there would have been a severe genetic bottleneck. A genetic bottleneck is when a species get very close to dying out but then recovers.
I guess total extinction was prevented due to the animals that were spared on the ark. First of all, we would have to be logical and realize that the ark would not have been able to hold a pair of every animal species on earth. There would be too much mass as well as volume.
Even it the ark story was true. It would take a very long time for two elephants to inbred to the reach the genetic diversity of elephants today.
If the flood did happen, there would have been a worldwide bottleneck on all species which could easily be determined by checking genetic diversity of the species. All would point to 4000 years of genetic diversity which is not found by scientists.
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