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  1. The junk DNA argument from that paper is (paraphrasing):
    1. Humans have 8.2% of their DNA in common with some other mammals.
    2. Therefore that 8.2% of DNA must have existed in the last common ancestor of humans and those mammals.
    3. They’re using neutral theory (standard in population genetics) so they assume that in time since those lineages diverged, evolution couldn’t have created much more function than that, so only around 8.2% of human DNA is functional.
    You can read it yourself and see that’s actually what they’re arguing. Pasting the relevant bits:
    “we address these issues by identifying and characterising sequence that has been constrained with respect to insertions and deletions for pairs of eutherian genomes over a range of divergences… From extrapolations we estimate that 8.2% (7.1–9.2%) of the human genome is presently subject to negative selection and thus is likely to be functional… Our estimate that 7.1%–9.2% of the human genome is functional is around ten-fold lower than the quantity of sequence covered by the ENCODE defined elements… This indicates that a large fraction of the sequence comprised by elements identified by ENCODE as having biochemical activity can be deleted without impacting on fitness… Nucleotide substitution rates in AR [ancient repetitive] sequences are very similar to estimates of the synonymous substitution rate (dS), hence our results appear insensitive to the choice of neutral sequence standard.”

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