Even for a physicist, this is bad: Larry Moran, in preparation for the appropriate dose of ridicule that this situation deserves, quotes physicist and pop-science author Paul Davies:

Another physical object with enormous longevity is DNA. Our bodies contain some genes that have remained little changed in 100 million years. An alien expedition to Earth might have used biotechnology to assist with mineral processing, agriculture or environmental projects. If they modified the genomes of some terrestrial organisms for this purpose, or created their own micro-organisms from scratch, the legacy of this tampering might endure to this day, hidden in the biological record. Which leads to an even more radical proposal. Life on Earth stores genetic information in DNA. A lot of DNA seems to be junk, however. If aliens, or their robotic surrogates, long ago wanted to leave us a message, they need not have used radio waves. They could have uploaded the data into the junk DNA of terrestrial organisms. It would be the modern equivalent of a message in a bottle, with the message being encoded digitally in nucleic acid and the bottle being a living, replicating cell. (It is possible—scientists today have successfully implanted messages of as many as 100 words into the genome of bacteria.) A systematic search for gerrymandered genomes would be relatively cheap and simple. Incredibly, a handful of (unsuccessful) computer searches have already been made for the tell-tale signs of an alien greeting.

(Yes, that's me you're now hearing, banging my head against the desk.) Larry uses this opportunity to pose the obvious question, for his molecular evolution students and everyone else:

Assume that the aliens inserted a 1000 bp message in the same place in the genomes of every member of our ancestral population from five million years ago... If you were to sequence that very same region of your own genome what would the message look like today?

(Go leave your answer in the comments over at Sandwalk.) Anyone who has the slightest comprehension of natural selection ought to see that the most implausible part of Paul Davies scenario is not the bit about aliens engineering the DNA of terrestrial organisms. From the context of the full article (go to Sandwalk for the link), it's not clear how seriously Davies takes this. I'm really, really, really hoping that this does not reflect the biological understanding of a public scientific figure, but I'm afraid it does.