Retro viruses are known to copy and paste bits of DNA between themselves and other organisms. An important part of the mammalian reproduction system is known to have come from a virus. So in that sense, there is gene swapping between totally unrelated organisms - most of which doesn't do anything or is "junk DNA" but occasionally the DNA does something harmful to the survival or the organism or even rarer something useful and a new evolutionary trait is born. Virus transfers are one of the natural mechanisms by which genes mutate. Only relatively short bits of DNA are transferred, so for example not enough to give a fly a human eyeball. Typically it means a new protein structure is formed or it folds in a different way, rather like having a different shaped building brick.
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I've left WP indefinitely.