The common ancestor of archaea and eukarya was not an archaeon.

I think that it is highly significant that Megavirales, retroviruses, and transposons with their associated defence/attack systems, which have been probably essential for the evolution of eukaryotes toward complexity, are missing in archaea and bacteria.

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This trend toward complexity is again only an overall trend and reductive evolution in eukaryotes led, for instance, several times independently to the transformation of multicellular fungi into unicellular yeasts [ 95 ].

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