What do they mean when they say they want to extend the Modern Synthesis?

As far as I'm concerned, the "Modern Synthesis" has been replaced by modern evolutionary theory that incorporates Nearly-Neutral Theory and random genetic drift as an important mechanism of evolution [see Is the "Modern Synthesis" effectively dead? ]. This extension, and replacement, of the 1940s version of evolutionary theory took place in mainly in the 1970s.

If I'm correct, then why all the fuss in the 21st century about extending the Modern Synthesis?

I think there are two things going on here. First, there are a bunch of biologists who want to incorporate their favorite fad into modern evolutionary theory. They think that their ideas are so revolutionary that this requires an extensive revision of evolutionary theory. Second, those biologists seem to have been asleep during the 1970s when the Modern Synthesis died so they are fighting a strawman.

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