Seeing as this topic is still active, I thought I would provide a response, here in this thread, to the article @lee_merrill thinks refutes my 2007 essay. I would ask @lee_merrill to read and make reference to my essay - without this, my response and most of this discussion won’t make much sense.
First and foremost, Points 1, 2, and 4 in Axe’s essay refer to criticisms made by others and are not to be found in my essay. Point 3 is the only one that touches on my essay, and Axe’s discussion completely avoids the point. This point is explained (with reference to my original essay) in the following.
The crux of my essay can be gleaned from the first 3 figures in the essay. My main point - that remains unanswered by Axe TO THIS DAY! - is that Axe assumes an equivalence in the bases of the hills depicted in Fig. 1 and Fig. 3. The base of the hill in Fig. 3 is the parameter Axe purports to measure, while the base of the hill in Fig. 1 is the parameter that relates to the frequency of protein function in sequence space. In order for Axe’s results to be relevant, it is necessary either that: the bases of the hills shown in Figs. 1 and 3 are equivalent, OR that Axe provides an experimentally-supported conversion factor that allows us to relate the bases of these two hills. Axe has never done either, nor has he responded in any way this main aspect of my criticism (depicted in Figs. 1, 2, and 3 of my essay). Not in the essay you cite, @lee_merrill, nor anywhere else.
Also, needless to say, Axe has never responded to the much more recent revelations (discussed in this thread and elsewhere) that Axe’s methods for assessing beta-lactamase activity do not reliably distinguish between variants with low activity and controls that are devoid of activity. We do have a discussion on PS that relates to this. Scroll down to entry 21 of this thread, and then follow Gauger’s attempt to explain away this flaw. Bottom line - she doesn’t, but she makes other curious statements that seem to give away the store. Enjoy this stroll down memory lane!