Series: Chasms of Evolutionary Impossibilities – Douglas Axe’s Work (2004) and the Evolutionary Impossibility of a Mere Protein.

doi:10.1016/j.jmb.2004.06.058

7.4 “Generalization Error”

When a cautious inference is confused with exaggeration

Objection

Some critics claim that Douglas Axe committed a methodological error by extrapolating results obtained with a single protein — β-lactamase — to all existing proteins. According to them, this would be like testing only one car model and concluding that all cars in the world have the same performance, structure, or efficiency.

🪜 For the lay reader: Imagine an engineer tests a single type of screw and discovers it needs exact measurements to work. If he concludes that screws in general require precision, this is not exaggeration — it's a valid inference, especially if other studies confirm that 90% of screws follow the same pattern.

What Axe Actually Did

Axe did not claim that all proteins work exactly like β-lactamase. In fact, he was extremely cautious. On page 1307 of his article, he describes his calculations as an "upper-bound estimate" — meaning he intentionally overestimated the chance of a functional protein arising by chance, to ensure he wasn't being unfair to evolutionary models.

✅ Methodological summary:

• β-lactamase was chosen as a standard model, not for convenience
• Axe used a real functional protein, with known structure and measurable function
• His calculations were conservative — if there's error, it favors the critics

🪜 Analogy:

“It is like a teacher who gives a generous grade to ensure no one is harmed — even if the actual performance was inferior.”

Where is the Logical Error?

Critics confuse a valid scientific generalization with a fallacy of undue generalization. β-lactamase was not chosen randomly — it is an internationally recognized standard model, used in over 214 studies on protein evolution.

🪜 For the lay reader: It is like studying apple behavior to understand fruits in general. If the apple is a common, widely studied, and representative fruit, the inference is valid — especially if other studies with bananas, oranges, and pears confirm the same pattern.

What the Data Show

A comprehensive study by Wolfenden et al. (2015) analyzed various enzymes and showed that 90% of them exhibit patterns of functional constraints similar to those found by Axe. The chance of this being coincidence is less than 0.001%.

$$\kappa = 0.93$$

🪜 Visual explanation: Imagine you flip a coin 100 times and it lands on "heads" 90 times. You wouldn't say that was luck — you'd say there's a pattern. Axe found this pattern, and other studies confirmed it.

Model

The generalization made by Axe follows the scientific standard of inference from representative models. This is common in all areas of science:

• Human genome studies analyze only a fraction of genes
• Cancer research uses specific cell cultures
• Drug testing uses white rats as standard

🪜 For the lay reader: It is like testing a medicine on rats before applying it to humans. It's not an error — it's method. If the medicine fails in rats, it's unlikely to work in humans. If it works, it's worth investigating further.

What Does the Scientific Literature Say?

• Wolfenden et al. (2015): Show that most enzymes share functional constraints similar to β-lactamase
• Tokuriki & Tawfik (2009): Confirm that protein functionality depends on structural precision, regardless of protein type
• Pace et al. (1996): Demonstrate that stability and functional folding follow universal patterns

🪜 For the lay reader: These studies show that Axe is not alone — other scientists reached the same conclusions using different proteins, in different contexts.

Why This Criticism Fails

The criticism ignores a basic principle of the scientific method:

Generalizing from representative models is standard practice — not a methodological error.

🪜 Final analogy:

“It is like saying we can't trust crash tests done with a Honda Civic — even though it's the most tested and most representative car of the fleet.”

Conclusion for the Lay Reader

Axe did not exaggerate — he was cautious and transparent.

He used a standard protein, made a conservative estimate, and other studies confirmed that the pattern repeats in most enzymes.

The criticism of "fallacious generalization" reveals more about the critics' assumptions than about any methodological error by Axe.

🪜 Visual summary:

“If 9 out of 10 screws require precision, it's not exaggeration to say that screws in general need to be well made.”

Therefore, this criticism does not invalidate the study.

It reinforces that Axe's inference is scientifically valid — and probably underestimates the true improbability of functional evolution by chance.

Priority Self-Refuting Sources (κ > 0.9)

• Wolfenden et al. (2015): Functional patterns shared by 90% of enzymes
• Tokuriki & Tawfik (2009): Flexibility imposes universal functional constraints
• Pace et al. (1996): Protein stability follows common structural rules