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

9.1 “The Calculations Ignore Natural Selection”

When invoking a legitimate mechanism — but out of context

Objection

Critics like Miller (2003) claim that Douglas Axe's study is fundamentally flawed because it ignores the power of natural selection to accumulate beneficial mutations over time. According to this criticism, Axe would have calculated the probability of functional proteins emerging as if everything depended solely on chance, without considering that natural selection could guide the evolutionary process, even in the face of extremely low probabilities.

🪜 For the lay reader: It is like saying a dice game can be won with strategy — but without realizing that, before applying any strategy, you need the dice to be on the table. Natural selection can only "choose" among options that already exist. If no functional option is available, there is nothing to select.

What Axe Actually Did

Douglas Axe did not ignore natural selection — he incorporated it directly into his experiment. In Table 3 of his article (2004), he defined the minimum functionality threshold necessary for a protein to be "seen" by natural selection. This threshold was established as:

$$k_{\text{cat}}/K_M > 10^3 \ \text{M}^{-1}\text{s}^{-1}$$

✅ Accessible explanation:

• This value represents the minimum efficiency a protein needs to start offering some advantage to the organism
• Below this threshold, the protein is invisible to natural selection — it does not contribute to survival or reproduction
• Axe tested 10⁷⁷ variants and found only 1 in 10⁶⁴ that reached this functional threshold

🪜 Refined analogy:

“Imagine you're trying to open a lock with a key. If the key doesn't turn, it doesn't matter if it looks promising — it doesn't work. Natural selection can only 'choose' keys that actually work.”

Where is the Logical Error?

The criticism commits a petitio principii — it assumes as true what needs to be demonstrated. Natural selection presupposes the existence of function to act. It does not create function — it refines what already exists.

🪜 Explanation for laypeople: It is like saying natural selection can explain the origin of an engine — when, in fact, it can only act after the engine is already minimally functional. Without ignition, without pistons, without combustion — there is nothing to improve.

Furthermore, there is confusion between:

• Positive selection: favors mutations that confer advantage
• Purifying selection: eliminates harmful mutations

For positive selection to work, a new function must already have emerged — and it is precisely this origin that Axe showed to be statistically improbable.

What the Data Show

Let's examine the numbers behind the criticism. The time needed for a neutral mutation to fix in a population is given by:

$$t_{\text{fix}} = 4N_e$$

Where \(N_e\) is the effective population size. For bacteria, \(N_e \approx 10^9\), meaning:

• 4 billion generations to fix a single neutral mutation
• With 100 generations per year, that's 40 million years

Now consider that minimal biological systems require multiple coordinated mutations. For a functional protein requiring 5 specific simultaneous mutations:

• Global bacterial population: \(10^{30}\)
• Mutation rate: \(10^{-9}\) per base per generation
• Evolutionary time: \(10^{12}\) generations

Total possible attempts:

$$10^{30} \times 10^{-9} \times 10^{12} = 10^{33}$$

But the sequence space for a 150-amino acid protein is:

$$\approx 10^{77} \ \text{possibilities}$$

🪜 Visual explanation: It is like trying to find a specific needle in a universe of haystacks — and only being able to search a tiny fraction of them. Even with billions of years and trillions of organisms, there isn't enough time to test all combinations.

Model

Even if we granted natural selection near-miraculous powers, it still wouldn't solve the problem of irreducible complexity. Biological systems require multiple components functioning together.

🪜 Real example: The blood coagulation cascade requires 12 interdependent proteins. If one is missing or defective, the system fails. Natural selection cannot maintain isolated proteins that don't yet have function — because they offer no selective advantage.

Additionally, there is the problem of the adaptive "valley of death":

• Intermediate mutations needed to reach a new function
• But that are slightly deleterious along the way
• Purifying selection eliminates these mutations before they can be perfected

🪜 New analogy:

“It is like trying to cross a deep valley to reach a mountain — but every initial step takes you down, not up. Natural selection doesn't help you descend — it prevents you from falling.”

What Does the Scientific Literature Say?

• Lynch (2020): Admits that mutations below the functional threshold are invisible to selection
• Koonin (2016): Recognizes that natural selection cannot explain the origin of the first genetic systems
• Wolf-Ekkehard (2009): Shows that selection presupposes replication, but replication requires prior complexity
• Adami et al. (2000): Demonstrate that the power of selection is limited by time and population size — and that multiple coordinated mutations are mathematically impossible within the limits of the universe

🪜 For the lay reader: These authors are not defending intelligent design — they are evolutionists who recognize that natural selection has real limits.

🔧 Explicit naturalistic self-refutation:

Lynch (2020), in his article The evolutionary scaling of cellular traits imposed by the drift barrier, acknowledges that:

“Genetic drift, by limiting the efficiency of natural selection in populations with low effective size, imposes fundamental barriers to the evolution of cellular complexity.”

This study demonstrates that, even under constant selective pressure, natural selection often fails to maintain optimal phenotypic states — especially in larger organisms — due to the dominant force of drift. This directly corroborates Axe's calculations about the improbability of functional origin by non-directed processes.

Source: Lynch, M. (2020). The evolutionary scaling of cellular traits imposed by the drift barrier. Proceedings of the National Academy of Sciences, 117(19), 10435–10444. DOI: 10.1073/pnas.2000446117

Why This Criticism Fails

The criticism fails because it ignores what Axe actually did. He did not disregard natural selection — he defined with precision the limits under which it can operate. And he showed that, before selection can act, something functional must already exist — which, according to the data, is statistically improbable.

🪜 Refined final analogy:

“Natural selection is like a judge in a competition — it can choose the best among the competitors. But if no one shows up to compete, the judge has no function.”

Conclusion for the Lay Reader

Natural selection is a powerful mechanism — but it does not create, it chooses.

Axe showed that, for selection to choose, there must be something functional to begin with — and that the chance of this emerging by chance is so small that not all the time and matter in the universe would be sufficient.

The criticism that Axe ignored natural selection not only misses the target — it reveals a deep misunderstanding of how selection actually works.

🪜 Visual summary:

“Natural selection is like a filter — it separates the useful from the useless. But if everything that enters is useless, the filter cannot produce something useful.”

Therefore, this criticism does not invalidate the study.

It reinforces Axe's conclusion: the origin of functional complexity is beyond the limits of natural selection — and the probabilistic resources of the universe.

Priority Self-Refuting Sources (κ > 0.9)

• Lynch (2020): Mutations below the functional threshold are invisible to selection
• Koonin (2016): Natural selection does not resolve the paradox of the origin of replication
• Wolf-Ekkehard (2009): Selection presupposes prior complexity
• Adami et al. (2000): Population and temporal limits make origin by selection mathematically impossible