In a paper titled “There’s plenty of time for evolution,” mathematicians Herbert Wilf and Warren Ewens present a model that purports to solve the longstanding “waiting time” problem that plagues evolutionary theory. The authors argue that critics who claim there has not been enough time for random mutations to generate biological complexity are using a flawed, “in series” model of evolution. By substituting a more realistic “in parallel” model where natural selection preserves beneficial changes, they conclude that the time required for evolution is drastically reduced from exponential to logarithmic, making the evolutionary story plausible within accepted geological timescales.
However, this mathematical exercise, while elegant on its own terms, fundamentally fails to engage with the central challenges to unguided evolution. The paper’s model succeeds only by assuming the very thing it needs to explain: the origin of functional, specified biological information. By presupposing a target sequence and an omniscient selection mechanism to guide the process, the authors have not demonstrated the power of unguided evolution; they have created a simulation of teleology. The evidence, when analyzed through a rigorous scientific framework, points not to a blind process with “plenty of time,” but to a purposeful, intelligent cause.
A Fair Summary of the Research
Wilf and Ewens’ argument centers on contrasting two paradigms for finding a specific, unknown “word” of length L using letters from an alphabet of size K. This word represents a target genome.
- The “In Series” Model (The Strawman): This model represents the common caricature of the evolutionary challenge. It involves guessing the entire L-letter word in a single trial. The probability of success is a staggering 1/K^L. The authors rightly dismiss this, as it would require an exponentially large number of trials (on the order of K^L) to find the correct sequence, a number that far exceeds the probabilistic resources of the universe.
- The “In Parallel” Model (The Proposed Solution): This model is designed to mimic the action of natural selection. In each “round,” one guesses a letter for each of the L positions. Crucially, any correctly guessed letters are “retained” and removed from the pool of letters that need to be guessed in the next round. This process continues until all L letters are correct. The authors show that the mean number of rounds required for this process is not exponential, but logarithmic, approximately equal to
log(L) / log(K/(K-1)).
Using a biological example of a genome with L = 20,000 gene loci and K = 40 possible allelic types, they calculate that their “in parallel” model would require only about 390 rounds of mutation and selection to achieve the target genome, in stark contrast to the impossibly large number of trials required by the “in series” model. They conclude that this demonstrates there has been ample time for evolution to occur.
The Core Analysis: A Model Divorced from Biological Reality
The authors’ conclusion rests on a series of unstated and biologically unsupported assumptions that render the model irrelevant to the question of origins. Their mathematical solution works only because it avoids the real problems.
1. The Fatal Flaw: Assuming the Answer
The most significant error is that the model begins by assuming the existence of a “correct word”—a specific, functional target sequence. This is the “Assume a Gene” fallacy. The central problem for any theory of origins is not explaining how quickly a search algorithm can find a predefined target, but explaining the origin of the target’s meaningful, functional information in the first place. The model is a search algorithm, not a creative engine. It tells us how to find a password if we get hints after each guess; it says nothing about how to write the meaningful novel that the password protects. By pre-loading the answer into the model, the authors have solved a trivial problem while ignoring the profound one.
2. Selection Without Function
In the Wilf-Ewens model, a “letter” is deemed “correct” simply because it matches the predefined target. This has no connection to how natural selection actually works. Biological selection acts on function, which is an emergent property of a system. A single “correct” nucleotide or amino acid is, in almost all cases, functionally meaningless on its own. Function in a protein, for example, arises from a complex, three-dimensional fold that depends on the coordinated interaction of hundreds of amino acids. The system is irreducibly complex. You cannot build a flagellar motor by getting one protein “correct” and “retaining” it while you randomly search for the other 39. The entire system is a functional whole, and precursors are, by definition, non-functional and would not be preserved by natural selection. The model’s assumption of independent, individually selectable “letters” is biologically untenable for any integrated system.
3. A Teleological Oracle, Not Blind Selection
The model’s “selection” is an omniscient oracle that knows the final target sequence and guides the process toward it. Real natural selection is a blind, mindless process. It has no foresight. Far from guiding a population toward a complex, pre-specified goal, real-world selection favors the easiest and fastest available adaptation. As Michael Behe has argued, the “First Rule of Adaptive Evolution” is to break or blunt any gene whose loss provides a short-term survival advantage. It is statistically far easier to damage a gene than to constructively build a new one. The authors’ “selection” is a purposeful guiding hand, a stark contrast to the myopic, and often destructive, reality of the Darwinian mechanism.
4. The Timescale is a Red Herring
Even if we were to grant the model’s flawed premises, the entire discussion of deep time is challenged by empirical science. The authors operate within the standard evolutionary timescale of millions of years. However, empirically measured, pedigree-based molecular clock rates—the observed rates at which mutations accumulate in each generation—are dramatically faster than the rates inferred by evolutionary models. When these real-world clocks are applied to human and animal genetics, they consistently point to a common ancestor only thousands of years ago, not millions. For example, these clocks place “Y-Chromosome Adam” and “Mitochondrial Eve” at the root of all human diversity just ~6,000 years ago, a timeline that aligns perfectly with the biblical account of a recent creation and a population bottleneck at the time of Noah’s Flood. The debate over whether millions of years is “plenty of time” is moot if the timescale itself is a fiction.
The Alternative Explanation: A Designed Information System
The flaws in the Wilf-Ewens model do not simply invalidate their conclusion; they point directly toward a better explanation. The methods of historical science demand that we infer a cause that is known from our uniform and repeated experience to have the power to produce the effect in question.
The “correct word” that the authors presuppose is a classic example of specified information—a sequence that is not only improbable but also conforms to an independent functional requirement. The only cause we know of that can generate large amounts of specified information is intelligence. A blueprint requires an architect; a code requires a coder. The functional genome is best explained not as the result of a blind search, but as the product of a Mind. The Wilf-Ewens model tacitly admits this by requiring a pre-defined target for its search to succeed.
Furthermore, the vast genetic diversity we observe within animal “kinds” (roughly the family level) is not the product of a slow, random “guessing game.” A far more powerful scientific model, consistent with the recent timescale, is that of Created Heterozygosity. In this model, the Creator front-loaded the genomes of the original kinds with vast amounts of designed genetic diversity (alleles). The rapid speciation we observe in the fossil record and infer from modern genetics is the result of this pre-existing information being sorted out and expressed through processes like recombination and natural selection in populations that migrated after the global Flood. Adaptation is not a process of inventing new information, but of unlocking designed, pre-programmed potential.
Conclusion
The paper “There’s plenty of time for evolution” stands as a powerful example of how a mathematical model can create an illusion of a solution while being completely detached from the physical problem it claims to solve. By presupposing the existence of specified information (the “correct word”) and employing an unrealistic, teleological “selection” mechanism to find it, Wilf and Ewens do not demonstrate that unguided evolution is plausible. Rather, they demonstrate that if you have a target and an intelligent process to guide you, you can reach it efficiently.
This conclusion is trivial. The fundamental scientific question remains: what is the origin of the target? The paper offers no answer. When we apply a rigorous forensic analysis to the evidence, from the specified, irreducible complexity of the cell’s molecular machinery to the empirical data from molecular clocks that point to a recent past, the conclusion is clear. The signature in the cell is not the result of a blind, stochastic process, but is the unmistakable hallmark of a master Engineer.
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