Do the Math: Evolution Cannot Create Novel Advances in Complexity11 min read

One of the central claims of Darwinian evolution is that random genetic mutations, filtered through natural selection, can generate the vast complexity of life we observe today. This process is said to unfold gradually over billions of years, across countless generations and organisms. To fairly evaluate this claim, we must consider the full scope of evolutionary “tries”—that is, the total number of mutational events available to nature since life began.

Assuming common ancestry and a roughly 3.5-billion-year history of life on Earth, with average generation times and population sizes across multicellular organisms, we can estimate the total number of mutational events to be on the order of 10¹⁸. While this figure may seem enormous, it pales in comparison to the astronomical improbabilities involved in assembling novel, functionally integrated biological systems—such as new protein domains or regulatory networks—through random variation alone.

This article explores whether the probabilistic resources available to evolution are sufficient to account for the emergence of biological complexity, and whether the math supports the claim that unguided processes can truly innovate at the levels required.

1.0 The Landscape of Mutation

Most mutations are either neutral or harmful. Studies across species consistently show that over 90–99% of mutations fall into these categories. Beneficial mutations are rare, typically comprising less than 1% of all mutations. Of those, a significant portion are either adaptive responses to environmental pressures or restorative—returning a degraded function to its previous state. Truly novel beneficial mutations, which introduce new functional information, are estimated to occur at a rate of approximately 0.01% or less. ¹

1.1 Error Correction Mechanisms

Beyond the rarity of such mutations, any supposed positive mutations must also overcome the stringent error correction mechanisms of the cell. DNA replication is governed by high-fidelity polymerases and repair enzymes that correct mismatches and prevent deviations from the genetic template. These systems do not distinguish between harmful and potentially beneficial mutations—they simply eliminate deviations. As a result, even rare beneficial mutations are often removed before they can be passed on. ²

1.2 Mutational Load

If such a mutation has survived the error correction, when moving to successive generations, it must survive the mutational load, i.e. the flow of negative mutations which threaten to erase it. Mutational load refers to the accumulation of deleterious mutations in a population. Even if a novel mutation survives error correction, it must compete within a genome burdened by harmful changes. This reduces the organism’s overall fitness and the likelihood that the beneficial mutation will be preserved across generations. ³

1.3 Genetic Drift and Selection Pressure

Next, in small populations, genetic drift can eliminate even beneficial mutations through random chance. Selection pressure must favor the mutation consistently for it to persist, but many beneficial mutations confer only marginal advantages and are easily lost. This further reduces the probability of long-term retention.

1.4 The Principle of Multiple Attempts

A central defense of Darwinian evolution is that, given enough time and enough mutational “tries,” even highly improbable biological innovations can emerge. This appeal to probabilistic resources is not unreasonable in principle: rare events do become more likely with repeated trials. But the validity of this argument depends entirely on the scale of those trials relative to the complexity of the outcome.

To evaluate this, we must first understand what constitutes a “try.” In evolutionary terms, each mutational event—each change in DNA across generations—represents a discrete attempt to explore biological possibility space. The more such events occur, the greater the chance that some will yield functional novelty. But how many attempts has evolution actually had?

Before calculating the mutational opportunities available to life on Earth, it’s helpful to anchor our expectations with a cosmic-scale comparison. Consider the physical universe itself:

• Estimated number of particles in the observable universe: ~10⁸⁰
• Maximum number of state changes per particle (assuming one per Planck time): ~10⁴³ per second
• Age of the universe: ~10¹⁷ seconds

Multiplying these together yields an upper bound on the number of particle-level changes possible in the entire history of the cosmos:

10⁸⁰ × 10⁴³ × 10¹⁷ = 10¹⁴⁰ total changes possible (max)

This figure—10¹⁴⁰—is often cited as the maximum number of physical events that could have occurred since the Big Bang. It represents the outer limit of brute-force search capacity available to any unguided process in the universe.

If solving a problem requires exploring a possibility space larger than 10¹⁴⁰, then even the entire cosmos lacks the resources to do so by chance.

And many biological systems—such as novel protein folds, multi-gene regulatory networks, or irreducibly complex molecular machines—appear to occupy precisely such vast combinatorial spaces.

Thus, before we accept that evolution can “try” its way into complexity, we must ask: how many tries has it actually had? And are those tries sufficient to overcome the probabilistic barriers involved?

Section 2.2 will begin that calculation.

2.0 Probability of Mutation Survival

Let’s conservatively estimate the probability that a truly novel beneficial mutation survives all biological filters:

• Probability of being truly novel and beneficial: 1 × 10^-4
• Survival after error correction: 1 × 10^-2
• Survival after mutational load: 1 × 10^-2
• Survival after drift and selection: 1 × 10^-2

Combined probability for one mutation:

• (1 × 10^-4) × (1 × 10^-2) × (1 × 10^-2) × (1 × 10^-2) = 1 × 10^-10

2.1 Coordinated Mutations for a New Protein

This probability, 1 × 10^-10, is still within the realm of faint possibility – the statistical bound for impossibility, called the universal probability bound, is about 1 × 10^-150.

However, a new functional protein typically requires at least 100 coordinated mutations. The probability of all 100 mutations persisting independently is:

• (1 × 10^-10)¹⁰⁰ = 1 × 10^-1000

This number is astronomically small—effectively zero. Even under generous assumptions, the probability of assembling a new protein through undirected mutation and selection is far below any meaningful biological threshold.

2.2 Estimating Evolution’s Probabilistic Resources

Having established the principle of multiple attempts and the cosmic upper bound of ~10¹⁴⁰ physical events (Section 1.4), we now turn to the actual mutational opportunities available to evolution on Earth. The goal is to estimate how many discrete “tries” nature has had to generate biological novelty through random mutation and selection.

Step 1: Total Number of Organisms

Let’s begin with a generous estimate of how many organisms have ever lived:

• Estimated total number of individual organisms since life began: approximately 10⁴⁰ (including microbes, insects, and multicellular life)

This figure is based on extrapolations from biomass, reproduction rates, and fossil records. It is intentionally generous, especially considering that most evolutionary innovation is attributed to multicellular organisms, which reproduce more slowly and in smaller numbers.

Step 2: Mutations per Generation

Next, we estimate the average number of mutations per organism per generation:

• Average mutations per genome per generation: approximately 10³

This includes point mutations, insertions, deletions, and other genomic changes. While mutation rates vary widely across species, this figure is intended to capture the total mutational “search” per organism.

Step 3: Total Mutational Events

Multiplying these together gives us the total number of mutational events across Earth’s history:

• 10⁴⁰ organisms × 10³ mutations = 10⁴³ mutational events

This is the total number of probabilistic “tries” evolution has had to explore biological possibility space.

Step 4: Comparing to Biological Search Spaces

Now consider the scale of the search space required to generate a novel protein domain of approximately 150 amino acids:

• 20 amino acids → 20¹⁵⁰ possible sequences
• 20¹⁵⁰ ≈ 10¹⁹⁵ possible combinations

Even if only 1 in 10⁷⁷ sequences folds into a stable, functional domain (a conservative estimate from protein studies), the number of functional targets is still:

10¹⁹⁵ / 10⁷⁷ = 10¹¹⁸

To find even one such domain by blind search, evolution would need to explore 10¹¹⁸ sequences. But as we’ve seen, it only had 10⁴³ tries.

Conclusion: A Deficit of Tries

The gap between the required search space and the available mutational events is staggering:

• Required: 10¹¹⁸
• Available: 10⁴³
• Deficit: 10⁷⁵ orders of magnitude

This is not a minor shortfall—it is a categorical mismatch. Even if we allow for selection, recombination, and other refinements, the probabilistic resources of evolution fall dramatically short of what’s needed to generate complex biological systems by chance.

In short, the math does not support the claim that unguided mutation and selection alone can traverse the vast combinatorial landscapes required for biological innovation.

3.0 Final Analysis: Multiple Tries are Not Enough

The claim that Darwinian evolution can generate biological complexity through unguided mutation and natural selection rests on the assumption that nature has had enough probabilistic “tries” to overcome the staggering improbabilities involved. But when we examine the actual mutational resources available to life on Earth—generously estimated at ~10⁴³ events—we find a profound mismatch between available attempts and required outcomes.

This shortfall is not merely a matter of scale; it is compounded by several biological constraints that further restrict evolutionary search:

• Error Correction Mechanisms: Cellular systems actively suppress mutations through proofreading and repair, reducing the number of viable exploratory changes.
• Genetic Drift: In small populations, neutral or even deleterious mutations can fix by chance, diverting evolutionary trajectories away from functional innovation.
• Mutational Load: Most mutations are either neutral or harmful; the accumulation of deleterious changes imposes a ceiling on how much variation a population can tolerate.
• Rarity of Functional Mutations: Functional protein domains, regulatory networks, and molecular machines occupy vanishingly small regions of the total sequence space—often less than 1 in 10⁷⁷ for proteins of modest length.
• Insufficient Number of Tries: Even with generous assumptions, evolution’s total mutational attempts (~10⁴³) fall short by dozens of orders of magnitude when compared to the combinatorial search spaces involved (often exceeding 10¹¹⁸).

Taken together, these factors reveal a system that is not only probabilistically constrained but actively resistant to the kind of blind search required by Darwinian mechanisms. The principle of multiple attempts, while valid in abstract, collapses under the weight of biological reality.

If the probabilistic resources of evolution are insufficient to generate functional complexity, then the explanatory framework must be reconsidered. Whether that involves invoking new principles of emergence, teleological causation, or intelligent agency is a matter for philosophical and scientific debate. But the empirical deficit remains: evolution, as currently framed, lacks the mathematical and biological footing to account for the origin of integrated biological systems.

Admittedly, statistics can be manipulated to prove almost any point, but this is a simple and honest approximation. I am sure that evolutionary supporters can imagine more complex machinations to support their theory, but really, this is just to show that as science stands now, evolution as an explanation of biological complexity is a fairy tale.