Evolution Doesn't Learn — It Runs Experiments: A New Mathematical Framework for Natural Selection

Every second, in every living cell, copying errors slip through. A base pair flips. A codon shifts. The organism that emerges from replication is not quite the same as the one that entered it. Most of those errors are invisible or ruinous. A handful, over geological time, become wings, eyes, immune systems. The question of why — the mathematical engine underneath this relentless tinkering — is one of the deepest in biology. And a new paper by Jacopo Iacovacci at Milan's Fondazione IRCCS Istituto Nazionale dei Tumori argues that scientists have been framing it wrong.

For the past fifteen years, a mathematically elegant idea has been gaining ground: that evolution by natural selection is, at its core, a form of Bayesian learning. Bayesian inference — named for the 18th-century minister Thomas Bayes — is a procedure for rationally updating beliefs in light of new evidence. You start with a prior probability, observe data, and revise. The analogy to evolution is seductive: populations "start" with some distribution of genotypes, experience selection, and update. In 2009, two researchers independently noticed that the equations governing each process are formally identical (Harper, 2009; Shalizi, 2009). The replicator equation and Bayes' theorem map onto each other term by term: type frequency corresponds to prior probability, fitness corresponds to likelihood, mean fitness corresponds to marginal likelihood.

But there is a problem. A serious one. The moment you introduce mutations — not an optional add-on, but the central generative force of evolutionary novelty — the analogy collapses. The mathematics simply stops working. As Iacovacci (2026) notes, Akyıldız showed in 2017 that the replicator-mutator equation (the version that includes mutation) cannot be written as a Bayesian update at all. It corresponds instead to something called the prediction step of a Hidden Markov Model. The Bayesian framing, however elegant, is describing a world without the very thing that makes evolution creative.

Iacovacci's proposal is to replace the analogy entirely. Evolution, he argues, is not a learning process. It is a process of causal inference — specifically, the kind of causal reasoning formalised in the Neyman–Rubin potential-outcomes framework, the same statistical foundation that underlies the design and analysis of randomised controlled trials.

The Science

The Neyman–Rubin framework is the bedrock of modern causal statistics. Its central insight is deceptively simple: to know whether a treatment caused an outcome, you need to compare what happened to a unit under treatment against what would have happened to the same unit without treatment. The problem is you can never observe both. A patient either gets the drug or doesn't. This is the "fundamental problem of causal inference." Clinical trials solve it statistically, by randomly assigning large groups to treatment and control arms and comparing averages.

Iacovacci's key observation is that evolution solves this problem naturally, for free, at the moment of replication. When a haploid organism (one carrying a single copy of each gene — bacteria, viruses, and many fungi work this way) reproduces and generates an offspring with a point mutation, something remarkable happens. Parent and offspring share the same genetic background. They inhabit the same environment. The parent is the control; the mutant offspring is the treated unit. The difference in their fitness is the Individual Mutation Effect, or $\mathrm{IME}$:

$$\delta =Y^{\text{off}}-Y^{\text{par}}=Y(1)-Y(0)=\mathrm{IME}$$

where $Y(1)$ is the fitness the offspring would have with the mutation and $Y(0)$ is the fitness it would have without — i.e., the parent's fitness. This is not a metaphor. It is a precise application of the potential-outcomes framework to biology.

From individual mutation effects, Iacovacci defines an Average Mutation Effect (AME): the expected value of the IME across a whole population of matched parent-offspring pairs carrying the same mutation. He then shows how the four canonical identification assumptions of causal inference — known in the field as SUTVA, Consistency, Unconfoundedness, and Positivity — map onto real biological conditions. Positivity (the assumption that every unit has a non-zero probability of receiving treatment) simply requires that the mutation rate $\mu >0$, which is always true in biological populations. Unconfoundedness (the assumption that treatment assignment is independent of potential outcomes) is satisfied by point mutations, which occur regardless of whether they will be beneficial or deleterious — they are, in the relevant sense, random. The paper's appendices systematically catalogue which fitness definitions and which mutation mechanisms satisfy or violate these assumptions.

What They Found

The centrepiece of the paper is a theorem that delivers something evolutionary biologists have wanted for decades: a clean, mechanistically interpretable decomposition of how mean fitness changes between generations.

Causal Decomposition of Mean Fitness Change (Δw̄)

Label	Value
Selection term: Var(w)/w̄	1
Mutation term: E[wτ]/w̄ (beneficial mutations)	0
Mutation term: E[wτ]/w̄ (deleterious mutations)	0

Schematic of Theorem 3.2 (Iacovacci, 2026). The selection term is always non-negative; the mutation term can be positive (beneficial) or negative (deleterious).

Iacovacci proves that for the quasispecies equation — a classical model of evolution in molecular populations, used to study viruses and early life — the change in mean fitness $\Delta \bar{w}$ between generations decomposes exactly as:

$$\Delta \bar{w}=\frac{\mathrm{Var}(w)}{\bar{w}}+\frac{1}{\bar{w}}\mathbb{E}[w\tau ]$$

The first term, $\mathrm{Var}(w)/\bar{w}$, is the selection component. It is always non-negative — selection can only increase mean fitness, never decrease it. This term is precisely the content of Fisher's Fundamental Theorem of Natural Selection, one of the most celebrated results in all of evolutionary biology, first stated by R.A. Fisher in 1930. It says that the rate of increase in mean fitness equals the additive genetic variance in fitness. Here it emerges as one half of a causal decomposition.

The second term, $\mathbb{E}[w\tau ]/\bar{w}$, is the mutation component. The ${\tau }_j$ is what Iacovacci calls the Total Mutation Effect for a parent of type $j$ — the probability-weighted average of the AMEs from all mutations that can arise from that parent. The whole term is the fitness-weighted average of these total mutation effects across all parent types. Crucially, this term can be positive or negative. Beneficial mutations push it up; deleterious mutations drag it down.

What makes this decomposition significant is not just its mathematical elegance but its interpretive precision. The Price equation — a more general mathematical identity in evolutionary biology, derived by George Price in the early 1970s — also partitions fitness change into a selection covariance and a transmission-bias term. But the Price equation is a mathematical identity. It makes no causal claims. Its transmission-bias term is a statistical residual: it absorbs whatever the selection term doesn't explain. Iacovacci shows that, under his causal assumptions, this residual acquires a mechanistic meaning — it is the causal effect of the mutation process on fitness change. The math was always right. Now it means something.

Causal Assumption Satisfaction by Fitness Definition

Label	Value
Wrightian (density-indep.)	4
Malthusian	4
Geometric mean	4
Euler–Lotka	4
Frequency-dependent	3
Inclusive fitness	3
Game-theoretic	3
Group fitness	3

Based on Appendix A of Iacovacci (2026). Individual-level fitness definitions satisfy all 4 assumptions; relational definitions violate SUTVA (score 3). SUTVA = Stable Unit Treatment Value Assumption.

Under a uniform mutation rate $\mu$, the decomposition becomes even more transparent (Corollary 3.3 in the paper):

$$\Delta \bar{w}=\frac{\mathrm{Var}(w)}{\bar{w}}+\mu \mathbb{E}[\gamma ]+\frac{\mu }{\bar{w}}\mathrm{Cov}(w,\gamma )$$

where ${\gamma }_j$ is the average causal effect of a mutation event from parent type $j$. Three limiting cases illuminate the biology. When $\mu =0$, the mutation terms vanish and you recover Fisher's Theorem in pure form. When there is no fitness variation ($\mathrm{Var}(w) = 0$), evolution is driven entirely by mutation: $\Delta \bar{w}=\mu \mathbb{E}[\gamma ]$. And at mutation-selection balance — when $\Delta \bar{w}=0$ — the selective advantage of fitter types is exactly cancelled by the mutational load from deleterious mutations. Balance is no longer just an equilibrium condition; it is a causal accounting identity.

The covariance term $\mathrm{Cov}(w,\gamma )$ carries its own biological story. When it is positive, fitter genotypes have access to more beneficial mutations — their mutational neighbourhood is richer. This is sometimes called positive evolvability-fitness correlation. When it is negative, fitter genotypes are surrounded by deleterious mutations — the phenomenon of diminishing returns epistasis, where the fittest types have the least room to improve. The framework puts these concepts on a common causal footing.

Bayesian Learning Analogy: Where It Holds vs. Breaks Down

Label	Value
Pure replicator equation (selection only)	1
Replicator-mutator equation (selection + mutation)	0

Synthesised from Iacovacci (2026) and Akyıldız (2017). The causal inference framework generalises across both settings; the Bayesian analogy does not.

The paper also reinterprets the error threshold of quasispecies theory — a concept introduced by Manfred Eigen and Peter Schuster in 1977. The error threshold is a critical mutation rate ${\mu }_c$ above which selection can no longer maintain the fittest genotype in the population; above it, the population delocalises across sequence space and genetic information is lost. This is thought to be relevant to RNA viruses, whose high mutation rates push them near the threshold, and has been explored as a potential target for antiviral strategies. In the causal framework, ${\mu }_c$ emerges naturally from mutation-selection balance: it is the mutation rate at which the fitness-weighted causal cost of mutations exactly cancels the selective benefit of fitness variance. The threshold is no longer just a spectral property of a matrix — it is the point where two causal forces reach parity.

Why This Changes Things

The significance here operates on multiple levels. At the most immediate level, it resolves a genuine mathematical puzzle. The Bayesian learning analogy was always known to have limits, but those limits were somewhat vague. Iacovacci (2026) makes them precise: the analogy fails specifically because the replicator-mutator equation is not a Bayesian update, and now we know what it is instead. It is a causal inference procedure. The substitution is not just aesthetically satisfying — it is mathematically exact. The paper proves that the frequency update in the replicator-mutator equation is proportional to the AME of mutations on fitness, which is a causal quantity, not a probabilistic one.

At a deeper level, the framework changes how we think about the relationship between evolutionary biology and statistics. The Neyman–Rubin potential-outcomes framework was developed to formalise the logic of randomised experiments — it is the foundation of the modern evidence hierarchy in medicine, the intellectual basis for why we trust randomised controlled trials more than observational studies. Iacovacci is arguing that nature has been running this kind of experiment, implicitly, for four billion years. Every replication event with a point mutation is a matched-pair experiment. Every round of selection is a screening of causal effects. Evolution is not an algorithm that learns; it is an algorithm that identifies causal structure in a fitness landscape.

This also has implications for how we classify what counts as a "fitness" at all. In Appendix A, the paper provides a systematic taxonomy of fitness definitions — viability, Wrightian, Malthusian, geometric mean, Euler-Lotka, frequency-dependent, inclusive, game-theoretic, and group fitness — and classifies each by whether it satisfies SUTVA. Individual-level definitions (viability, Wrightian under density-independence, Malthusian, geometric mean, Euler-Lotka) all satisfy SUTVA and can be used directly in the causal framework. Relational definitions (frequency-dependent, inclusive, invasion, game-theoretic, group) violate SUTVA because the fitness of one unit depends on the composition of the population — which is exactly the "interference" that SUTVA forbids. This is not a flaw in these concepts; it is a clarification of the conditions under which causal mutation effects can be cleanly identified. For relational fitness, you need an interference framework.

The broader conceptual payoff is a reframing of what natural selection does. In the Bayesian picture, selection is like a statistician updating beliefs. In the causal picture, selection is like a clinician screening experimental results — retaining interventions with non-negative effects and discarding the rest. The first framing is passive and epistemic. The second is active and mechanistic. They are not equivalent, and for Iacovacci, the second is closer to what biology actually does.

What's Next

The paper is explicit about its scope and its limits. The causal framework, as currently developed, applies to haploid asexual populations in static environments with point mutations — a deliberately narrow setting chosen to make the causal assumptions transparent. Sexual reproduction, diploid organisms, horizontal gene transfer, epigenetic inheritance, and fluctuating environments all introduce complications that the current framework does not handle. These are not small omissions; they describe the majority of complex life. Extending the causal decomposition to sexual populations, where recombination mixes parental genotypes in ways that break the clean parent-offspring matched pair, is a significant open problem.

The assumption of a static environment is also load-bearing. In changing environments, the fitness landscape itself shifts between generations, which undermines the Consistency assumption — the requirement that the observed fitness of a mutant is its fitness under that mutation, not under some confounded combination of mutation and environmental change. Dynamic causal models, perhaps drawing on time-series extensions of the potential-outcomes framework, will be needed here.

There is also the question of neutral evolution. A large fraction of molecular evolutionary change — perhaps the majority, by some estimates — is driven not by selection but by genetic drift: random fluctuations in allele frequencies in finite populations (Lynch, 2007). The current framework handles infinite populations; drift lives in finite ones. Connecting causal mutation effects to the neutral theory of molecular evolution is an intellectually rich open direction.

What the paper does establish, cleanly and rigorously, is a new mathematical language for talking about the interplay of selection and mutation — one that imports the most powerful toolkit in modern statistics into evolutionary theory and reveals that the two have been describing the same logical structure all along. The experiment nature runs every time a cell divides is not so different from the ones we design in clinical trials. We just didn't have the vocabulary to see it that way until now.

The implications could eventually reach beyond pure theory. Understanding mutation effects as causal quantities — estimable from matched parent-offspring observations — offers a new perspective for empirical evolutionary biology, directed evolution experiments, and potentially the study of somatic mutation in cancer, where the same logic of mutation-as-intervention applies to cells competing within a body. Iacovacci works at a cancer institute. That is probably not a coincidence.