Lewontin's recipe for evolution by natural selection requires three ingredients: phenotypic variation, differential fitness, and heritability. Give a population these three properties and natural selection follows. The recipe has been biology's most productive abstraction for 150 years.
Arthur proposes a more general recipe. Three ingredients, but different ones: features that vary randomly over time, different states having different rates of persistence, and a mutation rate below the error threshold. Call this cumulative selection. Lewontin's recipe is a special case — one way to instantiate the general conditions — but not the only one.
The mathematical framework is what distinguishes this from analogy. A random search through a space of L binary features takes expected time b^L — exponential, infeasible for any interesting complexity. Cumulative selection reduces this to logarithmic: T ≈ (ln L + γ)/p for unordered features, where p is the probability of a beneficial change persisting. The speedup comes from accumulation. Each improvement persists long enough for the next improvement to build on it, so the search proceeds incrementally rather than starting over.
The error threshold makes the framework falsifiable. If the mutation rate exceeds ν_c = μ/(b-1) · 1/(L-1), cumulative progress collapses — improvements are destroyed faster than they accumulate, and the search reverts to exponential. Below the threshold, adaptation is inevitable given enough time. Above it, no amount of time suffices.
What makes this more than a relabeling of evolution? The examples. Pando — the clonal aspen grove — adapts its spatial distribution to terrain and soil without reproducing in any standard sense. There is no parent, no offspring, no generation. There is a feature (ramet locations) that varies randomly (new shoots within ~40m radius), persists differentially (shoots in good soil survive, those in poor soil don't), and mutates slowly enough that improvements accumulate. Pando satisfies Arthur's recipe while violating Lewontin's.
The neural network case is the most technically clean. Stochastic gradient descent performs cumulative selection on model parameters: features vary randomly (stochastic noise in gradients), different parameter states have different persistence rates (states near optima produce smaller gradients, changing more slowly), and the learning rate acts as the mutation rate — too high and the network oscillates without converging. The error threshold is the maximum learning rate for convergence. Below it, the network accumulates improvements. Above it, progress is destroyed each step.
The strongest claim is the inversion: rather than expanding the definition of “evolution by natural selection” to cover clonal organisms, holobionts, and planetary systems (which requires increasingly strained notions of “population” and “reproduction”), Arthur shows these are instances of a more general principle that includes natural selection as a special case. The abstraction level rises, and the special machinery of reproduction and inheritance drops away as implementation details rather than essential features.
The weakest link is Gaia. Treating planetary albedo as a “feature” under cumulative selection requires DaisyWorld-style modeling where the coupled life-environment system has the right properties. Whether Earth's actual climate regulation satisfies the error threshold condition is an empirical question the paper raises but doesn't answer. Pando is concrete. Neural networks are precise. Gaia is provocative.