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Article summary

A guided account of the current manuscript, emphasizing the large-scale argument and the three theorem-level results.

Sex emerges at scale

The paper argues that the ubiquity of sex becomes less mysterious when the object of explanation is changed: from individual microevolutionary mechanisms to an ensemble of evolutionary trajectories. At that scale, contingency recedes and a universal statistical pattern appears.

bioRxiv preprint Back to research Sex Evolution Sandbox

The puzzle

A large immediate cost, many small delayed gains

Classical accounts of sex begin with an asymmetry. The costs of sex are conspicuous and immediate—genome dilution, mate finding, and the demographic cost of males—while the costs of asexuality arise incrementally through selective interference.

The manuscript groups the latter into two broad classes. Within-lineage interference includes Hill–Robertson interference and lineage contamination: beneficial alleles are less likely to fix, deleterious alleles are more likely to fix, and damaging mutations can accumulate irreversibly. Across-lineage interference includes Fisher–Muller interference and clonal interference: favorable alleles arising in different lineages compete because linkage prevents them from being assembled into the same genome.

Sex breaks linkage and can recover this lost efficiency. But the usual framing asks for a large benefit of sex capable of paying a large cost. The paper instead proposes that the relevant benefit is distributed across evolutionary time and across many interference episodes. The aggregate can be large even when the contribution from any one episode is small.

Local viewOne population, one path, one mechanism.

Path ensembleA probability distribution over many possible selective histories.

Scale changeContingent details are averaged over rather than explained one by one.

Universal outputNon-negative mean pressure, power-law surges, long correlations.

Core construction

Sex potential is a property of a trajectory

The central dynamical quantity is sex potential, defined as the potential fitness flux created by a selective-interference path. The manuscript adapts the fitness-flux framework of Mustonen and Lässig, but changes the level of description: sex potential is treated as a random variable over an ensemble of paths rather than as a value attached to one realized path.

Mean fitness is partitioned using an integrated Fisher–Ewens form of the fundamental theorem:

L(t) = T(t) − V(t), with V(t) = −2 ∫₀^t cov(X,Y) du.

Here T(t) is cumulative variance-driven fitness flux and V(t) is the cumulative fitness flux that would be recovered by freely breaking linkage. Under free genetic exchange, the covariance term vanishes and mean fitness rises as T(t). Thus V(t) measures the cumulative opportunity for sex.

The asymptotic quantity V^* is the total sex potential of an episode. A dissociation parameter r extends the definition to V_r^*, spanning the range from sex-enabling genes that remain linked to the genome they modify to highly promiscuous modifiers that rapidly move among genomic backgrounds.

The key conceptual move is that a genome can be locally well or poorly assembled, but the evolutionary fate of sex is determined by the statistics of many such assembly problems.

Three large-scale results

The universal pattern

The paper’s main claim is not simply that sex can be advantageous. It is that, under broad conditions, the distribution of selection for sex acquires a characteristic structure.

Theorem 1

Non-negative in expectation

The expected sex potential satisfies ⟨V_r^*⟩ ≥ 0 for every dissociation rate r.

Matched combinations are removed quickly by selection; mismatched combinations persist longer and therefore contribute more strongly to the time-integrated covariance.

Theorem 2

Heavy-tailed surges

For most realistic conditions, P(V_r^* > v) ∼ v⁻¹.

Large episodes arise near cancellation of total fitness differences, where selective relaxation is slow and the integrated opportunity for recombination becomes large.

Theorem 3

Long correlations

In the sex-enforcing limit, P(T > t) ∼ t⁻¹ and P(X > x) ∼ x⁻².

The same near-neutral episodes that create large sex potential also generate long-lived and spatially extended domains of selection for sex.

Hand-drawn heavy-pencil sketch of the C. elegans sex-potential plot, showing a downward-sloping relationship on log-log axes with handwritten labels and legend. — C. elegans sketch: a hand-drawn rendering of the empirical sex-potential tail with the universality-class guide.

Hand-drawn heavy-pencil sketch of the serial-host simulation tail plot, shown on the same handwritten axes and labels as the C. elegans sketch. — Serial-host sketch: a matching hand-drawn rendering of the simulation tail, using the same visual language and axis labels.

Why the tail appears

Criticality is derived, not assumed

For two genic fitness differences ΔX and ΔY, define the total-fitness gap U = ΔX + ΔY and its magnitude S = |U|. Near U = 0, the two competing genomes are nearly neutral in total fitness even though their component fitnesses can differ substantially.

That near-cancellation slows the selective episode. In the manuscript’s kernel representation, the sex potential behaves asymptotically like a constant times W²/|U|. If the density of evolutionary paths remains non-zero near U = 0, the probability of landing very close to that cancellation surface is proportional to its width. Combining those two facts produces the inverse tail P(V > v) ∼ 1/v.

The same small relaxation rate generates long temporal and spatial scales. With no dissociation, the temporal correlation length is proportional to 1/S and the spatial correlation length to 1/√S. Hence the corresponding tail laws t⁻¹ and x⁻². Positive dissociation rate r imposes finite cutoffs: T ≤ 1/r and X ≤ √(D/r).

Temporal correlations

Sex-favoring episodes can persist for very long times.

Spatial correlations

Local dispersal converts long relaxation times into scale-free spatial domains.

What survives coarse-graining

Additive fitness becomes the large-scale currency

A deliberately provocative part of the manuscript is its treatment of epistasis and other non-additive fitness effects. Many microevolutionary theories of sex depend critically on such details. Here, by contrast, the large-scale derivation is expressed in additive genic fitness components.

The manuscript argues that strong non-additive effects can be decisive along particular microevolutionary paths yet cancel when considered across an unbiased ensemble of paths. In renormalization language, they become irrelevant at scale unless there is a systematic large-scale bias making one sign of non-additivity more probable than the other. The additive component is what survives the coarse-graining and therefore controls the universal statistics.

This is not presented as a claim that epistasis is biologically absent or locally unimportant. It is a claim about explanatory scale: microscopic details can matter greatly for individual trajectories while contributing little to the ensemble-level law.

At scale, the paper’s thesis is that collective near-neutrality beats individual strong selection: many small opportunities, integrated over many trajectories, can repeatedly overcome even large immediate costs.

Interpretation

From a paradox of mechanisms to a statistical law

The paper does not attempt to replace the classical explanations of sex. Instead, it proposes that Hill–Robertson interference, Fisher–Muller interference, clonal interference, and related mechanisms are different microscopic routes into a common large-scale structure.

Seen this way, the ubiquity of sex need not be explained by one universally dominant mechanism. The universal object is the path ensemble itself: selection for sex is non-negative in expectation, is punctuated by rare heavy-tailed surges, and possesses long temporal and spatial correlations. The associated criticality follows mathematically from the density of nearly neutral trajectories rather than from an assumed critical state.

The manuscript closes with a phase-transition analogy. A description of every molecule is not the natural explanation of melting; likewise, a catalogue of every microevolutionary advantage may not be the natural explanation of the prevalence of sex. At the appropriate scale, the claim is that the exceptional-looking phenomenon becomes a collective one.

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This page summarizes the current manuscript supplied by the author; it is an explanatory guide, not a substitute for the paper's formal statements and proofs.