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Scaffold S16 — The Dobzhansky–Muller snowball

Five rounds. Two populations have been isolated for divergence time t (millions of years). Each population has been fixing new alleles at an approximately constant rate. Any allele fixed in population A can potentially be incompatible with any allele fixed in population B. Predict the expected number of hybrid incompatibilities as t doubles.

Locked — answer the pretest above first.

Running tally — incompatibilities vs. divergence time (log–log)

What you just did has a name

The number of hybrid incompatibilities between two isolated populations grows as I(t) ≈ α · t². The exponent of 2 is the "snowball": every new substitution in one lineage must be tested against every substitution in the other. If each lineage fixes alleles at a rate ∝ t, the number of pairs grows as t · t = t².

On the tally above, the five points should fall very close to a straight line with slope 2 in log–log space. The line is not additive (t¹) — doubling t quadruples the number of potential incompatibilities. This is exactly what Moyle & Nakazato 2010 observed in 64 Drosophila sister-species pairs and what Matute et al. report in other clades. Divergence time is the single best predictor of hybrid dysfunction, and the scaling relationship confirms the mechanism.

This is why reproductive isolation accelerates. Early in divergence, incompatibilities accumulate slowly. Once there are enough of them, every new mutation has many targets to fail against. Speciation does not happen at a fixed rate — it happens on a curve.