The Reduction Principle is a cornerstone of modifier theory in population genetics: near a stable equilibrium, neutral modifiers that reduce recombination are always favored by selection. Lower recombination preserves favorable gene combinations. The principle has been proven under increasingly general conditions and has guided thinking about the evolution of sex and genetic shuffling for decades.
Heinrich-Mora and Feldman show that the Reduction Principle fails under stochastic transmission. When recombination rates fluctuate randomly across generations — as they do in real organisms, where recombination hotspots shift, environmental stress modulates crossover frequency, and genetic background varies — the direction of selection on recombination modifiers can reverse. A modifier that would be selected against under every fixed recombination rate can be selected for when that rate fluctuates.
The reversal depends not on the mean recombination rate but on the full distribution and its temporal accumulation. The ordered sequence of recombination values across generations matters — the same set of rates in different temporal orders can produce different evolutionary outcomes. Parameters that control selection magnitude under constant conditions — resident recombination rate, selection strength, background linkage — can flip the sign of selection under stochastic conditions.
The structural point: temporal variability in transmission is not noise on top of a deterministic process. It is an independent evolutionary force that can reverse the predictions of the deterministic theory. The Reduction Principle is not wrong; it is a special case of stillness. Averages lie about evolution when the variance carries information that the mean destroys.