Recombination Rate Modifiers under Stochastic Transmission

TL;DR

This paper investigates how stochastic variation in recombination rates across generations can reverse the predictions of the classical Reduction Principle, highlighting the importance of temporal variability in the evolution of recombination modifiers.

Contribution

It extends the deterministic model by analyzing the effects of stochastic recombination rate variation, showing it can reverse the direction of selection on modifiers.

Findings

Stochastic recombination variation can reverse the Reduction Principle.

Outcomes depend on the full distribution of recombination rates, not just the mean.

Temporal variability acts as a distinct evolutionary force.

Abstract

The Reduction Principle states that, near a stable equilibrium under fixed viability selection, a selectively neutral modifier allele that reduces recombination rate among selected loci is favored, whereas one that increases recombination rate is eliminated. This result assumes constant transmission parameters across generations, so that invasion is determined by the dominant eigenvalue of a single transmission-selection matrix. Here we analyze a minimal departure from this framework. In a diploid model, two loci experience symmetric multiplicative viability selection and a third, neutral locus modifies their recombination rate. All parameters are fixed except that recombination in modifier heterozygotes varies randomly across generations according to a stochastic process. When the recombination rate in modifier heterozygotes is constant, the Reduction Principle holds exactly: invasion occurs if the rare modifier allele reduces recombination relative to the resident rate. When recombination varies randomly across generations, invasion is governed by the top Lyapunov exponent of a product of random matrices. We show that temporal variation in recombination rate alone, in the absence of fluctuating viability selection, can reverse the direction of selection on the modifier locus predicted by the deterministic model. The mean recombination rate is insufficient to determine invasion of $M_2$; instead, outcomes depend on the full distribution of recombination rates and their ordered accumulation across generations. Parameters that affect only the magnitude of selection under constant transmission - including resident recombination, selection strength, and background linkage - can alter its sign under stochastic transmission. These results demonstrate that temporal variability in transmission constitutes an independent and qualitatively distinct force in the evolution of recombination rates.