How Fisherian runaway halts: Genomic architecture determines the long-term evolutionary consequences of sexual selection.

Sexual selection explains the evolution of exaggerated sexual displays, but less obvious is why biased mate preferences--a requirement for sexual selection--evolve. Fisher (1930) proposed that biased mate preferences can spark self-reinforcing evolutionary process (runaway) that drives their own evolution. This occurs because mate choice imposes sexual selection on sexual displays and links them genetically to mate preferences, producing indirect selection on the preferences themselves. While mathematical models have demonstrated the plausibility of the runaway theory, they rely on several idealized assumptions. Consequently, it remains poorly understood how runaway halts once populations deviate from these idealized conditions as a consequence of evolution via runaway, and how the genetic architecture underlying sexual displays influences the resulting evolutionary dynamics. Here, we address these gaps using two complementary approaches. First, we review and synthesize existing theories to classify the mechanisms that halt runaway into four categories, based on which idealized assumptions of Lande's (1981) classic model are violated during evolution via runaway. Second, we conduct individual-based evolutionary simulations varying the genetic architecture of sexual displays from conventional additive to omnigenic inheritance models. Our results show that genetic architecture determines how runaway process halts, thereby governing long-term evolutionary dynamics under sexual selection.