The Fisher process of sexual selection with the coevolution of preference strength.

Sexual selection has a rich history of mathematical models that consider why preferences favor one trait phenotype over another (for population genetic models) or what specific trait value is preferred (for quantitative genetic models). Less common is exploration of the evolution of choosiness or preference strength: i.e., by how much a trait is preferred. We examine both population and quantitative genetic models of the evolution of preferences, specifically developing "baseline models" of the evolution of preference strength during the Fisher process. Using a population genetic approach, we find selection for stronger and stronger preferences when trait variation is maintained by mutation. However, this force is quite weak and likely to be swamped by drift in moderately-sized populations. In a quantitative genetic model, unimodal preferences will generally not evolve to be increasingly strong without bounds when male traits are under stabilizing viability selection, but evolve to extreme values when viability selection is directional. Our results highlight that different shapes of fitness and preference functions lead to qualitatively different trajectories for preference strength evolution ranging from no evolution to extreme evolution of preference strength.