Fisher's lost model of runaway sexual selection: Sexy sons theory survives math modeling better than good genes theory

Fisher's lost model of runaway sexual selection. Jonathan M. Henshaw  Adam G. Jones. Evolution, December 30 2019. https://doi.org/10.1111/evo.13910

Abstract: The bizarre elaboration of sexually selected traits like the peacock's tail was a puzzle to Charles Darwin and his 19th century followers. Ronald A. Fisher crafted an ingenious solution in the 1930s, positing that female preferences would become genetically correlated with preferred traits due to non‐random mating. These genetic correlations would translate selection for preferred traits into selection for stronger preferences, leading to a self‐reinforcing process of ever‐elaborating traits and preferences. It is widely believed that Fisher provided only a verbal model of this ‘runaway’ process. However, in correspondence with Charles Galton Darwin, Fisher also laid out a simple mathematical model, which purportedly confirms his verbal prediction of runaway sexual selection. Unfortunately, Fisher's model contains inconsistencies that render his quantitative conclusions inaccurate. Here we correct Fisher's model and show that it contains all the ingredients of a working runaway process. We derive quantitative predictions of his model using numerical techniques that were unavailable in Fisher's time. Depending on parameter values, mean traits and preferences may increase until genetic variance is depleted by selection, exaggerate exponentially while their variances remain stable, or both means and variances may increase super‐exponentially. We thus present the earliest mathematical model of runaway sexual selection.

Check also Meta-Analysis Suggests Choosy Females Get Sexy Sons More Than 'Good Genes'. Zofia M. Prokop, Łukasz Michalczyk, Szymon M. Drobniak, Magdalena Herdegen, Jacek Radwan. Evolution, https://www.bipartisanalliance.com/2018/05/meta-analysis-suggests-choosy-females.html