A theory of oligogenic adaptation of a quantitative trait

Rapid phenotypic adaptation is widespread in nature, but the underlying genetic dynamics remain controversial. Whereas population genetics envisages sequential beneficial substitutions, quantitative genetics assumes a collective response through subtle shifts in allele frequencies. This dichotomy of a monogenic and a highly polygenic view of adaptation raises the question of a middle ground, as well as the factors controlling the transition. Here, we consider an additive quantitative trait with equal locus effects under Gaussian stabilizing selection that adapts to a new trait optimum after an environmental change. We present an analytical framework based on Yule branching processes to describe how phenotypic adaptation is achieved by collective changes in allele frequencies at the underlying loci. In particular, we derive an approximation for the joint allele-frequency distribution at threshold levels of the trait mean as a comprehensive descriptor of the adaptive architecture. Dependi..., The included raw data was generated by evolutionary (Wright-Fisher) simulations. The used C++ simulation scripts are included as source codes and compiled executables.The raw data is processed, plotted and complemented with modeling results by Wolfram Mathematica scripts. The used code snippets are presented in Mathematica Notebooks.We provide all code and data to recreate the figures in the publication., Wolfram Research, Inc., Mathematica, Version 12.0, Champaign, IL (2019). For *.nb (Mathematica Notebooks) and *.mx (Wolfram Language MX files).Executables and corresponding C++ code (Stroustrup, Bjarne. The C++ Programming Language. Reading, Mass.: Addison-Wesley, 1995; *.cpp) can be compiled with g++. We use the GNU Scientific Library (GSL).Besides, the repository contains plain text files (*.csv, *.txt), Bash scripts (*.sh), OpenDocument Presentation (*.odp), vector graphics (*.pdf) and raster graphics (*.png).