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. Depending on the
model parameters, this architecture reproduces the well-known patterns of
sequential, monogenic sweeps, or of subtle, polygenic frequency shifts.
Between these endpoints, we observe oligogenic architecture types that
exhibit characteristic patterns of partial sweeps. We find that a single
compound parameter, the population-scaled background mutation rate Θbg, is
the most important predictor of the type of adaptation, while selection
strength, the number of loci in the genetic basis, and linkage only play a
minor role.