Phases of polygenic adaptation.

The adaptive process is partitioned into two phases. The initial, stochastic phase describes the establishment of mutant alleles. Ignoring epistasis during this phase, it can be described by a Yule process (panel a), with two types of events (yellow box). Either a new mutation occurs and establishes with rate Θl ⋅ sb or an existing mutant line splits into two daughter lines at rate sb. Mutations and splits can occur in parallel at all loci of the polygenic basis, (here 2 loci, shown in green and blue). Yellow and red stars at the blue locus indicate establishment of two redundant mutations at this locus. When mutants have grown to higher frequencies, the adaptive process enters its second, deterministic phase, where drift can be ignored (panel b). During the deterministic phase, the trajectories of mutations at different loci constrain each other due to epistasis. We refer to the locus ending up at the highest frequency as the major locus (here in blue) and to all others as minor loci (here one in green).