Open Access

Jochen Blath, Tobias Paul, András József Tóbiás, Maite Wilke Berenguer

• Highlights • We study dormancy in the ‘rare mutation’ regime of stochastic adaptive dynamics. • We first derive the polymorphic evolution sequence, based on prior work. • Our evolutionary branching criterion extends a result by Champagnat and Méléard. • In a classical model dormancy can favour evolutionary branching. • Dormancy also affects several more population characteristics. Abstract In this paper, we investigate the consequences of dormancy in the ‘rare mutation’ and ‘large population’ regime of stochastic adaptive dynamics. Starting from an individual-based micro-model, we first derive the Polymorphic Evolution Sequence of the population, based on a previous work by Baar and Bovier (2018). After passing to a second ‘small mutations’ limit, we arrive at the Canonical Equation of Adaptive Dynamics, and state a corresponding criterion for evolutionary branching, extending a previous result of Champagnat and Méléard (2011). The criterion allows a quantitative and qualitative analysis of the effects of dormancy in the well-known model of Dieckmann and Doebeli (1999) for sympatric speciation. In fact, quite an intuitive picture emerges: Dormancy enlarges the parameter range for evolutionary branching, increases the carrying capacity and niche width of the post-branching sub-populations, and, depending on the model parameters, can either increase or decrease the ‘speed of adaptation’ of populations. Finally, dormancy increases diversity by increasing the genetic distance between subpopulations.