The impact of dormancy on evolutionary branching. (English) Zbl 07874519
Summary: 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 M. Baar and A. Bovier [Electron. J. Probab. 23, Paper No. 72, 27 p. (2018; Zbl 1415.92120)]. 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 N. Champagnat and S. Méléard [Probab. Theory Relat. Fields 151, No. 1–2, 45–94 (2011; Zbl 1225.92040)]. The criterion allows a quantitative and qualitative analysis of the effects of dormancy in the well-known model of U. Dieckmann and M. Doebeli [Nature 400, No. 6748, 354–357 (1999 doi:10.1038/22521)] 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.
MSC:
| 92-XX | Biology and other natural sciences |
| 60J85 | Applications of branching processes |
| 92D25 | Population dynamics (general) |
Keywords:
dormancy; evolutionary branching; adaptive dynamics; sympatric speciation; polymorphic evolution sequence; diversity in trait spaceReferences:
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