Fitness landscapes and adaptive dynamics

• Applicants: Professor Dr. Anton Bovier; Professor Dr. Joachim Krug
• Subject Area: Mathematics
• Term: from 2012 to 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 221844245

The adaptive evolution of a population under the influenceof mutation and selection is governed by the structure of theunderlying fitness landscape. Here fitness can either be assigned directly to genotypes, or it arises dynamically from ecological interactions. In the first case thefitness landscape is modeled as a random function on the space of genotypes, andthe interest is in characterizing the evolutionary accessibility of high-fitnessregions, for example, in terms of pathways of ascending fitness and the properties of uphilladaptive walks. Building on results achieved in the first funding period, the project willcontinue the investigation of accessibility properties for classes of correlated landscapesand introduce more realistic models incorporating explicit intermediate phenotypes. The application of adaptive walks for the exploration of high-dimensional empirical data sets will also be developed. An important achievement of the investigation of adaptive dynamics in the first funding period was a rigorous control of various scaling limits, and these results can now be exploited to provide an underpinning of the simplified adaptive walk models in terms of individual-based ecological dynamics. Moreover, the analysis will be extended to the regime of evolutionary branching, and the effects of higher mutation rates and diploid recombination on genetic diversity will be addressed. A further focus of the project will be on adaptive dynamics models with phenotypic switchingthat arise in the context of tumor growth and immunotherapy.

• DFG Programme: Priority Programmes
• Subproject of: SPP 1590: Probabilistic Structures in Evolution