SPP 1590:  Probabilistic Structures in Evolution

• Subject Area: Mathematics
• Term: from 2012 to 2020
• Website: Homepage
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 198501163

Biological evolution is a complex phenomenon driven by various underlying processes, such as mutation and recombination of genetic material, reproduction of individuals, competition and selection of favourable types. Studying the interplay of these processes requires a substantial use of mathematical models and methods. Over the past decades, much of this modelling and analysis took place on a deterministic level, using dynamical systems and differential equations, and this has led to an elaborate theory. However, the processes of evolution have intrinsically random elements, such as random reproduction, which leads to stochastic fluctuations of gene frequencies and the emergence of random genealogies. The underlying stochastic processes are receiving increased attention, not least because they have shaped present-day genomes. Indeed, the study of these processes is crucial for understanding observations and interpreting data that arise in modern empirical evolutionary biology. From the point of view of mathematics, challenging new structures emerge, such as Fleming-Viot and ancestral processes with high offspring variation, coalescents with spatial and genetic structure, and individual-based models of adaptive dynamics. The main objective of the Priority Programme is the in-depth theoretical study of (1) stochastic processes in population genetics (that is, describing the evolution of the genetic structure of populations under the action of the various evolutionary forces, in particular in the presence of selection and recombination), (2) stochastic models of adaptive dynamics (that is, individual-based models for the joint description of ecology and evolution), and probabilistic aspects of evolutionary game theory. Retrospective genealogical aspects are an inherent part of population genetics theory, but should also be developed for game theory and adaptive dynamics. Therefore, random genealogies and trees form a conceptual anchor to all themes in the Priority Programme. In this context, structures such as evolving genealogies, coalescents with highly variable offspring distribution and genealogies with genetic and geographic structure will be targeted. The Priority Programme thus aims at the further development of the mathematical theory of biological evolution. In addition, projects involving the analysis of related experimental data will be targeted; here, approaches will be model driven rather than purely statistical.

• DFG Programme: Priority Programmes
• International Connection: Denmark, Iceland, United Kingdom

Projects

• Accounting for spatial heterogeneity of parameters in the sequentially Markov coalescent process (Applicant Dutheil, Ph.D., Julien )
• Ancestral lineages and long-time behaviour of population models with interactions (Applicants Birkner, Matthias ;  Gantert, Nina Jael )
• Branching random walks in random enviroment and their applications to population genetics (Applicant König, Wolfgang )
• Combinatoric and probabilistic properties regarding the topology of genealogical trees and application in population genetics (Applicant Wiehe, Thomas )
• Constrained branching random walks as a minimal stochastic model of asexual adaptation (Applicant Hallatschek, Oskar )
• Coordination Funds (Applicant Baake, Ellen )
• Evolution of altruistic defense traits in structured populations (Applicants Hutzenthaler, Martin ;  Metzler, Dirk )
• Evolutionary game theoretic models with underlying genetic architecture (Applicant Traulsen, Arne )
• Evolving coalescents (Applicants Kersting, Götz ;  Wakolbinger, Anton )
• Evolving genealogies under recombination (Applicant Pfaffelhuber, Peter )
• Evolving pathogen phylogenies: a two-level branching approach (Applicant Winter, Anita )
• Fitness landscapes and adaptive dynamics (Applicants Bovier, Anton ;  Krug, Joachim )
• Genealogical aspects of symbiotic and mutually catalytic branching processes (Applicant Klenke, Achim )
• Genealogies and inference for populations with highly skewed offspring distributions under further evolutionary forces (Applicants Birkner, Matthias ;  Blath, Jochen )
• Genealogies of populations with competition and large variation in the offspring distribution in multi locus and spatially structured settings (Applicant Sturm, Anja )
• Genotype-Phenotype Maps and Signatures of Selection in Genomic Sequences (Applicant Stadler, Peter Florian )
• Interacting stochastic (partial) differential equations, combinatorial stochastic processes and duality in spatial population dynamics (Applicant Blath, Jochen )
• Interfaces in spatial population dynamics (Applicant Ortgiese, Marcel )
• Lines of descent under selection (Applicants Baake, Ellen ;  Wakolbinger, Anton )
• Multiple-merger coalescents - suitable models for gene genealogies in real populations? (Applicant Freund, Fabian )
• Recombination processes and ancestral partitioning (Applicants Baake, Ellen ;  Baake, Michael )
• Recurrent selective sweeps versus trench warfare in host-parasite coevolution: the influence of population size changes (Applicants Stephan, Wolfgang ;  Tellier, Aurélien )
• Stochastic evolution under selection, rare mutation and recombination: From configurations to genealogical structures and back (Applicant Greven, Andreas )
• The effect of natural selection on genealogies (Applicants Hutzenthaler, Martin ;  Pfaffelhuber, Peter )
• The population genetics of the CRISPR-Cas system in bacteria (Applicants Backofen, Rolf ;  Pfaffelhuber, Peter )
• The role of dormancy in population genetics (Applicants Blath, Jochen ;  Kurt, Noemi )

• Spokesperson: Professorin Dr. Ellen Baake