We use the theory of adaptive dynamics to construct and analyse a generic example of cycling evolution with alternating levels of polymorphism. A monomorphic population evolves towards larger trait values until it reaches a so-called evolutionary branching point. Disruptive selection at the...

Matrix game theory and optimization models offer two radically different perspectives on the outcome of evolution. Optimization models consider frequency-independent selection and envisage evolution as a hill-climbing process on a constant fitness landscape, with the optimal strategy...

I investigate the evolution of a continuous trait, such as body size or arms level, which affects the outcome of competitive contests such that the contestant with the larger trait value has a higher probability of winning. I show that a polymorphism of distinctly different strategies can evolve...

We investigate how a plymorphism of distinctly different alleles can evolve in an initially monomorphic population under frequency-dependent selection if mutations have only a small phenotypic effect. We consider the case of a single additive locus with a continuum of potential allele types in a...

We present a formal framework for modeling evolutionary dynamics with special emphasis on the generation of diversity through branching of the evolutionary tree. Fitness is defined as the long term growth rate which is influenced by the biotic environment leading to frequency-dependent...

We present a general framework for modeling adaptive traitdynamics in which we integrate various concepts and techniques from modern ESS-theory. The concept of evolutionarily singular strategies is introduced as a generalization of the ESS-concept. We give a full classification of the singular...