We show that non-linear diffusion equations can describe state-dependent diffusion, i.e., fission–fusion dynamics. We thereby provide a new dynamical basis for understanding Tsallis distributions (q-Gaussian distributions), anomalous diffusion (subdiffusion, superdiffusion and superballistic...

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...

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...

Adaptation to an environment consisting of two patches (each with different optimal strategy) is investigated. The patches have independent density regulation ('soft selection'). If the patches are similar enough and migration between them is strong, then evolution ends up with a generalist ESS....

We present a model for the evolutionary dynamics of seed size when seedlings from large seeds are better competitors than seedling from small seeds and there is a trade-off between seed size and seed number. We first consider two limiting cases where seed size either has no effect on the...

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...

We set out to explore a class of stochastic processes called, 'adaptive dynamics', which supposedly capture some of the essentials of the long-term biological evolution. These processes have a strong deterministic component. This allows a classification of their qualitative features which in...