Dispersal is a significant characteristic of life history of many species. Dispersal polymorphisms in nature propose that dispersal can have significant effect on species diversity. Evolution of dispersal is one probable reason to speciation. I consider an environment of well-connected and separate living sites and study how connectivity difference between different sites can affect the evolution of a two-dimensional dispersal strategy. Two-dimensionality means that the strategy consists of two separate traits.
Adaptive dynamics is a mathematical framework for analysis of evolution. It assumes small phenotypic mutations and considers invasion possibility of a rare mutant. Generally invasion of a sufficiently similar mutant leads to substitution of the former resident. Consecutive invasion-substitution processes can lead to a singular strategy where directional evolution vanishes and evolution may stop or result in evolutionary branching.
First I introduce some fundamental elements of adaptive dynamics. Then I construct a mathematical model for studying evolution. The model is created from the basis of the Hamilton-May model (1977). Last I analyse the model using tools I introduced previously.
The analysis predicts evolution to a unique singular strategy in a monomorphic resident population. This singularity can be evolutionarily stable or branching depending on survival probabilities during different phases of dispersal. After branching the resident population becomes dimorphic. There seems to be always an evolutionarily stable dimorphic singularity. At the singularity one resident specializes fully to the well-connected sites while the other resides both types of sites.
Connectivity difference of sites can lead to evolutionary branching in a monomorphic population and maintain a stable dimorphic population.
