In the thesis the dynamics of strategies is studied from two perspectives.In the first part of the thesis strategies are considered to be opinions present in a community. Firstly, the change of... Show moreIn the thesis the dynamics of strategies is studied from two perspectives.In the first part of the thesis strategies are considered to be opinions present in a community. Firstly, the change of support in time for two opinions is being analysed in case opinion bearers repeatedly meet in groups of size three. An opinion bearer is either an inflexible or a floater. An inflexible always adheres to the supported opinion, whereas a floater changes from opinion if the originally supported opinion has the minority in the group. A second chapter on opinion dynamics allows floaters to show either contrarian or non-contrarian behaviour. Both types of floaters adopt the opinion that has the majority in the group of size three, but a contrarian floater subsequently shifts to the alternative opinion.The second part deals with adaptive dynamics. Adaptive dynamics mathematically models the formation of evolutionary trees. The focus here is on phenotypic strategies present in ecological communities. The interest does not so much lie in the densities these strategies have, but in which strategies are present in the course of evolutionary time. The changes in presence are caused by repeated invasions of a mutant population in which the individuals express a strategy that deviates from those present in the invaded community. Show less
"Adaptive dynamics" is the study of evolution driven by rare mutations with small effects. The essential tool is the "invasion fitness", the expected number of offspring for a rare mutant in a... Show more"Adaptive dynamics" is the study of evolution driven by rare mutations with small effects. The essential tool is the "invasion fitness", the expected number of offspring for a rare mutant in a resident community at equilibrium. The first part of this thesis starts by generalising the "canonical equation of adaptive dynamics", a first-order approximation of the speed of change of multidimensional traits under directional selection, so that it holds for general physiologically structured (i.e., arbitrarily complex) population models. Secondly, it proves that near evolutionary singularities and up to second-order terms, such models have the same invasion fitness as the much simpler Lotka-Volterra models (but third-order terms can differ). Thirdly, it combines those results in a recipe for studying analytically the complete dynamics of evolutionary models with limited mutational effects. A prerequisite for models of sympatric speciation to work is the evolution of assortative mating, which has never been validated against alternatives. Therefore the second part compares in a general setting the relative probabilities of the evolution of assortative mate choice to that of dominance interactions, and the conditions favouring each one. This part also shows that allowing for the possibility of sexual dimorphism makes sympatric speciation much less likely. Show less
The course of evolution is restricted by constraints. A special type of constraint is a trade-off where different traits are negatively correlated. In this situation a mutant type that shows an... Show moreThe course of evolution is restricted by constraints. A special type of constraint is a trade-off where different traits are negatively correlated. In this situation a mutant type that shows an improvement in one trait suffers from a decreased performance through another trait. In a fixed fitness landscape evolution is expected to come up with a compromise of the competing fitness components that is optimal in the sense that no other realized compromise can be more successful. However, in most ecological settings the resident community will form a vital part of the selective environment experienced by a mutant. In this case each component in a fitness trade-off can be affected by the phenotype of the conspecifics, which causes the fitness landscape to change as evolution proceeds. We refer to selection in a changing fitness landscape as frequency dependent. With frequency dependence the concept of optimality cannot be applied anymore. This thesis explores, by means of mathematical models, how frequency dependence can be detected and how it alters the evolutionary dynamics of traits that are coupled by a trade-off. Special attention is paid to the phenomenon of evolutionary branching where directional selection drives a population's trait distribution into a region of the trait space where selection turns disruptive. Show less
