Individuals on the Move : Body Condition Dependent Dispersal and Quasi-Local Competition in Metapopulations

Individual movement is very versatile and inevitable in ecology. In this thesis, I investigate two kinds of movement body condition dependent dispersal and small-range foraging movements resulting in quasi-local competition and their causes and consequences on the individual, population and metapopulation level. Body condition dependent dispersal is a widely evident but barely understood phenomenon. In nature, diverse relationships between body condition and dispersal are observed. I develop the first models that study the evolution of dispersal strategies that depend on individual body condition. In a patchy environment where patches differ in environmental conditions, individuals born in rich (e.g. nutritious) patches are on average stronger than their conspecifics that are born in poorer patches. Body condition (strength) determines competitive ability such that stronger individuals win competition with higher probability than weak individuals. Individuals compete for patches such that kin competition selects for dispersal. I determine the evolutionarily stable strategy (ESS) for different ecological scenarios. My models offer explanations for both dispersal of strong individuals and dispersal of weak individuals. Moreover, I find that within-family dispersal behaviour is not always reflected on the population level. This supports the fact that no consistent pattern is detected in data on body condition dependent dispersal. It also encourages the refining of empirical investigations. Quasi-local competition defines interactions between adjacent populations where one population negatively affects the growth of the other population. I model a metapopulation in a homogeneous environment where adults of different subpopulations compete for resources by spending part of their foraging time in the neighbouring patches, while their juveniles only feed on the resource in their natal patch. I show that spatial patterns (different population densities in the patches) are stable only if one age class depletes the resource very much but mainly the other age group depends on it.

Composition operators, Aleksandrov measures and value distribution of analytic maps in the unit disc

A composition operator is a linear operator that precomposes any given function with another function, which is held fixed and called the symbol of the composition operator. This dissertation studies such operators and questions related to their theory in the case when the functions to be composed are analytic in the unit disc of the complex plane. Thus the subject of the dissertation lies at the intersection of analytic function theory and operator theory. The work contains three research articles. The first article is concerned with the value distribution of analytic functions. In the literature there are two different conditions which characterize when a composition operator is compact on the Hardy spaces of the unit disc. One condition is in terms of the classical Nevanlinna counting function, defined inside the disc, and the other condition involves a family of certain measures called the Aleksandrov (or Clark) measures and supported on the boundary of the disc. The article explains the connection between these two approaches from a function-theoretic point of view. It is shown that the Aleksandrov measures can be interpreted as kinds of boundary limits of the Nevanlinna counting function as one approaches the boundary from within the disc. The other two articles investigate the compactness properties of the difference of two composition operators, which is beneficial for understanding the structure of the set of all composition operators. The second article considers this question on the Hardy and related spaces of the disc, and employs Aleksandrov measures as its main tool. The results obtained generalize those existing for the case of a single composition operator. However, there are some peculiarities which do not occur in the theory of a single operator. The third article studies the compactness of the difference operator on the Bloch and Lipschitz spaces, improving and extending results given in the previous literature. Moreover, in this connection one obtains a general result which characterizes the compactness and weak compactness of the difference of two weighted composition operators on certain weighted Hardy-type spaces.

Tests for Cointegration Rank and the Initial Condition

Many economic events involve initial observations that substantially deviate from long-run steady state. Initial conditions of this type have been found to impact diversely on the power of univariate unit root tests, whereas the impact on multivariate tests is largely unknown. This paper investigates the impact of the initial condition on tests for cointegration rank. We compare the local power of the widely used likelihood ratio (LR) test with the local power of a test based on the eigenvalues of the companion matrix. We find that the power of the LR test is increasing in the magnitude of the initial condition, whereas the power of the other test is decreasing. The behaviour of the tests is investigated in an application to price convergence.