Tannakian Formalism Applied to the Category of Mixed Hodge Structures

Many problems in analysis have been solved using the theory of Hodge structures. P. Deligne started to treat these structures in a categorical way. Following him, we introduce the categories of mixed real and complex Hodge structures. Category of mixed Hodge structures over the field of real or complex numbers is a rigid abelian tensor category, and in fact, a neutral Tannakian category. Therefore it is equivalent to the category of representations of an affine group scheme. The direct sums of pure Hodge structures of different weights over real or complex numbers can be realized as a representation of the torus group, whose complex points is the Cartesian product of two punctured complex planes. Mixed Hodge structures turn out to consist of information of a direct sum of pure Hodge structures of different weights and a nilpotent automorphism. Therefore mixed Hodge structures correspond to the representations of certain semidirect product of a nilpotent group and the torus group acting on it.

Dung beetle radiations in Madagascar

Speciation on islands is affected by island size and the range of habitats and resources available and often also by limited interactions with other taxa. An ancestral population may evolve into a large number of species via an adaptive radiation. In Madagascar, most groups of animals and plants have radiated on the island, having arrived via oceanic dispersal during the long isolation of Madagascar. Characteristic features of Malagasy biota are exceptionally high level of endemism, high species richness as well as lack of many higher taxa that are dominant on the African mainland. Malagasy dung beetles are dominated by two tribes, Canthonini and Helictopleurina, with more than 250 endemic species. In this thesis I have reconstructed molecular phylogenies for the two tribes using several gene regions and different phylogenetic methods. Evolution of closely related species and among populations of the same species was examined with haplotype networks. The Malagasy Canthonini consists of three large lineages, while Helictopleurina forms a monophyletic group. The ancestors of each of the four clades colonised Madagascar at different times during Cenozoic. The subsequent radiations differ in terms of the number of extant species (from 37 to more than 100) and the level of ecological differentiation. In addition, Onthophagini (6 species) and Scarabaeini (3) have colonised Madagascar several times, but they have not radiated and the few species have not entered forests where Canthonini and Helictopleurina mostly occur. Among the three Canthonini radiations, speciation appears to have been mostly allopatric in the oldest and the youngest clades, while in the Epactoides clade sister species have diverged in their ecologies but have similar geographical distributions, indicating that speciation may have occurred in regional sympatry. The most likely isolating mechanisms have been rivers and forest refugia during dry and cool geological periods. Most species are generalists feeding on both carrion and dung, and competition among ecologically similar species may prevent their coexistence in the same communities. Some species have evolved to forage in the canopy and a few species have shifted to use cattle dung, a new resource in the open habitats following the introduction of cattle 1500 years ago. The latter shift has allowed species to expand their geographical ranges.

Root system traits of Norway spruce, Scots pine, and silver birch in mixed boreal forests: an analysis of root architecture, morphology, and anatomy

The aim of this thesis was to unravel the functional-structural characteristics of root systems of Betula pendula Roth., Picea abies (L.) Karst., and Pinus sylvestris L. in mixed boreal forest stands differing in their developmental stage and site fertility. The root systems of these species had similar structural regularities: horizontally-oriented shallow roots defined the horizontal area of influence, and within this area, each species placed fine roots in the uppermost soil layers, while sinker roots defined the maximum rooting depth. Large radial spread and high ramification of coarse roots, and the high specific root length (SRL) and root length density (RLD) of fine roots indicated the high belowground competitiveness and root plasticity of B. pendula. Smaller radial root spread and sparser branching of coarse roots, and low SRL and RLD of fine roots of the conifers could indicate their more conservative resource use and high association with and dependence on ectomycorrhiza-forming fungi. The vertical fine root distributions of the species were mostly overlapping, implying the possibility for intense belowground competition for nutrients. In each species, conduits tapered and their frequency increased from distal roots to the stem, from the stem to the branches, and to leaf petioles in B. pendula. Conduit tapering was organ-specific in each species violating the assumptions of the general vascular scaling model (WBE). This reflects the hierarchical organization of a tree and differences between organs in the relative importance of transport, safety, and mechanical demands. The applied root model was capable of depicting the mass, length and spread of coarse roots of B. pendula and P. abies, and to the lesser extent in P. sylvestris. The roots did not follow self-similar fractal branching, because the parameter values varied within the root systems. Model parameters indicate differences in rooting behavior, and therefore different ecophysiological adaptations between species.