Systematics and evolution of coastal and deepwater Hydrozoa from the NE Atlantic

The study of the Portuguese Hydrozoa fauna has been abandoned for more than half a century, except for the Azores archipelago. One of the main aims of this Ph.D. project was to contribute new hydrozoan records leading to a more accurate perception of the actual hydrozoan diversity found in Portuguese waters, including the archipelagos of Azores and Madeira, and neighbouring geographical areas, for habitats ranging from the deep sea to the intertidal. Shallow water hydroids from several Portuguese marine regions (including the Gorringe Bank) were sampled by scuba-diving. Deep-water hydroids, from the Azores, Madeira, Gulf of Cadiz and Alboran Sea, were collected by researchers of different institutions during several oceanographic campaigns. Occasional hydroid sampling by scuba-diving was performed in the UK, Malta and Spain. Over 300 hydroid species were identified and about 600 sequences of the hydrozoan ‘DNA barcode’ 16S mRNA were generated. The families Sertulariidae, Plumulariidae, Lafoeidae, Hebellidae, Aglaopheniidae, Campanulinidae, Halopterididae, Kirchenpaueriidae, Haleciidae and Eudendriidae, were studied in greater detail. About 350 16S sequences were generated for these taxa, allowing phylogenetic, phylogeographic and evolutionary inferences, and also more accurate taxonomic identifications. Phylogenetic analyses integrated molecular and morphological characters. Subsequent results revealed: particularly high levels of cryptic biodiversity, polyphyly in many taxonomic groups, pairs of species that were synonymous, the identity of several varieties as valid species, and highlighted phylogeographic associations of hydroids in deep and shallow-water areas of the NE Atlantic and W Mediterranean. It was proved that many (but not all) marine hydroid species with supposedly widespread vertical and/or horizontal geographical distributions, correspond in fact to complexes of cryptic taxa. This study further revealed that, in the NE Atlantic, shallow environments sustain higher hydrozoan diversity and abundance, but the importance of bathyal habitats as a source of phylogenetic diversity was also revealed. The Azorean seamounts were shown to be particularly important in the segregation of populations of hydroids with reduced dispersive potential. The bathyal habitats of the Gulf of Cadiz proved to harbour a considerably high number of cryptic species, which may mainly be a consequence of habitat heterogeneity and convergence of various water masses in the Gulf. The main causes proposed for speciation and population divergence of hydroids were: species population size, dispersal mechanisms and plasticity to inhabit different environmental conditions, but also the influence of oceanic currents (and its properties), habitat heterogeneity, climate change and continental drift. Higher phylogenetic resolution obtained for the family Plumulariidae revealed particularly that glacial cycles likely facilitated population divergence, ultimately speciation, and also faunal evolutionary transitions from deep to shallow waters.

Regularity of Wiener-Hopf plus Hankel operators

In this thesis we consider Wiener-Hopf-Hankel operators with Fourier symbols in the class of almost periodic, semi-almost periodic and piecewise almost periodic functions. In the first place, we consider Wiener-Hopf-Hankel operators acting between L2 Lebesgue spaces with possibly different Fourier matrix symbols in the Wiener-Hopf and in the Hankel operators. In the second place, we consider these operators with equal Fourier symbols and acting between weighted Lebesgue spaces Lp(R;w), where 1 < p < 1 and w belongs to a subclass of Muckenhoupt weights. In addition, singular integral operators with Carleman shift and almost periodic coefficients are also object of study. The main purpose of this thesis is to obtain regularity properties characterizations of those classes of operators. By regularity properties we mean those that depend on the kernel and cokernel of the operator. The main techniques used are the equivalence relations between operators and the factorization theory. An invertibility characterization for the Wiener-Hopf-Hankel operators with symbols belonging to the Wiener subclass of almost periodic functions APW is obtained, assuming that a particular matrix function admits a numerical range bounded away from zero and based on the values of a certain mean motion. For Wiener-Hopf-Hankel operators acting between L2-spaces and with possibly different AP symbols, criteria for the semi-Fredholm property and for one-sided and both-sided invertibility are obtained and the inverses for all possible cases are exhibited. For such results, a new type of AP factorization is introduced. Singular integral operators with Carleman shift and scalar almost periodic coefficients are also studied. Considering an auxiliar and simpler operator, and using appropriate factorizations, the dimensions of the kernels and cokernels of those operators are obtained. For Wiener-Hopf-Hankel operators with (possibly different) SAP and PAP matrix symbols and acting between L2-spaces, criteria for the Fredholm property are presented as well as the sum of the Fredholm indices of the Wiener-Hopf plus Hankel and Wiener-Hopf minus Hankel operators. By studying dependencies between different matrix Fourier symbols of Wiener-Hopf plus Hankel operators acting between L2-spaces, results about the kernel and cokernel of those operators are derived. For Wiener-Hopf-Hankel operators acting between weighted Lebesgue spaces, Lp(R;w), a study is made considering equal scalar Fourier symbols in the Wiener-Hopf and in the Hankel operators and belonging to the classes of APp;w, SAPp;w and PAPp;w. It is obtained an invertibility characterization for Wiener-Hopf plus Hankel operators with APp;w symbols. In the cases for which the Fourier symbols of the operators belong to SAPp;w and PAPp;w, it is obtained semi-Fredholm criteria for Wiener-Hopf-Hankel operators as well as formulas for the Fredholm indices of those operators.