Energy norm a-posteriori error estimation for hp-adaptive discontinuous Galerkin methods for elliptic problems in three dimensions

We develop the energy norm a-posteriori error estimation for hp-version discontinuous Galerkin (DG) discretizations of elliptic boundary-value problems on 1-irregularly, isotropically refined affine hexahedral meshes in three dimensions. We derive a reliable and efficient indicator for the errors measured in terms of the natural energy norm. The ratio of the efficiency and reliability constants is independent of the local mesh sizes and weakly depending on the polynomial degrees. In our analysis we make use of an hp-version averaging operator in three dimensions, which we explicitly construct and analyze. We use our error indicator in an hp-adaptive refinement algorithm and illustrate its practical performance in a series of numerical examples. Our numerical results indicate that exponential rates of convergence are achieved for problems with smooth solutions, as well as for problems with isotropic corner singularities.

Wave impedance selection for passivity-based bilateral teleoperation

When a task must be executed in a remote or dangerous environment, teleoperation systems may be employed to extend the influence of the human operator. In the case of manipulation tasks, haptic feedback of the forces experienced by the remote (slave) system is often highly useful in improving an operator's ability to perform effectively. In many of these cases (especially teleoperation over the internet and ground-to-space teleoperation), substantial communication latency exists in the control loop and has the strong tendency to cause instability of the system. The first viable solution to this problem in the literature was based on a scattering/wave transformation from transmission line theory. This wave transformation requires the designer to select a wave impedance parameter appropriate to the teleoperation system. It is widely recognized that a small value of wave impedance is well suited to free motion and a large value is preferable for contact tasks. Beyond this basic observation, however, very little guidance exists in the literature regarding the selection of an appropriate value. Moreover, prior research on impedance selection generally fails to account for the fact that in any realistic contact task there will simultaneously exist contact considerations (perpendicular to the surface of contact) and quasi-free-motion considerations (parallel to the surface of contact). The primary contribution of the present work is to introduce an approximate linearized optimum for the choice of wave impedance and to apply this quasi-optimal choice to the Cartesian reality of such a contact task, in which it cannot be expected that a given joint will be either perfectly normal to or perfectly parallel to the motion constraint. The proposed scheme selects a wave impedance matrix that is appropriate to the conditions encountered by the manipulator. This choice may be implemented as a static wave impedance value or as a time-varying choice updated according to the instantaneous conditions encountered. A Lyapunov-like analysis is presented demonstrating that time variation in wave impedance will not violate the passivity of the system. Experimental trials, both in simulation and on a haptic feedback device, are presented validating the technique. Consideration is also given to the case of an uncertain environment, in which an a priori impedance choice may not be possible.

A Mutational Hotspot and Strong Selection Contribute to the Order of Mutations Selected for during Escherichia coli Adaptation to the Gut

The relative role of drift versus selection underlying the evolution of bacterial species within the gut microbiota remains poorly understood. The large sizes of bacterial populations in this environment suggest that even adaptive mutations with weak effects, thought to be the most frequently occurring, could substantially contribute to a rapid pace of evolutionary change in the gut. We followed the emergence of intra-species diversity in a commensal Escherichia coli strain that previously acquired an adaptive mutation with strong effect during one week of colonization of the mouse gut. Following this first step, which consisted of inactivating a metabolic operon, one third of the subsequent adaptive mutations were found to have a selective effect as high as the first. Nevertheless, the order of the adaptive steps was strongly affected by a mutational hotspot with an exceptionally high mutation rate of 10-5. The pattern of polymorphism emerging in the populations evolving within different hosts was characterized by periodic selection, which reduced diversity, but also frequency-dependent selection, actively maintaining genetic diversity. Furthermore, the continuous emergence of similar phenotypes due to distinct mutations, known as clonal interference, was pervasive. Evolutionary change within the gut is therefore highly repeatable within and across hosts, with adaptive mutations of selection coefficients as strong as 12% accumulating without strong constraints on genetic background. In vivo competitive assays showed that one of the second steps (focA) exhibited positive epistasis with the first, while another (dcuB) exhibited negative epistasis. The data shows that strong effect adaptive mutations continuously recur in gut commensal bacterial species.

FROM GENES TO GENOMES: LOCAL ADAPTATION AND ADAPTIVE POTENTIAL IN TWO ARCTIC SEABIRDS

By investigating the mechanisms underlying the evolution and the maintenance of local adaptations we can help predict how species will adapt to future environmental change. In this thesis I investigate local adaptation and adaptive potential in thick-billed and common murres (Uria lomvia and U. aalge), two arctic seabirds of international conservation concern. Thanks to the recent development of new genomic methods, I address three major themes that are relevant for both the development of evolutionary theory and conservation: 1) the role of gene flow in the origin and maintenance of adaptation; 2) levels and distribution of standing genetic variation, and their contribution to adaptive potential; and 3) the genomic mechanisms maintaining an adaptive dimorphism within a single interbreeding population. First, I review the literature on genomics of local adaptation with gene flow and find that adaptation can be maintained despite gene flow, that gene flow itself can promote adaptation, and that genetic architecture is important in the origin and maintenance of local adaptations. Second, I genotype genome-wide markers and toll-like receptor genes (TLRs) to investigate local adaptation and adaptive potential in thick-billed murres. Thick-billed murres do not show signatures of local adaptation to their breeding grounds, but outlier loci group birds according to their non-breeding distributions, suggesting that selection and/or demographic connectivity in the winter may explain patterns of differentiation in this species. Genetic variation at TLRs does not decrease with increasing latitude as predicted, but tests of selection and measures of genetic diversity suggest differences in local selective regimes at most genes. Thick-billed murres show high levels of standing genetic variation and their adaptive potential will mostly depend on rate and magnitude of environmental change. Finally, I improve and annotate the assembly of the highly heterozygous genome of the thick-billed murre. Using this assembly as a reference, I perform whole genome analyses to investigate the genomic basis of an adaptive dimorphism in Atlantic common murres. I show for the first time that a 60 kb complex copy number variant in a non-coding region maintains differences in plumage and cold adaptation despite high gene flow.

Adaptive strategies of two Portuguese grapevines varieties (Aragonês. syn. Tempranillo and Trincadeira) face drought: physiological and structural responses.

At Mediterranean regions and particularly in southern Portugal, it is imperative to identify grape varieties more adapted to warm and dry climates in order to overcome future climatic changes. Two Vitis vinifera genotypes, Aragonez (syn. Tempranillo) and Trincadeira, were selected to assess their physiological responses to soil water stress. Vines were subjected to four irrigation regimes: irrigated during all phenological cycle, non-irrigated during all phenological cycle, non irrigated until veraison, irrigated after veraison. Predawn leaf water potential was much higher in Trincadeira than Aragonez in non- irrigated plants. This result is in accordance with its higher stomatal control efficiency in this variety (Trincadeira). Photosynthetic capacity (Amax at saturating light intensity) decreased due to stomatal and biochemical limitations under water stress. However, recovery capacity of leaf water status after irrigation was faster in Trincadeira. Yield and yield x Brix increased when irrigation occurred after veraison, particularly in Trincadeira. These results show that Trincadeira presents a drought adaptation than Aragonez. Ratio of variable to maximum fluorescence Fv/Fm and total leaf chlorophyll related with leaf water potential for both species. Reflectance Normalized Difference Vegetation Index (NDVI705), Red Edge Inflexion Point Index and Photochemical Reflectance Index were related with irrigation treatment. Relative water content and specific leaf area were similar between varieties. In conclusion, we suggested that there is variation among the genotypes and the main physiological parameters for variety selection, for drought, were leaf water potential, stomatal conductance and reflectance indexes.

Wild carrot differentiation in Europe and positive selection at DcAOX1 gene

By definition, the domestication process leads to an overall reduction of crop genetic diversity. This lead to the current search of genomic regions in wild crop relatives (CWR), an important task for modern carrot breeding. Nowadays massive sequencing possibilities can allow for discovery of novel genetic resources in wild populations, but this quest could be aided by the use of a surrogate gene (to first identify and prioritize novel wild populations for increased sequencing effort). Alternative oxidase (AOX) gene family seems to be linked to all kinds of abiotic and biotic stress reactions in various organisms and thus have the potential to be used in the identification of CWR hotspots of environment-adapted diversity. High variability of DcAOX1 was found in populations of wild carrot sampled across a West-European environmental gradient. Even though no direct relation was found with the analyzed climatic conditions or with physical distance, population differentiation exists and results mainly from the polymorphisms associated with DcAOX1 exon 1 and intron 1. The relatively high number of amino acid changes and the identification of several unusually variable positions (through a likelihood ratio test), suggests that DcAOX1 gene might be under positive selection. However, if positive selection is considered, it only acts on some specific populations (i.e. is in the form of adaptive differences in different population locations) given the observed high genetic diversity. We were able to identify two populations with higher levels of differentiation which are promising as hot spots of specific functional diversity.

Sexual selection in a tropical fruit fly : role of a plant derived chemical in mate choice

The specific mechanisms by which selective pressures affect individuals are often difficult to resolve. In tephritid fruit flies, males respond strongly and positively to certain plant derived chemicals. Sexual selection by female choice has been hypothesized as the mechanism driving this behaviour in certain species, as females preferentially mate with males that have fed on these chemicals. This hypothesis is, to date, based on studies of only very few species and its generality is largely untested. We tested the hypothesis on different spatial scales (small cage and seminatural field-cage) using the monophagous fruit fly, Bactrocera cacuminata. This species is known to respond to methyl eugenol (ME), a chemical found in many plant species and one upon which previous studies have focused. Contrary to expectation, no obvious female choice was apparent in selecting ME-fed males over unfed males as measured by the number of matings achieved over time, copulation duration, or time of copulation initiation. However, the number of matings achieved by ME-fed males was significantly greater than unfed males 16 and 32 days after exposure to ME in small cages (but not in a field-cage). This delayed advantage suggests that ME may not influence the pheromone system of B. cacuminata but may have other consequences, acting on some other fitness consequence (e.g., enhancement of physiology or survival) of male exposure to these chemicals. We discuss the ecological and evolutionary implications of our findings to explore alternate hypotheses to explain the patterns of response of dacine fruit flies to specific plant-derived chemicals.