Technical efficiency of blood component preparation in blood centres of 10 European countries

Various reasons, such as ethical issues in maintaining blood resources, growing costs, and strict requirements for safe blood, have increased the pressure for efficient use of resources in blood banking. The competence of blood establishments can be characterized by their ability to predict the volume of blood collection to be able to provide cellular blood components in a timely manner as dictated by hospital demand. The stochastically varying clinical need for platelets (PLTs) sets a specific challenge for balancing supply with requests. Labour has been proven a primary cost-driver and should be managed efficiently. International comparisons of blood banking could recognize inefficiencies and allow reallocation of resources. Seventeen blood centres from 10 countries in continental Europe, Great Britain, and Scandinavia participated in this study. The centres were national institutes (5), parts of the local Red Cross organisation (5), or integrated into university hospitals (7). This study focused on the departments of blood component preparation of the centres. The data were obtained retrospectively by computerized questionnaires completed via Internet for the years 2000-2002. The data were used in four original articles (numbered I through IV) that form the basis of this thesis. Non-parametric data envelopment analysis (DEA, II-IV) was applied to evaluate and compare the relative efficiency of blood component preparation. Several models were created using different input and output combinations. The focus of comparisons was on the technical efficiency (II-III) and the labour efficiency (I, IV). An empirical cost model was tested to evaluate the cost efficiency (IV). Purchasing power parities (PPP, IV) were used to adjust the costs of the working hours and to make the costs comparable among countries. The total annual number of whole blood (WB) collections varied from 8,880 to 290,352 in the centres (I). Significant variation was also observed in the annual volume of produced red blood cells (RBCs) and PLTs. The annual number of PLTs produced by any method varied from 2,788 to 104,622 units. In 2002, 73% of all PLTs were produced by the buffy coat (BC) method, 23% by aphaeresis and 4% by the platelet-rich plasma (PRP) method. The annual discard rate of PLTs varied from 3.9% to 31%. The mean discard rate (13%) remained in the same range throughout the study period and demonstrated similar levels and variation in 2003-2004 according to a specific follow-up question (14%, range 3.8%-24%). The annual PLT discard rates were, to some extent, associated with production volumes. The mean RBC discard rate was 4.5% (range 0.2%-7.7%). Technical efficiency showed marked variation (median 60%, range 41%-100%) among the centres (II). Compared to the efficient departments, the inefficient departments used excess labour resources (and probably) production equipment to produce RBCs and PLTs. Technical efficiency tended to be higher when the (theoretical) proportion of lost WB collections (total RBC+PLT loss) from all collections was low (III). The labour efficiency varied remarkably, from 25% to 100% (median 47%) when working hours were the only input (IV). Using the estimated total costs as the input (cost efficiency) revealed an even greater variation (13%-100%) and overall lower efficiency level compared to labour only as the input. In cost efficiency only, the savings potential (observed inefficiency) was more than 50% in 10 departments, whereas labour and cost savings potentials were both more than 50% in six departments. The association between department size and efficiency (scale efficiency) could not be verified statistically in the small sample. In conclusion, international evaluation of the technical efficiency in component preparation departments revealed remarkable variation. A suboptimal combination of manpower and production output levels was the major cause of inefficiency, and the efficiency did not directly relate to production volume. Evaluation of the reasons for discarding components may offer a novel approach to study efficiency. DEA was proven applicable in analyses including various factors as inputs and outputs. This study suggests that analytical models can be developed to serve as indicators of technical efficiency and promote improvements in the management of limited resources. The work also demonstrates the importance of integrating efficiency analysis into international comparisons of blood banking.

Search for genetic variants influencing human height

Human growth and attained height are determined by a combination of genetic and environmental effects and in modern Western societies > 80% of the observed variation in height is determined by genetic factors. Height is a fundamental human trait that is associated with many socioeconomic and psychosocial factors and health measures, however little is known of the identity of the specific genes that influence height variation in the general population. This thesis work aimed to identify the genetic variants that influence height in the general population by genome-wide linkage analysis utilizing large family samples. The study focused on analysis of three separate sets of families consisting of: 1) 1,417 individuals from 277 Finnish families (FinnHeight), 2) 8,450 individuals from 3,817 families from Australia and Europe (EUHeight) and 3) 9,306 individuals from 3,302 families from the United States (USHeight). The most significant finding in this study was found in the Finnish family sample where we a locus in the chromosomal region 1p21 was linked to adult height. Several regions showed evidence for linkage in the Australian, European and US families with 8q21 and 15q25 being the most significant. The region on 1p21 was followed up with further studies and we were able to show that the collagen 11-alpha-1 gene (COL11A1) residing at this location was associated with adult height. This association was also confirmed in an independent Finnish population cohort (Health 2000) consisting of 6,542 individuals. From this population sample, we estimated that homozygous males and females for this gene variant were 1.1 and 0.6 cm taller than the respective controls. In this thesis work we identified a gene variant in the COL11A1 gene that influences human height, although this variant alone explains only 0.1% of height variation in the Finnish population. We also demonstrated in this study that special stratification strategies such as performing sex-limited analyses, focusing on dizygous twin pairs, analyzing ethnic groups within a population separately and utilizing homogenous populations such as the Finns can improve the statistical power of finding QTL significantly. Also, we concluded from the results of this study that even though genetic effects explain a great proportion of height variance, it is likely that there are tens or even hundreds of genes with small individual effects underlying the genetic architecture of height.

Feasibility of assimilating ASCAT surface winds into a Limited Area Model

Sea-surface wind observations of previous generation scatterometers have been successfully assimilated into Numerical Weather Prediction (NWP) models. Impact studies conducted with these assimilation implementations have shown a distinct improvement to model analysis and forecast accuracies. The Advanced Scatterometer (ASCAT), flown on Metop-A, offers an improved sea-surface wind accuracy and better data coverage when compared to the previous generation scatterometers. Five individual case studies are carried out. The effect of including ASCAT data into High Resolution Limited Area Model (HIRLAM) assimilation system (4D-Var) is tested to be neutral-positive for situations with general flow direction from the Atlantic Ocean. For northerly flow regimes the effect is negative. This is later discussed to be caused by problems involving modeling northern flows, and also due to the lack of a suitable verification method. Suggestions and an example of an improved verification method is presented later on. A closer examination of a polar low evolution is also shown. It is found that the ASCAT assimilation scheme improves forecast of the initial evolution of the polar low, but the model advects the strong low pressure centre too fast eastward. Finally, the flaws of the implementation are found small and implementing the ASCAT assimilation scheme into the operational HIRLAM suite is feasible, but longer time period validation is still required.

Boundedness and convergence of singular integrals on fractal type sets

The topic of this dissertation lies in the intersection of harmonic analysis and fractal geometry. We particulary consider singular integrals in Euclidean spaces with respect to general measures, and we study how the geometric structure of the measures affects certain analytic properties of the operators. The thesis consists of three research articles and an overview. In the first article we construct singular integral operators on lower dimensional Sierpinski gaskets associated with homogeneous Calderón-Zygmund kernels. While these operators are bounded their principal values fail to exist almost everywhere. Conformal iterated function systems generate a broad range of fractal sets. In the second article we prove that many of these limit sets are porous in a very strong sense, by showing that they contain holes spread in every direction. In the following we connect these results with singular integrals. We exploit the fractal structure of these limit sets, in order to establish that singular integrals associated with very general kernels converge weakly. Boundedness questions consist a central topic of investigation in the theory of singular integrals. In the third article we study singular integrals of different measures. We prove a very general boundedness result in the case where the two underlying measures are separated by a Lipshitz graph. As a consequence we show that a certain weak convergence holds for a large class of singular integrals.

On Games on Non-Wellfounded Sets and Stationary Sets

In this thesis we study a few games related to non-wellfounded and stationary sets. Games have turned out to be an important tool in mathematical logic ranging from semantic games defining the truth of a sentence in a given logic to for example games on real numbers whose determinacies have important effects on the consistency of certain large cardinal assumptions. The equality of non-wellfounded sets can be determined by a so called bisimulation game already used to identify processes in theoretical computer science and possible world models for modal logic. Here we present a game to classify non-wellfounded sets according to their branching structure. We also study games on stationary sets moving back to classical wellfounded set theory. We also describe a way to approximate non-wellfounded sets with hereditarily finite wellfounded sets. The framework used to do this is domain theory. In the Banach-Mazur game, also called the ideal game, the players play a descending sequence of stationary sets and the second player tries to keep their intersection stationary. The game is connected to precipitousness of the corresponding ideal. In the pressing down game first player plays regressive functions defined on stationary sets and the second player responds with a stationary set where the function is constant trying to keep the intersection stationary. This game has applications in model theory to the determinacy of the Ehrenfeucht-Fraisse game. We show that it is consistent that these games are not equivalent.

Construction of a global map of human gene expression : the process, tools and analysis

This thesis studies human gene expression space using high throughput gene expression data from DNA microarrays. In molecular biology, high throughput techniques allow numerical measurements of expression of tens of thousands of genes simultaneously. In a single study, this data is traditionally obtained from a limited number of sample types with a small number of replicates. For organism-wide analysis, this data has been largely unavailable and the global structure of human transcriptome has remained unknown. This thesis introduces a human transcriptome map of different biological entities and analysis of its general structure. The map is constructed from gene expression data from the two largest public microarray data repositories, GEO and ArrayExpress. The creation of this map contributed to the development of ArrayExpress by identifying and retrofitting the previously unusable and missing data and by improving the access to its data. It also contributed to creation of several new tools for microarray data manipulation and establishment of data exchange between GEO and ArrayExpress. The data integration for the global map required creation of a new large ontology of human cell types, disease states, organism parts and cell lines. The ontology was used in a new text mining and decision tree based method for automatic conversion of human readable free text microarray data annotations into categorised format. The data comparability and minimisation of the systematic measurement errors that are characteristic to each lab- oratory in this large cross-laboratories integrated dataset, was ensured by computation of a range of microarray data quality metrics and exclusion of incomparable data. The structure of a global map of human gene expression was then explored by principal component analysis and hierarchical clustering using heuristics and help from another purpose built sample ontology. A preface and motivation to the construction and analysis of a global map of human gene expression is given by analysis of two microarray datasets of human malignant melanoma. The analysis of these sets incorporate indirect comparison of statistical methods for finding differentially expressed genes and point to the need to study gene expression on a global level.

GPRA and the asthma locus on chromosome 7p14-p15

The basis of this work was the identification of a genomic region on chromosome 7p14-p15 that strongly associated with asthma and high serum total immunoglobulin E in a Finnish founder population from Kainuu. Using a hierarchical genotyping approach the linkage region was narrowed down until an evolutionary collectively inherited 133-kb haplotype block was discovered. The results were confirmed in two independent data sets: Asthma families from Quebec and allergy families from North-Karelia. In all the three cohorts studied, single nucleotide polymorphisms tagging seven common gene variants (haplotypes) were identified. Over half of the asthma patients carried three evolutionary closely related susceptibility haplotypes as opposed to approximately one third of the healthy controls. The risk effects of the gene variants varied from 1.4 to 2.5. In the disease-associated region, there was one protein-coding gene named GPRA (G Protein-coupled Receptor for Asthma susceptibility also known as NPSR1) which displayed extensive alternative splicing. Only the two isoforms with distinct intracellular tail sequences, GPRA-A and -B, encoded a full-length G protein-coupled receptor with seven transmembrane regions. Using various techniques, we showed that GPRA is expressed in multiple mucosal surfaces including epithelial cells throughout the respiratory tract. GPRA-A has additional expression in respiratory smooth muscle cells. However, in bronchial biopsies with unknown haplotypes, GPRA-B was upregulated in airways of all patient samples in contrast to the lack of expression in controls. Further support for GPRA as a common mediator of inflammation was obtained from a mouse model of ovalbumin-induced inflammation, where metacholine-induced airway hyperresponsiveness correlated with elevated GPRA mRNA levels in the lung and increased GPRA immunostaining in pulmonary macrophages. A novel GPRA agonist, Neuropeptide S (NPS), stimulated phagocytosis of Esterichia coli bacteria in a mouse macrophage cell line indicating a role for GPRA in the removal of inhaled allergens. The suggested GPRA functions prompted us to study, whether GPRA haplotypes associate with respiratory distress syndrome (RDS) and bronchopulmonary dysplasia (BPD) in infants sharing clinical symptoms with asthma. According to the results, near-term RDS and asthma may also share the same susceptibility and protective GPRA haplotypes. As in asthma, GPRA-B isoform expression was induced in bronchial smooth muscle cells in RDS and BPD suggesting a role for GPRA in bronchial hyperresponsiveness. In conclusion, the results of the present study suggest that the dysregulation of the GPRA/NPS pathway may not only be limited to the individuals carrying the risk variants of the gene but is also involved in the regulation of immune functions of asthma.

Cooperation and conflict in conspecific brood parasitism : an alternative reproductive tactic

Interactions among individuals give rise to both cooperation and conflict. Individuals will behave selfishly or altruistically depending on which gives the higher payoff. The reproductive strategies of many animals are flexible and several alternative tactics may be present from which the most suitable one is applied. Generally, alternative reproductive tactics may be defined as a response to competition from individuals of the same sex. These alternative reproductive tactics are means by which individuals may fine-tune their fitness to the reigning circumstances and which are shaped by the environment individuals are occupying as well as by the behaviour of other individuals sharing the environment. By employing such alternative ways of achieving reproductive output, individuals may alleviate competition from others. Conspecific brood parasitism (CBP) is an alternative reproductive strategy found in several egg laying animal groups, and it is especially common among waterfowl. Within this alternative reproductive strategy, four reproductive options can be identified. These four options represent a continuum from low reproductive effort coupled with low fitness returns, to high reproductive effort and consequently high benefits. It may not be evident how individuals should allocate reproductive effort between eggs laid in their own nest vs. in nests of others, however. Limited fecundity will constrain the number of eggs donated by a parasite, but also the tendency for hosts to accept parasitic eggs may affect the allocation decision. Furthermore, kinship, individual quality and the costs of breeding may play a role in complicating the allocation decision. In this thesis, I view the seemingly paradoxical effects of kinship on conflict resolution in the context of alternative reproductive tactics, examining the resulting features of cooperation and conflict. Conspecific brood parasitism sets the stage for investigating these questions. By using both empirical and theoretical approaches, I examine the nature of CBP in a brood parasitic duck, the Barrow's goldeneye (Bucephala islandica). The theoretical chapter of this thesis gives rise to four main conclusions. Firstly, variation in individual quality plays a central role in shaping breeding strategies. Secondly, kinship plays a central role in the evolution of CBP. Thirdly, egg recognition ability may affect the prevalence of parasitism. If egg recognition is perfect, higher relatedness between host and parasite facilitates CBP. Finally, I show that the relative costs of egg laying and post-laying care play a so far underestimated role in determining the prevalence of parasitism. The costs of breeding may outweigh possible inclusive fitness benefits accrued from receiving eggs from relatives. Several of the patterns brought out by the theoretical work are then confirmed empirically in the following chapters. Findings include confirmation of the central role of relatedness in determining the extent of parasitism as well as inducing a counterintuitive host clutch reduction. Furthermore, I demonstrate a cost of CBP inflicted on hosts, as well as results suggesting that host age reflects individual quality, affecting the ability to overcome costs inflicted by CBP. In summary, I demonstrate both theoretically and empirically the presence of cooperation and conflict in the interactions between conspecific parasites and their hosts. The field of CBP research has traditionally been divided, but the first steps have now been taken toward the acceptance of the opposite side of the divide. Especially the theoretical findings of chapter 1 offer the possibility to view seemingly contrasting results of various studies within the same framework, and may direct future research toward more general features underlying differences in the patterns of CBP between populations or species.

Asteroid identification using statistical orbital inversion methods

An efficient and statistically robust solution for the identification of asteroids among numerous sets of astrometry is presented. In particular, numerical methods have been developed for the short-term identification of asteroids at discovery, and for the long-term identification of scarcely observed asteroids over apparitions, a task which has been lacking a robust method until now. The methods are based on the solid foundation of statistical orbital inversion properly taking into account the observational uncertainties, which allows for the detection of practically all correct identifications. Through the use of dimensionality-reduction techniques and efficient data structures, the exact methods have a loglinear, that is, O(nlog(n)), computational complexity, where n is the number of included observation sets. The methods developed are thus suitable for future large-scale surveys which anticipate a substantial increase in the astrometric data rate. Due to the discontinuous nature of asteroid astrometry, separate sets of astrometry must be linked to a common asteroid from the very first discovery detections onwards. The reason for the discontinuity in the observed positions is the rotation of the observer with the Earth as well as the motion of the asteroid and the observer about the Sun. Therefore, the aim of identification is to find a set of orbital elements that reproduce the observed positions with residuals similar to the inevitable observational uncertainty. Unless the astrometric observation sets are linked, the corresponding asteroid is eventually lost as the uncertainty of the predicted positions grows too large to allow successful follow-up. Whereas the presented identification theory and the numerical comparison algorithm are generally applicable, that is, also in fields other than astronomy (e.g., in the identification of space debris), the numerical methods developed for asteroid identification can immediately be applied to all objects on heliocentric orbits with negligible effects due to non-gravitational forces in the time frame of the analysis. The methods developed have been successfully applied to various identification problems. Simulations have shown that the methods developed are able to find virtually all correct linkages despite challenges such as numerous scarce observation sets, astrometric uncertainty, numerous objects confined to a limited region on the celestial sphere, long linking intervals, and substantial parallaxes. Tens of previously unknown main-belt asteroids have been identified with the short-term method in a preliminary study to locate asteroids among numerous unidentified sets of single-night astrometry of moving objects, and scarce astrometry obtained nearly simultaneously with Earth-based and space-based telescopes has been successfully linked despite a substantial parallax. Using the long-term method, thousands of realistic 3-linkages typically spanning several apparitions have so far been found among designated observation sets each spanning less than 48 hours.

Studies on orographic effects in a numerical weather prediction model

Numerical models, used for atmospheric research, weather prediction and climate simulation, describe the state of the atmosphere over the heterogeneous surface of the Earth. Several fundamental properties of atmospheric models depend on orography, i.e. on the average elevation of land over a model area. The higher is the models' resolution, the more the details of orography directly influence the simulated atmospheric processes. This sets new requirements for the accuracy of the model formulations with respect to the spatially varying orography. Orography is always averaged, representing the surface elevation within the horizontal resolution of the model. In order to remove the smallest scales and steepest slopes, the continuous spectrum of orography is normally filtered (truncated) even more, typically beyond a few gridlengths of the model. This means, that in the numerical weather prediction (NWP) models, there will always be subgridscale orography effects, which cannot be explicitly resolved by numerical integration of the basic equations, but require parametrization. In the subgrid-scale, different physical processes contribute in different scales. The parametrized processes interact with the resolved-scale processes and with each other. This study contributes to building of a consistent, scale-dependent system of orography-related parametrizations for the High Resolution Limited Area Model (HIRLAM). The system comprises schemes for handling the effects of mesoscale (MSO) and small-scale (SSO) orographic effects on the simulated flow and a scheme of orographic effects on the surface-level radiation fluxes. Representation of orography, scale-dependencies of the simulated processes and interactions between the parametrized and resolved processes are discussed. From the high-resolution digital elevation data, orographic parameters are derived for both momentum and radiation flux parametrizations. Tools for diagnostics and validation are developed and presented. The parametrization schemes applied, developed and validated in this study, are currently being implemented into the reference version of HIRLAM.

Forest governance and climate change adaptation : Case studies of four African countries

Africa is threatened by climate change. The adaptive capacity of local communities continues to be weakened by ineffective and inefficient livelihood strategies and inappropriate development interventions. One of the greatest challenges for climate change adaptation in Africa is related to the governance of natural resources used by vulnerable poor groups as assets for adaptation. Practical and good governance activities for adaptation in Africa is urgently and much needed to support adaptation actions, interventions and planning. The adaptation role of forests has not been as prominent in the international discourse and actions as their mitigation role. This study therefore focused on the forest as one of the natural resources used for adaptation. The general objective of this research was to assess the extent to which cases of current forest governance practices in four African countries Burkina Faso, The Democratic Republic of Congo (DRC), Ghana and Sudan are supportive to the adaptation of vulnerable societies and ecosystems to impacts of climate change. Qualitative and quantitative analyses from surveys, expert consultations and group discussions were used in analysing the case studies. The entire research was guided by three conceptual sets of thinking forest governance, climate change vulnerability and ecosystem services. Data for the research were collected from selected ongoing forestry activities and programmes. The study mainly dealt with forest management policies and practices that can improve the adaptation of forest ecosystems (Study I) and the adaptive capacity through the management of forest resources by vulnerable farmers (Studies II, III, IV and V). It was found that adaptation is not part of current forest policies, but, instead, policies contain elements of risk management practices, which are also relevant to the adaptation of forest ecosystems. These practices include, among others, the management of forest fires, forest genetic resources, non-timber resources and silvicultural practices. Better livelihood opportunities emerged as the priority for the farmers. These vulnerable farmers had different forms of forest management. They have a wide range of experience and practical knowledge relevant to ensure and achieve livelihood improvement alongside sustainable management and good governance of natural resources. The contributions of traded non-timber forest products to climate change adaptation appear limited for local communities, based on their distribution among the stakeholders in the market chain. Plantation (agro)forestry, if well implemented and managed by communities, has a high potential in reducing socio-ecological vulnerability by increasing the food production and restocking degraded forest lands. Integration of legal arrangements with continuous monitoring, evaluation and improvement may drive this activity to support short, medium and long term expectations related to adaptation processes. The study concludes that effective forest governance initiatives led by vulnerable poor groups represent one practical way to improve the adaptive capacities of socio-ecological systems against the impacts of climate change in Africa.

Hyperfine effects in the nuclear magnetic resonance of paramagnetic molecules

Paramagnetic, or open-shell, systems are often encountered in the context of metalloproteins, and they are also an essential part of molecular magnets. Nuclear magnetic resonance (NMR) spectroscopy is a powerful tool for chemical structure elucidation, but for paramagnetic molecules it is substantially more complicated than in the diamagnetic case. Before the present work, the theory of NMR of paramagnetic molecules was limited to spin-1/2 systems and it did not include relativistic corrections to the hyperfine effects. It also was not systematically expandable. --- The theory was first expanded by including hyperfine contributions up to the fourth power in the fine structure constant α. It was then reformulated and its scope widened to allow any spin state in any spatial symmetry. This involved including zero-field splitting effects. In both stages the theory was implemented into a separate analysis program. The different levels of theory were tested by demonstrative density functional calculations on molecules selected to showcase the relative strength of new NMR shielding terms. The theory was also tested in a joint experimental and computational effort to confirm assignment of 11 B signals. The new terms were found to be significant and comparable with the terms in the earlier levels of theory. The leading-order magnetic-field dependence of shielding in paramagnetic systems was formulated. The theory is now systematically expandable, allowing for higher-order field dependence and relativistic contributions. The prevailing experimental view of pseudocontact shift was found to be significantly incomplete, as it only includes specific geometric dependence, which is not present in most of the new terms introduced here. The computational uncertainty in density functional calculations of the Fermi contact hyperfine constant and zero-field splitting tensor sets a limit for quantitative prediction of paramagnetic shielding for now.

Playing Games on Sets and Models

The most prominent objective of the thesis is the development of the generalized descriptive set theory, as we call it. There, we study the space of all functions from a fixed uncountable cardinal to itself, or to a finite set of size two. These correspond to generalized notions of the universal Baire space (functions from natural numbers to themselves with the product topology) and the Cantor space (functions from natural numbers to the {0,1}-set) respectively. We generalize the notion of Borel sets in three different ways and study the corresponding Borel structures with the aims of generalizing classical theorems of descriptive set theory or providing counter examples. In particular we are interested in equivalence relations on these spaces and their Borel reducibility to each other. The last chapter shows, using game-theoretic techniques, that the order of Borel equivalence relations under Borel reduciblity has very high complexity. The techniques in the above described set theoretical side of the thesis include forcing, general topological notions such as meager sets and combinatorial games of infinite length. By coding uncountable models to functions, we are able to apply the understanding of the generalized descriptive set theory to the model theory of uncountable models. The links between the theorems of model theory (including Shelah's classification theory) and the theorems in pure set theory are provided using game theoretic techniques from Ehrenfeucht-Fraïssé games in model theory to cub-games in set theory. The bottom line of the research declairs that the descriptive (set theoretic) complexity of an isomorphism relation of a first-order definable model class goes in synch with the stability theoretical complexity of the corresponding first-order theory. The first chapter of the thesis has slightly different focus and is purely concerned with a certain modification of the well known Ehrenfeucht-Fraïssé games. There we (me and my supervisor Tapani Hyttinen) answer some natural questions about that game mainly concerning determinacy and its relation to the standard EF-game

Distributed algorithms for edge dominating sets

An edge dominating set for a graph G is a set D of edges such that each edge of G is in D or adjacent to at least one edge in D. This work studies deterministic distributed approximation algorithms for finding minimum-size edge dominating sets. The focus is on anonymous port-numbered networks: there are no unique identifiers, but a node of degree d can refer to its neighbours by integers 1, 2, ..., d. The present work shows that in the port-numbering model, edge dominating sets can be approximated as follows: in d-regular graphs, to within 4 − 6/(d + 1) for an odd d and to within 4 − 2/d for an even d; and in graphs with maximum degree Δ, to within 4 − 2/(Δ − 1) for an odd Δ and to within 4 − 2/Δ for an even Δ. These approximation ratios are tight for all values of d and Δ: there are matching lower bounds.