A phylogenetic study of the subtribe Dicrepidiina (Elateridae, Elaterinae, Ampedini)

It is presented a cladistic analysis of the Dicrepidiina aiming to test the monophyletism of the subtribe and to establish the relationships among the genera. The subtribe is composed by 36 genera and all of them, except Asebis, Lamononia, Neopsephus, Semiotopsis and Spilomorphus were included in the analysis. Fifty two species, especially the type-species of each genus were studied: Achrestus flavocinctus (Candèze, 1859), A. venustus Champion, 1895, Adiaphorus gracilis Schwarz, 1901, A. ponticerianus Candèze, 1859, Anoplischiopsis bivittatus Champion, 1895, Anoplischius bicarinatus Candèze, 1859, A. conicus Candèze, 1900, A. haematopus Candèze, 1859, A. pyronotus Candèze, 1859, Atractosomus flavescens (Germar, 1839), Blauta cribraria (Germar, 1844), Calopsephus apicalis (Schwarz, 1903), Catalamprus angustus (Fleutiaux, 1902), Crepidius flabellifer (Erichson, 1847), C. resectus Candèze, 1859, Cyathodera auripilosus Costa, 1968, C. lanugicollis (Candèze, 1859), C. longicornis Blanchard, 1843, Dayakus angularis Candèze, 1893, Dicrepidius ramicornis (Palisot de Beauvois, 1805), Dipropus brasilianus (Germar, 1824), D. factuellus Candèze, 1859, D. laticollis (Eschscholtz, 1829), D. pinguis (Candèze, 1859), D. schwarzi (Becker, 1961), Elius birmanicus Candèze, 1893, E. dilatatus Candèze, 1878, Heterocrepidius gilvellus Candèze, 1859, H. ventralis Guérin-Méneville, 1838, Lampropsephus cyaneus (Candèze, 1878), Loboederus appendiculatus (Perty, 1830), Olophoeus gibbus Candèze, 1859, Ovipalpus pubescens Solier, 1851, Pantolamprus ligneus Candèze, 1896, P. mirabilis Candèze, 1896, P. perpulcher Westwood, 1842, Paraloboderus glaber Golbach, 1990, Proloboderus crassipes Fleutiaux, 1912, Propsephus beniensis (Candèze, 1859), P. cavifrons (Erichson, 1843), Pseudolophoeus guineensis (Candèze, 1881), Rhinopsephus apicalis (Schwarz, 1903), Sephilus formosanus Schwarz, 1912, S. frontalis Candèze, 1878, Singhalenus gibbus Candèze, 1892, S. taprobanicus Candèze, 1859, Sphenomerus antennalis Candèze, 1859, S. brunneus Candèze, 1865, Spilus atractomorphus Candèze, 1859, S. nitidus Candèze, 1859, Stenocrepidius simonii Fleutiaux, 1891 and Trielasmus varians Blanchard, 1846. Chalcolepidius zonatus (Hemirhipini, Agrypninae), Ctenicera silvatica (Prosternini, Prosterninae), and species of the other subtribes of Ampedini (Elaterinae): Ampedus sanguineus (Ampedina), Melanotus spernendus (Melanotina) and Anchastus digittatus and Physorhinus xanthocephalus (Physorhinina) were used as outgroups. The results of the phylogenetic analysis demonstrated that Dicrepidiina, as formerly defined, does not form a monophyletic group. One genus, represented by Ovipalpus pubescens, was removed from the subtribe. The subtribe is characterized by presence of lamella under 2nd and 3rd tarsomeres of all legs. Also, it was revealed that the genera Achrestus, Anoplischius, Dipropus and Propsephus are not monophyletic. Due to the scarcity of information, all the studied species are redescribed and illustrated.

Adaptive approach heuristics for the generalized assignment problem

The Generalized Assignment Problem consists in assigning a setof tasks to a set of agents with minimum cost. Each agent hasa limited amount of a single resource and each task must beassigned to one and only one agent, requiring a certain amountof the resource of the agent. We present new metaheuristics forthe generalized assignment problem based on hybrid approaches.One metaheuristic is a MAX-MIN Ant System (MMAS), an improvedversion of the Ant System, which was recently proposed byStutzle and Hoos to combinatorial optimization problems, and itcan be seen has an adaptive sampling algorithm that takes inconsideration the experience gathered in earlier iterations ofthe algorithm. Moreover, the latter heuristic is combined withlocal search and tabu search heuristics to improve the search.A greedy randomized adaptive search heuristic (GRASP) is alsoproposed. Several neighborhoods are studied, including one basedon ejection chains that produces good moves withoutincreasing the computational effort. We present computationalresults of the comparative performance, followed by concludingremarks and ideas on future research in generalized assignmentrelated problems.

Effect of genetic convergence on phylogenetic inference.

Phylogenetic reconstructions are a major component of many studies in evolutionary biology, but their accuracy can be reduced under certain conditions. Recent studies showed that the convergent evolution of some phenotypes resulted from recurrent amino acid substitutions in genes belonging to distant lineages. It has been suggested that these convergent substitutions could bias phylogenetic reconstruction toward grouping convergent phenotypes together, but such an effect has never been appropriately tested. We used computer simulations to determine the effect of convergent substitutions on the accuracy of phylogenetic inference. We show that, in some realistic conditions, even a relatively small proportion of convergent codons can strongly bias phylogenetic reconstruction, especially when amino acid sequences are used as characters. The strength of this bias does not depend on the reconstruction method but varies as a function of how much divergence had occurred among the lineages prior to any episodes of convergent substitutions. While the occurrence of this bias is difficult to predict, the risk of spurious groupings is strongly decreased by considering only 3rd codon positions, which are less subject to selection, as long as saturation problems are not present. Therefore, we recommend that, whenever possible, topologies obtained with amino acid sequences and 3rd codon positions be compared to identify potential phylogenetic biases and avoid evolutionarily misleading conclusions.

Non-monophyly of the woody bamboos (Bambuseae; Poaceae): a multi-gene region phylogenetic analysis of Bambusoideae s.s.

The taxonomy of Bambusoideae is in a state of flux and phylogenetic studies are required to help resolve systematic issues. Over 60 taxa, representing all subtribes of Bambuseae and related non-bambusoid grasses were sampled. A combined analysis of five plastid DNA regions, trnL intron, trnL-F intergenic spacer, atpB-rbcL intergenic spacer, rps16 intron, and matK, was used to study the phylogenetic relationships among the bamboos in general and the woody bamboos in particular. Within the BEP clade (Bambusoideae s.s., Ehrhartoideae, Pooideae), Pooideae were resolved as sister to Bambusoideae s.s. Tribe Bambuseae, the woody bamboos, as currently recognized were not monophyletic because Olyreae, the herbaceous bamboos, were sister to tropical Bambuseae. Temperate Bambuseae were sister to the group consisting of tropical Bambuseae and Olyreae. Thus, the temperate Bambuseae would be better treated as their own tribe Arundinarieae than as a subgroup of Bambuseae. Within the tropical Bambuseae, neotropical Bambuseae were sister to the palaeotropical and Austral Bambuseae. In addition, Melocanninae were found to be sister to the remaining palaeotropical and Austral Bambuseae. We discuss phylogenetic and morphological patterns of diversification and interpret them in a biogeographic context.

Description and phylogenetic analysis of the Calycopidina (Lepidoptera, Lycaenidae, Theclinae, Eumaeini): a subtribe of detritivores

Description and phylogenetic analysis of the Calycopidina (Lepidoptera, Lycaenidae, Theclinae, Eumaeini): a subtribe of detritivores. The purpose of this paper is to establish a phylogenetic basis for a new Eumaeini subtribe that includes those lycaenid genera in which detritivory has been recorded. Morphological characters were coded for 82 species of the previously proposed "Lamprospilus Section" of the Eumaeini (19 of these had coding identical to another species), and a phylogenetic analysis was performed using the 63 distinct ingroup terminal taxa and six outgroups belonging to four genera. Taxonomic results include the description in the Eumaeini of Calycopidina Duarte & Robbins new subtribe (type genus Calycopis Scudder, 1876), which contains Lamprospilus Geyer, Badecla Duarte & Robbins new genus (type species Thecla badaca Hewitson), Arzecla Duarte & Robbins new genus (type species Thecla arza Hewitson), Arumecla Robbins & Duarte, Camissecla Robbins & Duarte, Electrostrymon Clench, Rubroserrata K. Johnson & Kroenlein revalidated status, Ziegleria K. Johnson, Kisutam K. Johnson & Kroenlein revalidated status, and Calycopis. Previous "infratribe" names Angulopina K. Johnson & Kroenlein, 1993, and Calycopina K. Johnson & Kroenlein, 1993, are nomenclaturally unavailable and polyphyletic as proposed. New combinations include Badecla badaca (Hewitson), Badecla picentia (Hewitson), Badecla quadramacula (Austin & K. Johnson), Badecla lanckena (Schaus), Badecla argentinensis (K. Johnson & Kroenlein), Badecla clarissa (Draudt), Arzecla arza (Hewitson), Arzecla tarpa (Godman & Salvin), Arzecla canacha (Hewitson), Arzecla calatia (Hewitson), Arzecla tucumanensis (K. Johnson & Kroenlein), Arzecla sethon (Godman & Salvin), Arzecla nubilum (H. H. Druce), Arzecla paralus (Godman & Salvin), Arzecla taminella (Schaus), Arzecla albolineata (Lathy), Electrostrymon denarius (Butler & H.Druce), Electrostrymon guzanta (Schaus), Electrostrymon perisus (H. H. Druce), Rubroserrata mathewi (Hewitson), Rubroserrata ecbatana (Hewitson), Kisutam micandriana (K. Johnson), and Kisutam syllis (Godman & Salvin). The structure of the male genitalia lateral window, labides, and brush organs are described and discussed, as are the female genitalia signa of the corpus bursae and 8th abdominal tergum. Widespread wing pattern sexual dimorphism in the Calycopidina is noted and illustrated, and the presence of alternating dark and light bands on the ventral wings of both sexes is discussed. The evidence for detritivory in Lamprospilus, Badecla, Arzecla, Arumecla, Camissecla, Electrostrymon, Ziegleria, Kisutam, and Calycopis is summarized using the new classification.

Phylogenetic analyses of C4 photosynthesis evolution in grasses: genetics of convergence and convergence of genes

Summary : During the evolutionary diversification of organisms, similar ecological constraints led to the recurrent appearances of the same traits (phenotypes) in distant lineages, a phenomenon called convergence. In most cases, the genetic origins of the convergent traits remain unknown, but recent studies traced the convergent phenotypes to recurrent alterations of the same gene or, in a few cases, to identical genetic changes. However, these cases remain anecdotal and there is a need for a study system that evolved several times independently and whose genetic determinism is well resolved and straightforward, such as C4 photosynthesis. This adaptation to warm environments, possibly driven by past atmospheric CO2 decreases, consists in a CO2-concentrating pump, created by numerous morphological and biochemical novelties. All genes encoding C4 enzymes already existed in C3 ancestors, and are supposed to have been recruited through gene duplication followed by neo-functionalization, to acquire the cell specific expression pattern and altered kinetic properties that characterize Ca-specific enzymes. These predictions have so far been tested only in species-poor and ecologically marginal C4 dicots. The monocots, and especially the grass family (Poaceae), the most important C4 family in terms of species number, ecological dominance and economical importance, have been largely under-considered as suitable study systems. This thesis aimed at understanding the evolution of the C4 trait in grasses at a molecular level and to use the genetics of C4 photosynthesis to infer the evolutionary history of the C4 phenotype and its driving selective pressures. A molecular phylogeny of grasses and affiliated monocots identified 17 to 18 independent acquisitions of the C4 pathway in the grass family. A relaxed molecular clock was used to date these events and the first C4 evolution was estimated in the Chloridoideae subfamily, between 32-25 million years ago, at a period when atmospheric CO2 abruptly declined. Likelihood models showed that after the COZ decline the probability of evolving the C4 pathway strongly increased, confirming low CO2 as a likely driver of C4 photosynthesis evolution. In order to depict the genetic changes linked to the numerous C4 origins, genes encoding phopshoenolpyruvate carboxylase (PEPC), the key-enzyme responsible for the initial fixation of atmospheric CO2 in the C4 pathway, were isolated from a large sample of C3 and C4 grasses. Phylogenetic analyses were used to reconstruct the evolutionary history of the PEPC multigene family and showed that the evolution of C4-specific PEPC had been driven by positive selection on 21 codons simultaneously in up to eight C4 lineages. These selective pressures led to numerous convergent genetic changes in many different C4 clades, highlighting the repeatability of some evolutionary processes, even at the molecular level. PEPC C4-adaptive changes were traced and used to show multiple appearances of the C, pathway in clades where species tree inferences were unable to differentiate multiple C4 appearances and a single appearance followed by C4 to C3 reversion. Further investigations of genes involved in some of the C4 subtypes only (genes encoding decarboxylating enzymes NADP-malic enzyme and phosphoenolpyruvate carboxykinase) showed that these C4-enzymes also evolved through strong positive selection and underwent parallel genetic changes during the different Ca origins. The adaptive changes on these subtype-specific C4 genes were used to retrace the history of the C4-subtypes phenotypes, which revealed that the evolution of C4-PEPC and C4-decarboxylating enzymes was in several cases disconnected, emphasizing the multiplicity of the C4 trait and the gradual acquisition of the features that create the CO2-pump. Finally, phylogenetic analyses of a gene encoding the Rubisco (the enzyme responsible for the fixation of CO2 into organic compounds in all photosynthetic organisms) showed that C4 evolution switched the selective pressures on this gene. Five codons were recurrently mutated to adapt the enzyme kinetics to the high CO2 concentrations of C4 photosynthetic cells. This knowledge could be used to introgress C4-like Rubisco in C3 crops, which could lead to an increased yield under predicted future high CO2 atmosphere. Globally, the phylogenetic framework adopted during this thesis demonstrated the widespread occurrence of genetic convergence on C4-related enzymes. The genetic traces of C4 photosynthesis evolution allowed reconstructing events that happened during the last 30 million years and proved the usefulness of studying genes directly responsible for phenotype variations when inferring evolutionary history of a given trait. Résumé Durant la diversification évolutive des organismes, des pressions écologiques similaires ont amené à l'apparition récurrente de certains traits (phénotypes) dans des lignées distantes, un phénomène appelé évolution convergente. Dans la plupart des cas, l'origine génétique des traits convergents reste inconnue mais des études récentes ont montré qu'ils étaient dus dans certains cas à des changements répétés du même gène ou, dans de rares cas, à des changements génétiques identiques. Malgré tout, ces cas restent anecdotiques et il y a un réel besoin d'un système d'étude qui ait évolué indépendamment de nombreuses fois et dont le déterminisme génétique soit clairement identifié. La photosynthèse dite en Ça répond à ces critères. Cette adaptation aux environnements chauds, dont l'évolution a pu être encouragé par des baisses passées de la concentration atmosphérique en CO2, est constituée de nombreuses nouveautés morphologiques et biochimiques qui créent une pompe à CO2. La totalité des gènes codant les enzymes Ç4 étaient déjà présents dans les ancêtres C3. Leur recrutement pour la photosynthèse Ç4 est supposé s'être fait par le biais de duplications géniques suivies par une néo-fonctionnalisation pour leur conférer l'expression cellule-spécifique et les propriétés cinétiques qui caractérisent les enzymes C4. Ces prédictions n'ont jusqu'à présent été testées que dans des familles C4 contenant peu d'espèces et ayant un rôle écologique marginal. Les graminées (Poaceae), qui sont la famille C4 la plus importante, tant en termes de nombre d'espèces que de dominance écologique et d'importance économique, ont toujours été considérés comme un système d'étude peu adapté et ont fait le sujet de peu d'investigations évolutives. Le but de cette thèse était de comprendre l'évolution de la photosynthèse en C4 chez les graminées au niveau génétique et d'utiliser les gènes pour inférer l'évolution du phénotype C4 ainsi que les pressions de sélection responsables de son évolution. Une phylogénie moléculaire de la famille des graminées et des monocotylédones apparentés a identifié 17 à 18 acquisitions indépendantes de la photosynthèse chez les graminées. Grâce à une méthode d'horloge moléculaire relâchée, ces évènements ont été datés et la première apparition C4 a été estimée dans la sous-famille des Chloridoideae, il y a 32 à 25 millions d'années, à une période où les concentrations atmosphériques de CO2 ont décliné abruptement. Des modèles de maximum de vraisemblance ont montré qu'à la suite du déclin de CO2, la probabilité d'évoluer la photosynthèse C4 a fortement augmenté, confirmant ainsi qu'une faible concentration de CO2 est une cause potentielle de l'évolution de la photosynthèse C4. Afin d'identifier les mécanismes génétiques responsables des évolutions répétées de la photosynthèse C4, un segment des gènes codant pour la phosphoénolpyruvate carboxylase (PEPC), l'enzyme responsable de la fixation initiale du CO2 atmosphérique chez les plantes C4, ont été séquencés dans une centaine de graminées C3 et C4. Des analyses phylogénétiques ont permis de reconstituer l'histoire évolutive de la famille multigénique des PEPC et ont montré que l'évolution de PEPC spécifiques à la photosynthèse Ça a été causée par de la sélection positive agissant sur 21 codons, et ce simultanément dans huit lignées C4 différentes. Cette sélection positive a conduit à un grand nombre de changements génétiques convergents dans de nombreux clades différents, ce qui illustre la répétabilité de certains phénomènes évolutifs, et ce même au niveau génétique. Les changements sur la PEPC liés au C4 ont été utilisés pour confirmer des évolutions indépendantes du phénotype C4 dans des clades où l'arbre des espèces était incapable de différencier des apparitions indépendantes d'une seule apparition suivie par une réversion de C4 en C3. En considérant des gènes codant des protéines impliquées uniquement dans certains sous-types C4 (deux décarboxylases, l'enzyme malique à NADP et la phosphoénolpyruvate carboxykinase), des études ultérieures ont montré que ces enzymes C4 avaient elles-aussi évolué sous forte sélection positive et subi des changements génétiques parallèles lors des différentes origines de la photosynthèse C4. Les changements adaptatifs sur ces gènes liés seulement à certains sous-types C4 ont été utilisés pour retracer l'histoire des phénotypes de sous-types C4, ce qui a révélé que les caractères formant le trait C4 ont, dans certains cas, évolué de manière déconnectée. Ceci souligne la multiplicité du trait C4 et l'acquisition graduelle de composants participant à la pompe à CO2 qu'est la photosynthèse C4. Finalement, des analyses phylogénétiques des gènes codant pour la Rubisco (l'enzyme responsable de la fixation du CO2 en carbones organiques dans tous les organismes photosynthétiques) ont montré que l'évolution de la photosynthèse Ça a changé les pressions de sélection sur ce gène. Cinq codons ont été mutés de façon répétée afin d'adapter les propriétés cinétiques de la Rubisco aux fortes concentrations de CO2 présentes dans les cellules photosynthétiques des plantes C4. Globalement, l'approche phylogénétique adoptée durant cette thèse de doctorat a permis de démontré des phénomène fréquents de convergence génétique sur les enzymes liées à la photosynthèse C4. Les traces génétiques de l'évolution de la photosynthèse C4 ont permis de reconstituer des évènements qui se sont produits durant les derniers 30 millions d'années et ont prouvé l'utilité d'étudier des gènes directement responsables des variations phénotypiques pour inférer l'histoire évolutive d'un trait donné.

Distributional patterns of the Neotropical genus Thecomyia Perty (Diptera, Sciomyzidae) and phylogenetic support

Distributional patterns of the Neotropical genus Thecomyia Perty (Diptera, Sciomyzidae) and phylogenetic support. The distributional pattern of the genus Thecomyia Perty, 1833 was defined using panbiogeographic tools, and analyzed based on the phylogeny of the group. This study sought to establish biogeographical homologies in the Neotropical region between different species of the genus, based on their distribution pattern and later corroboration through its phylogeny. Eight individual tracks and 16 generalized tracks were identified, established along nearly the entire swath of the Neotropics. Individual tracks are the basic units of a panbiogeographic study, and correspond to the hypothesis of minimum distribution of the organisms involved. The generalized tracks, obtained from the spatial congruence between two or more individual tracks, are important in the identification of smaller areas of endemism. Thus, we found evidence from the generalized tracks in support of previous classification for the Neotropical region. The Amazon domain is indicated as an area of outstanding importance in the diversification of the group, by the confluence of generalized tracks and biogeographic nodes in the region. Most of the generalized tracks and biogeographical nodes were congruent with the phylogenetic hypothesis of the genus, indicating support of the primary biogeographical homologies originally defined by the track analysis.

A phylogenetic study of the phosphoenolpyruvate carboxylase multigene family in Poaceae: understanding the molecular changes linked to C4 photosynthesis evolution

Phylogenetic reconstructions have supported several independent appearances of C₄ photosynthesis within grasses (Poaceae). These recurrent appearances appear to contradict the large number of biochemical and morphological changes required to change from C₃ to C₄, a paradox that leads to questions about the genetic changes underlying C₄ evolution. In this study, we analysed sequences encoding phosphoenolpyruvate carboxylases (PEPCs) in grasses in order to gain insights into the origin of the ppc-C₄ gene, which encodes a key enzyme in the C₄ pathway. We screened databanks for PEPC genes or cDNAs in grasses. A coding sequence of 1130 base pairs was used to build phylogenetic trees that supported the existence of four distinct PEPC gene lineages. Ppc-C₄ present in all C₄ grasses was also found in two C₃ species. The ppc-C₄ clade was congruent with the species tree, suggesting orthologous evolution. This result would imply that ppc-C₄ appeared without any duplication event. Nevertheless, caution is needed since the sampling of our study is still far from comprehensive. Further investigation with an increased sampling is recommended to elucidate the evolutionary changes underlying ppc-C₄ gene evolution in grasses.

Staphylococcus aureus clfB and spa alleles of the repeat regions are segregated into major phylogenetic lineages.

To reliably differentiate among Staphylococcus aureus isolates we recently developed the Double Locus Sequence Typing (DLST) based on the analysis of partial sequences of clfB and spa genes. This method is highly discriminatory and gives unambiguous definition of types. The highly clonal population structure of S. aureus suggests that isolates with identical clfB or spa alleles belong to the same clonal complex (CC) defined by Multi-Locus Sequence Typing (MLST). To test this hypothesis as well as to investigate putative intra-CC genetic structure, we analyzed a total of 289 isolates (186 MSSA and 103 MRSA) with DLST-, spa- and MLST-typing. Among the 289 strains, 242 were clustered into 7 major MLST CCs, 40 into minor CCs and 7 were not grouped into CCs. A total of 205 DLST- and 129 spa-types were observed. With one exception, all DLST-clfB, DLST-spa and spa-type alleles were segregated into CCs. DLST-types sharing an identical allele (clfB or spa) were clustered using eBURST. Except for one strain, all isolates from each DLST cluster belonged to the same CC. However, using both DLST- and spa-typing we were not able to disclose a clear intra-CC structure. Nevertheless, the high diversity of these loci confirmed that they are good markers for local epidemiological investigations.

Phylogenetic relatedness and proboscis length contribute to structuring bumblebee communities in the extremes of abiotic and biotic gradients

Aim To improve our understanding of how biological communities assemble, we investigated changes in bumblebee communities in space along an elevation gradient. We assessed how much deterministic abiotic and biotic factors shape community assembly. We focused on proboscis length (influencing the species' dietary regime) and phylogenetic relatedness to investigate if competition and environmental filtering occur in more and less productive climates, respectively. Location Western Swiss Alps. Methods We recorded bumblebee species in 149 plots along a 1800-m wide elevation gradient. We contrasted two major clades of bumblebees, a short-tongued and a long-tongued clade. We calculated the phylogenetic and proboscis-length diversity of the bumblebee communities and compared these observed data with a random distribution to detect clustering likely to be caused by environmental filtering or overdispersion likely to be caused by competition. We compared the prevalence of clustered and overdispersed communities along the gradients of plant species richness (biotic) and temperature (abiotic). Results Under colder conditions, where plant species richness is lower and floral resources are scarcer, the clade with shorter proboscides prevails over the clade with longer proboscides, and communities are functionally and phylogenetic clustered. Under warmer conditions, we found phylogenetic but not functional overdispersion in communities. Main conclusions We show for the first time a strong correlation between phylogenetic relatedness, proboscis length and species distribution along temperature and plant richness gradients shaping bumblebee communities. The low temperatures and low levels of plant species richness limit the dispersal of the species from the long-tongued clade, which have more specialized diets, into high-elevation areas. Competition under warmer conditions may produce communities composed of less closely related species that share distinct ecological preferences. Our empirical results corroborate theoretical expectation as well as experiments on the prevalence of deterministic processes in the most severe and most productive parts of environmental gradients.

On the dimension of the core of the assignment game

The set of optimal matchings in the assignment matrix allows to define a reflexive and symmetric binary relation on each side of the market, the equal-partner binary relation. The number of equivalence classes of the transitive closure of the equal-partner binary relation determines the dimension of the core of the assignment game. This result provides an easy procedure to determine the dimension of the core directly from the entries of the assignment matrix and shows that the dimension of the core is not as much determined by the number of optimal matchings as by their relative position in the assignment matrix.

Multi-sided Böhm-Bawerk assignment markets: the nucleolus and the core-center

En aquest treball mostrem que, a diferència del cas bilateral, per als mercats multilaterals d'assignació coneguts amb el nom de Böhm-Bawerk assignment games, el nucleolus i el core-center, i. e. el centre de masses del core, no coincideixen en general. Per demostrar-ho provem que donant un m-sided Böhm-Bawerk assignment game les dues solucions anteriors poden obtenir-se respectivament del nucleolus i el core-center d'un joc convex definit en el conjunt format pels m sectors. Encara més, provem que per calcular el nucleolus d'aquest últim joc només les coalicions formades per un jugador o m-1 jugadors són importants. Aquests resultats simplifiquen el càlcul del nucleolus d'un multi-sided ¿¿ohm-Bawerk assignment market amb un número molt elevat d'agents.

The Lorenz-maximal core allocations and the kernel in some classes of assignment games

En aquest treball demostrem que en la classe de jocs d'assignació amb diagonal dominant (Solymosi i Raghavan, 2001), el repartiment de Thompson (que coincideix amb el valor tau) és l'únic punt del core que és maximal respecte de la relació de dominància de Lorenz, i a més coincideix amb la solucié de Dutta i Ray (1989), també coneguda com solució igualitària. En segon lloc, mitjançant una condició més forta que la de diagonal dominant, introduïm una nova classe de jocs d'assignació on cada agent obté amb la seva parella òptima almenys el doble que amb qualsevol altra parella. Per aquests jocs d'assignació amb diagonal 2-dominant, el repartiment de Thompson és l'únic punt del kernel, i per tant el nucleolo.

Monge assignment games

Un juego de asignación se define por una matriz A; donde cada fila representa un comprador y cada columna un vendedor. Si el comprador i se empareja a un vendedor j; el mercado produce aij unidades de utilidad. Estudiamos los juegos de asignación de Monge, es decir, aquellos juegos bilaterales de asignación en los cuales la matriz satisface la propiedad de Monge. Estas matrices pueden caracterizarse por el hecho de que en cualquier submatriz 2x2 un emparejamiento óptimo está situado en la diagonal principal. Para mercados cuadrados, describimos sus núcleos utilizando sólo la parte central tridiagonal de elementos de la matriz. Obtenemos una fórmula cerrada para el reparto óptimo de los compradores dentro del núcleo y para el reparto óptimo de los vendedores dentro del núcleo. Analizamos también los mercados no cuadrados reduciéndolos a matrices cuadradas apropiadas.

On the nucleolus of 2 x 2 assignment games

[spa] En este artículo hallamos fórmulas para el nucleolo de juegos de asignación arbitrarios con dos compradores y dos vendedores. Se analizan cinco casos distintos, dependiendo de las entradas en la matriz de asignación. Los resultados se extienden a los casos de juegos de asignación de tipo 2 x m o m x 2.