Climate-based empirical models show biased predictions of butterfly communities along environmental gradients

A better understanding of the factors that mould ecological community structure is required to accurately predict community composition and to anticipate threats to ecosystems due to global changes. We tested how well stacked climate-based species distribution models (S-SDMs) could predict butterfly communities in a mountain region. It has been suggested that climate is the main force driving butterfly distribution and community structure in mountain environments, and that, as a consequence, climate-based S-SDMs should yield unbiased predictions. In contrast to this expectation, at lower altitudes, climate-based S-SDMs overpredicted butterfly species richness at sites with low plant species richness and underpredicted species richness at sites with high plant species richness. According to two indices of composition accuracy, the Sorensen index and a matching coefficient considering both absences and presences, S-SDMs were more accurate in plant-rich grasslands. Butterflies display strong and often specialised trophic interactions with plants. At lower altitudes, where land use is more intense, considering climate alone without accounting for land use influences on grassland plant richness leads to erroneous predictions of butterfly presences and absences. In contrast, at higher altitudes, where climate is the main force filtering communities, there were fewer differences between observed and predicted butterfly richness. At high altitudes, even if stochastic processes decrease the accuracy of predictions of presence, climate-based S-SDMs are able to better filter out butterfly species that are unable to cope with severe climatic conditions, providing more accurate predictions of absences. Our results suggest that predictions should account for plants in disturbed habitats at lower altitudes but that stochastic processes and heterogeneity at high altitudes may limit prediction success of climate-based S-SDMs.

Stochastic time-concentration activity models for cytotoxicity in 3D brain cell cultures.

BACKGROUND: In vitro aggregating brain cell cultures containing all types of brain cells have been shown to be useful for neurotoxicological investigations. The cultures are used for the detection of nervous system-specific effects of compounds by measuring multiple endpoints, including changes in enzyme activities. Concentration-dependent neurotoxicity is determined at several time points. METHODS: A Markov model was set up to describe the dynamics of brain cell populations exposed to potentially neurotoxic compounds. Brain cells were assumed to be either in a healthy or stressed state, with only stressed cells being susceptible to cell death. Cells may have switched between these states or died with concentration-dependent transition rates. Since cell numbers were not directly measurable, intracellular lactate dehydrogenase (LDH) activity was used as a surrogate. Assuming that changes in cell numbers are proportional to changes in intracellular LDH activity, stochastic enzyme activity models were derived. Maximum likelihood and least squares regression techniques were applied for estimation of the transition rates. Likelihood ratio tests were performed to test hypotheses about the transition rates. Simulation studies were used to investigate the performance of the transition rate estimators and to analyze the error rates of the likelihood ratio tests. The stochastic time-concentration activity model was applied to intracellular LDH activity measurements after 7 and 14 days of continuous exposure to propofol. The model describes transitions from healthy to stressed cells and from stressed cells to death. RESULTS: The model predicted that propofol would affect stressed cells more than healthy cells. Increasing propofol concentration from 10 to 100 μM reduced the mean waiting time for transition to the stressed state by 50%, from 14 to 7 days, whereas the mean duration to cellular death reduced more dramatically from 2.7 days to 6.5 hours. CONCLUSION: The proposed stochastic modeling approach can be used to discriminate between different biological hypotheses regarding the effect of a compound on the transition rates. The effects of different compounds on the transition rate estimates can be quantitatively compared. Data can be extrapolated at late measurement time points to investigate whether costs and time-consuming long-term experiments could possibly be eliminated.

A non-possibility theorem for joint-stability in interindustry models

Joint-stability in interindustry models relates to the mutual simultaneous consistency of the demand-driven and supply-driven models of Leontief and Ghosh, respectively. Previous work has claimed joint-stability to be an acceptable assumption from the empirical viewpoint, provided only small changes in exogenous variables are considered. We show in this note, however, that the issue has deeper theoretical roots and offer an analytical demonstration that shows the impossibility of consistency between demand-driven and supply-driven models.

Entrevistant infants pre-escolars víctimes d’abús sexual i/o maltractament familiar : Eficàcia dels models d’entrevista forense

Entrevistant infants pre-escolars víctimes d’abús sexual i/o maltractament familiar: eficàcia dels models d’entrevista forense Entrevistar infants en edat preescolar que han viscut una situació traumàtica és una tasca complexa que dins l’avaluació psicològica forense necessita d’un protocol perfectament delimitat, clar i temporalitzat. Per això, s’han seleccionat 3 protocols d’entrevista: el Protocol de Menors (PM) de Bull i Birch, el model del National Institute for Children Development (NICHD) de Michel Lamb, a partir del qual es va desenvolupar l’EASI (Evaluación del Abuso Sexual Infantojuvenil) i l’Entrevista Cognitiva (EC) de Fisher i Geiselman. La hipòtesi de partida vol comprovar si els anteriors models permeten obtenir volums informatius diferents en infants preescolars. Conseqüentment, els objectius han estat determinar quin dels models d’entrevista permet obtenir un volum informatiu amb més precisions i menys errors, dissenyar un model d’entrevista propi i consensuar aquest model. En el treball s’afegeixen esquemes pràctics que facilitin l’obertura, desenvolupament i tancament de l’entrevista forense. La metodologia ha reproduït el binomi infant - esdeveniment traumàtic, mitjançant la visualització i l’explicació d’un fet emocionalment significatiu amb facilitat per identificar-se: l’accident en bicicleta d’un infant que cau, es fa mal, sagna i el seu pare el cura. A partir d’aquí, hem entrevistat 135 infants de P3, P4 i P5, mitjançant els 3 models d’entrevista referits, enfrontant-los a una demanda específica: recordar i narrar aquest esdeveniment. S’ha conclòs que el nivell de record correcte, quan s’utilitza un model d’entrevista adequat amb els infants en edat preescolar, oscil•la entre el 70-90%, fet que permet defensar la confiança en els records dels infants. Es constata que el percentatge d’emissions incorrectes dels infants en edat preescolar és mínim, al voltant d’un 5-6%. L’estudi remarca la necessitat d’establir perfectament les regles de l’entrevista i, per últim, en destaca la ineficàcia de les tècniques de memòria de l’entrevista cognitiva en els infants de P3 i P4. En els de P5 es comencen a veure beneficis gràcies a la tècnica de la reinstauració contextual (RC), estant les altres tècniques fora de la comprensió i utilització dels infants d’aquestes edats. Interviewing preschoolers victims of sexual abuse and/or domestic abuse: Effectiveness of forensic interviews models 135 preschool children were interviewed with 3 different interview models in order to remember a significant emotional event. Authors conclude that the correct recall of children ranging from 70-90% and the percentage of error messages is 5-6%. It is necessary to fully establish the rules of the interview. The present research highlights the effectiveness of the cognitive interview techniques in children from P3 and P4. Entrevistando niños preescolares víctimas de abuso sexual y/o maltrato familiar: eficacia de los modelos de entrevista forense Se han entrevistado 135 niños preescolares con 3 modelos de entrevista diferentes para recordar un hecho emocionalmente significativo. Se concluye que el recuerdo correcto de los niños oscila entre el 70-90% y el porcentaje de errores de mensajes es del 5-6%. El estudio remarca la necesidad de establecer perfectamente las reglas de la entrevista y se destaca la ineficacia de las técnicas de la entrevista cognitiva en los niños de P3 y P4.

Rest/nrsf governs the expression of dense-core vesicle gliosecretion in astrocytes

Astrocytes are the brain nonnerve cells that are competent for gliosecretion, i.e., for expression and regulated exocytosis of clear and dense-core vesicles (DCVs). We investigated whether expression of astrocyte DCVs is governed by RE-1-silencing transcription factor (REST)/neuron-restrictive silencer factor, the transcription repressor that orchestrates nerve cell differentiation. Rat astrocyte cultures exhibited high levels of REST and expressed neither DCVs nor their markers (granins, peptides, and membrane proteins). Transfection of dominant-negative construct of REST induced the appearance of DCVs filled with secretogranin 2 and neuropeptide Y (NPY) and distinct from other organelles. Total internal reflection fluorescence analysis revealed NPY-monomeric red fluorescent protein-labeled DCVs to undergo Ca21 -dependent exocytosis, which was largely prevented by botulinum toxin B. In the I-II layers of the human temporal brain cortex, all neurons and microglia exhibited the expected inappreciable and high levels of REST, respectively. In contrast, astrocyte RESTwas variable, going from inappreciable to high, and accompanied by a variable expression of DCVs. In conclusion, astrocyte DCV expression and gliosecretion are governed by REST. The variable in situ REST levels may contribute to the wellknown structural/ functional heterogeneity of astrocytes.

Three-dimensional models of 14α-sterol demethylase (Cyp51A) from Aspergillus lentulus and Aspergillus fumigatus: an insight into differences in voriconazole interaction.

Aspergillus lentulus, an Aspergillus fumigatus sibling species, is increasingly reported in corticosteroid-treated patients. Its clinical significance is unknown, but the fact that A. lentulus shows reduced antifungal susceptibility, mainly to voriconazole, is of serious concern. Heterologous expression of cyp51A from A. fumigatus and A. lentulus was performed in Saccharomyces cerevisiae to assess differences in the interaction of Cyp51A with the azole drugs. The absence of endogenous ERG11 was efficiently complemented in S. cerevisiae by the expression of either Aspergillus cyp51A allele. There was a marked difference between azole minimum inhibitory concentration (MIC) values of the clones expressing each Aspergillus spp. cyp51A. Saccharomyces cerevisiae clones expressing A. lentulus alleles showed higher MICs to all of the azoles tested, supporting the hypothesis that the intrinsic azole resistance of A. lentulus could be associated with Cyp51A. Homology models of A. fumigatus and A. lentulus Cyp51A protein based on the crystal structure of Cyp51p from Mycobacterium tuberculosis in complex with fluconazole were almost identical owing to their mutual high sequence identity. Molecular dynamics (MD) was applied to both three-dimensional protein models to refine the homology modelling and to explore possible differences in the Cyp51A-voriconazole interaction. After 20ns of MD modelling, some critical differences were observed in the putative closed form adopted by the protein upon voriconazole binding. A closer study of the A. fumigatus and A. lentulus voriconazole putative binding site in Cyp51A suggested that some major differences in the protein's BC loop could differentially affect the lock-up of voriconazole, which in turn could correlate with their different azole susceptibility profiles.

Homer1a is a core brain molecular correlate of sleep loss.

Sleep is regulated by a homeostatic process that determines its need and by a circadian process that determines its timing. By using sleep deprivation and transcriptome profiling in inbred mouse strains, we show that genetic background affects susceptibility to sleep loss at the transcriptional level in a tissue-dependent manner. In the brain, Homer1a expression best reflects the response to sleep loss. Time-course gene expression analysis suggests that 2,032 brain transcripts are under circadian control. However, only 391 remain rhythmic when mice are sleep-deprived at four time points around the clock, suggesting that most diurnal changes in gene transcription are, in fact, sleep-wake-dependent. By generating a transgenic mouse line, we show that in Homer1-expressing cells specifically, apart from Homer1a, three other activity-induced genes (Ptgs2, Jph3, and Nptx2) are overexpressed after sleep loss. All four genes play a role in recovery from glutamate-induced neuronal hyperactivity. The consistent activation of Homer1a suggests a role for sleep in intracellular calcium homeostasis for protecting and recovering from the neuronal activation imposed by wakefulness.

Systems biology of plants : from intraspecific genome variation to computational morphodynamics

Recently, the introduction of second generation sequencing and further advance-ments in confocal microscopy have enabled system-level studies for the functional characterization of genes. The degree of complexity intrinsic to these approaches needs the development of bioinformatics methodologies and computational models for extracting meaningful biological knowledge from the enormous amount of experi¬mental data which is continuously generated. This PhD thesis presents several novel bioinformatics methods and computational models to address specific biological questions in Plant Biology by using the plant Arabidopsis thaliana as a model system. First, a spatio-temporal qualitative analysis of quantitative transcript and protein profiles is applied to show the role of the BREVIS RADIX (BRX) protein in the auxin- cytokinin crosstalk for root meristem growth. Core of this PhD work is the functional characterization of the interplay between the BRX protein and the plant hormone auxin in the root meristem by using a computational model based on experimental evidence. Hyphotesis generated by the modelled to the discovery of a differential endocytosis pattern in the root meristem that splits the auxin transcriptional response via the plasma membrane to nucleus partitioning of BRX. This positional information system creates an auxin transcriptional pattern that deviates from the canonical auxin response and is necessary to sustain the expression of a subset of BRX-dependent auxin-responsive genes to drive root meristem growth. In the second part of this PhD thesis, we characterized the genome-wide impact of large scale deletions on four divergent Arabidopsis natural strains, through the integration of Ultra-High Throughput Sequencing data with data from genomic hybridizations on tiling arrays. Analysis of the identified deletions revealed a considerable portion of protein coding genes affected and supported a history of genomic rearrangements shaped by evolution. In the last part of the thesis, we showed that VIP3 gene in Arabidopsis has an evo-lutionary conserved role in the 3' to 5' mRNA degradation machinery, by applying a novel approach for the analysis of mRNA-Seq data from random-primed mRNA. Altogether, this PhD research contains major advancements in the study of natural genomic variation in plants and in the application of computational morphodynamics models for the functional characterization of biological pathways essential for the plant. - Récemment, l'introduction du séquençage de seconde génération et les avancées dans la microscopie confocale ont permis des études à l'échelle des différents systèmes cellulaires pour la caractérisation fonctionnelle de gènes. Le degrés de complexité intrinsèque à ces approches ont requis le développement de méthodologies bioinformatiques et de modèles mathématiques afin d'extraire de la masse de données expérimentale générée, des information biologiques significatives. Ce doctorat présente à la fois des méthodes bioinformatiques originales et des modèles mathématiques pour répondre à certaines questions spécifiques de Biologie Végétale en utilisant la plante Arabidopsis thaliana comme modèle. Premièrement, une analyse qualitative spatio-temporelle de profiles quantitatifs de transcripts et de protéines est utilisée pour montrer le rôle de la protéine BREVIS RADIX (BRX) dans le dialogue entre l'auxine et les cytokinines, des phytohormones, dans la croissance du méristème racinaire. Le noyau de ce travail de thèse est la caractérisation fonctionnelle de l'interaction entre la protéine BRX et la phytohormone auxine dans le méristème de la racine en utilisant des modèles informatiques basés sur des preuves expérimentales. Les hypothèses produites par le modèle ont mené à la découverte d'un schéma différentiel d'endocytose dans le méristème racinaire qui divise la réponse transcriptionnelle à l'auxine par le partitionnement de BRX de la membrane plasmique au noyau de la cellule. Cette information positionnelle crée une réponse transcriptionnelle à l'auxine qui dévie de la réponse canonique à l'auxine et est nécessaire pour soutenir l'expression d'un sous ensemble de gènes répondant à l'auxine et dépendant de BRX pour conduire la croissance du méristème. Dans la seconde partie de cette thèse de doctorat, nous avons caractérisé l'impact sur l'ensemble du génome des délétions à grande échelle sur quatre souches divergentes naturelles d'Arabidopsis, à travers l'intégration du séquençage à ultra-haut-débit avec l'hybridation génomique sur puces ADN. L'analyse des délétions identifiées a révélé qu'une proportion considérable de gènes codant était affectée, supportant l'idée d'un historique de réarrangement génomique modelé durant l'évolution. Dans la dernière partie de cette thèse, nous avons montré que le gène VÏP3 dans Arabidopsis a conservé un rôle évolutif dans la machinerie de dégradation des ARNm dans le sens 3' à 5', en appliquant une nouvelle approche pour l'analyse des données de séquençage d'ARNm issue de transcripts amplifiés aléatoirement. Dans son ensemble, cette recherche de doctorat contient des avancées majeures dans l'étude des variations génomiques naturelles des plantes et dans l'application de modèles morphodynamiques informatiques pour la caractérisation de réseaux biologiques essentiels à la plante. - Le développement des plantes est écrit dans leurs codes génétiques. Pour comprendre comment les plantes sont capables de s'adapter aux changements environnementaux, il est essentiel d'étudier comment leurs gènes gouvernent leur formation. Plus nous essayons de comprendre le fonctionnement d'une plante, plus nous réalisons la complexité des mécanismes biologiques, à tel point que l'utilisation d'outils et de modèles mathématiques devient indispensable. Dans ce travail, avec l'utilisation de la plante modèle Arabidopsis thalicinci nous avons résolu des problèmes biologiques spécifiques à travers le développement et l'application de méthodes informatiques concrètes. Dans un premier temps, nous avons investigué comment le gène BREVIS RADIX (BRX) régule le développement de la racine en contrôlant la réponse à deux hormones : l'auxine et la cytokinine. Nous avons employé une analyse statistique sur des mesures quantitatives de transcripts et de produits de gènes afin de démontrer que BRX joue un rôle antagonisant dans le dialogue entre ces deux hormones. Lorsque ce-dialogue moléculaire est perturbé, la racine primaire voit sa longueur dramatiquement réduite. Pour comprendre comment BRX répond à l'auxine, nous avons développé un modèle informatique basé sur des résultats expérimentaux. Les simulations successives ont mené à la découverte d'un signal positionnel qui contrôle la réponse de la racine à l'auxine par la régulation du mouvement intracellulaire de BRX. Dans la seconde partie de cette thèse, nous avons analysé le génome entier de quatre souches naturelles d'Arabidopsis et nous avons trouvé qu'une grande partie de leurs gènes étaient manquant par rapport à la souche de référence. Ce résultat indique que l'historique des modifications génomiques conduites par l'évolution détermine une disponibilité différentielle des gènes fonctionnels dans ces plantes. Dans la dernière partie de ce travail, nous avons analysé les données du transcriptome de la plante où le gène VIP3 était non fonctionnel. Ceci nous a permis de découvrir le rôle double de VIP3 dans la régulation de l'initiation de la transcription et dans la dégradation des transcripts. Ce rôle double n'avait jusqu'alors été démontrée que chez l'homme. Ce travail de doctorat supporte le développement et l'application de méthodologies informatiques comme outils inestimables pour résoudre la complexité des problèmes biologiques dans la recherche végétale. L'intégration de la biologie végétale et l'informatique est devenue de plus en plus importante pour l'avancée de nos connaissances sur le fonctionnement et le développement des plantes.

Predictive models of syncope causes in an outpatient clinic

The investigation of unexplained syncope remains a challenging clinical problem. In the present study we sought to evaluate the diagnostic value of a standardized work-up focusing on non invasive tests in patients with unexplained syncope referred to a syncope clinic, and whether certain combinations of clinical parameters are characteristic of rhythmic and reflex causes of syncope. METHODS AND RESULTS: 317 consecutive patients underwent a standardized work-up including a 12-lead ECG, physical examination, detailed history with screening for syncope-related symptoms using a structured questionnaire followed by carotid sinus massage (CSM), and head-up tilt test. Invasive testings including an electrophysiological study and implantation of a loop recorder were only performed in those with structural heart disease or traumatic syncope. Our work-up identified an etiology in 81% of the patients. Importantly, three quarters of the causes were established non invasively combining head-up tilt test, CSM and hyperventilation testing. Invasive tests yielded an additional 7% of diagnoses. Logistic analysis identified age and number of significant prodromes as the only predictive factors of rhythmic syncope. The same two factors, in addition to the duration of the ECG P-wave, were also predictive of vasovagal and psychogenic syncope. These factors, optimally combined in predictive models, showed a high negative and a modest positive predictive value. CONCLUSION: A standardized work-up focusing on non invasive tests allows to establish more than three quarters of syncope causes. Predictive models based on simple clinical parameters may help to distinguish between rhythmic and other causes of syncope

NS2 protein of hepatitis C virus interacts with structural and non-structural proteins towards virus assembly.

Growing experimental evidence indicates that, in addition to the physical virion components, the non-structural proteins of hepatitis C virus (HCV) are intimately involved in orchestrating morphogenesis. Since it is dispensable for HCV RNA replication, the non-structural viral protein NS2 is suggested to play a central role in HCV particle assembly. However, despite genetic evidences, we have almost no understanding about NS2 protein-protein interactions and their role in the production of infectious particles. Here, we used co-immunoprecipitation and/or fluorescence resonance energy transfer with fluorescence lifetime imaging microscopy analyses to study the interactions between NS2 and the viroporin p7 and the HCV glycoprotein E2. In addition, we used alanine scanning insertion mutagenesis as well as other mutations in the context of an infectious virus to investigate the functional role of NS2 in HCV assembly. Finally, the subcellular localization of NS2 and several mutants was analyzed by confocal microscopy. Our data demonstrate molecular interactions between NS2 and p7 and E2. Furthermore, we show that, in the context of an infectious virus, NS2 accumulates over time in endoplasmic reticulum-derived dotted structures and colocalizes with both the envelope glycoproteins and components of the replication complex in close proximity to the HCV core protein and lipid droplets, a location that has been shown to be essential for virus assembly. We show that NS2 transmembrane region is crucial for both E2 interaction and subcellular localization. Moreover, specific mutations in core, envelope proteins, p7 and NS5A reported to abolish viral assembly changed the subcellular localization of NS2 protein. Together, these observations indicate that NS2 protein attracts the envelope proteins at the assembly site and it crosstalks with non-structural proteins for virus assembly.

Oligo-Miocene extensional tectonics and fluid flow across the Northern Snake Range detachment system, Nevada

The Northern Snake Range (Nevada) represents a spectacular example of a metamorphic core complex and exposes a complete section from the mylonitic footwall into the hanging wall of a fossil detachment system. Paired geochronological and stable isotopic data of mylonitic quartzite within the detachment footwall reveal that ductile deformation and infiltration of meteoric fluids occurred between 27 and 23 Ma. Ar-40/Ar-39 ages display complex recrystallization-cooling relationships but decrease systematically from 26.9 +/- 0.2 Ma at the top to 21.3 +/- 0.2 Ma at the bottom of footwall mylonite. Hydrogen isotope (delta D) values in white mica are very low (-150 to -145 %) within the top 80-90 m of detachment footwall, in contrast to values obtained from the deeper part of the section where values range from -77 to -64 %, suggesting that time-integrated interaction between rock and meteoric fluid was restricted to the uppermost part of the mylonitic footwall. Pervasive mica-water hydrogen isotope exchange is difficult to reconcile with models of Ar-40 loss during mylonitization solely by volume diffusion. Rather, we interpret the Ar-40/Ar-39 ages of white mica with low-delta D values to date syn-mylonitic hydrogen and argon isotope exchange, and we conclude that the hydrothermal system of the Northern Snake Range was active during late Oligocene (27-23 Ma) and has been exhumed by the combined effects of ductile strain, extensional detachment faulting, and erosion.

Evaluation of an enzyme immunoassay for hepatitis C virus antibody detection using a recombinant protein derived from the core region of hepatitis C virus genome

This study was undertaken to evaluate an enzyme immunoassay (EIA) for hepatitis C virus antibody detection (anti-HCV), using just one antigen. Anti-HCV EIA was designed to detect anti-HCV IgG using on the solid-phase a recombinant C22 antigen localized at the N-terminal end of the core region of HCV genome, produced by BioMérieux. The serum samples diluted in phosphate buffer saline were added to wells coated with the C22, and incubated. After washings, the wells were loaded with conjugated anti-IgG, and read in a microtiter plate reader (492 nm). Serum samples of 145 patients were divided in two groups: a control group of 39 patients with non-C hepatitis (10 acute hepatitis A, 10 acute hepatitis B, 9 chronic hepatitis B, and 10 autoimmune hepatitis) and a study group consisting of 106 patients with chronic HCV hepatitis. In the study group all patients had anti-HCV detected by a commercially available EIA (Abbott®), specific for HCV structural and nonstructural polypeptides, alanine aminotransferase elevation or positive serum HCV-RNA detected by nested-PCR. They also had a liver biopsy compatible with chronic hepatitis. The test was positive in 101 of the 106 (95%) sera from patients in the study group and negative in 38 of the 39 (97%) sera from those in the control group, showing an accuracy of 96%. According to these results, our EIA could be used to detect anti-HCV in the serum of patients infected with hepatitis C virus.

An investigation on the pay-off to generic competences for core employees in Catalan manufacturing firms

The aim of this paper is to measure the returns to human capital. We use a unique data set consisting of matched employer-employee information. Data on individuals' human capital include a set of 26 competences that capture the utilization of workers' skills in a very detailed way. Thus, we can expand the concept of human capital and discuss the type of skills that are more productive in the workplace and, hence, generate a higher payoff for the workers. The rich information on firm's and workplace characteristics allows us to introduce a broad range of controls and to improve previous research in this field. This paper gives evidence that the returns to generic competences differ depending on the position of the worker in the firm. Only numeracy skills are reward independent of the occupational status of the worker. The level of technology used by the firm in the production process does not directly increase workers’ pay, but it influences the pay-off to some of the competences. JEL Classification: J24, J31

Multi-stage oligopoly models with nested logit demand structures: A simplifying approach

Solving multi-stage oligopoly models by backward induction can easily become a com- plex task when rms are multi-product and demands are derived from a nested logit frame- work. This paper shows that under the assumption that within-segment rm shares are equal across segments, the analytical expression for equilibrium pro ts can be substantially simpli ed. The size of the error arising when this condition does not hold perfectly is also computed. Through numerical examples, it is shown that the error is rather small in general. Therefore, using this assumption allows to gain analytical tractability in a class of models that has been used to approach relevant policy questions, such as for example rm entry in an industry or the relation between competition and location. The simplifying approach proposed in this paper is aimed at helping improving these type of models for reaching more accurate recommendations.