(1,1)-forms acting on Spinors on K\"ahler Surfaces

It is known that, for Dirac operators on Riemann surfaces twisted by line bundles with Hermitian-Einstein connections, it is possible to obtain estimates for the first eigenvalue in terms of the topology of the twisting bundle \cite{JL2}. Attempts to generalize topological estimates for higher rank bundles or higher dimensional manifolds have been so far unsuccessful. In this work we construct a class of examples which indicates one problem that arises on such attempts to derive topological estimates

On the spectrum of the twisted Dolbeault Laplacian over K\"ahler manifolds

We use Dirac operator techniques to a establish sharp lower bound for the first eigenvalue of the Dolbeault Laplacian twisted by Hermitian-Einstein connections on vector bundles of negative degree over compact K\"ahler manifolds.Comment: 14 pages. Completely revised: estimates corrected and shown to be shar

Rarity of monodominance in hyperdiverse Amazonian forests.

Tropical forests are known for their high diversity. Yet, forest patches do occur in the tropics where a single tree species is dominant. Such "monodominant" forests are known from all of the main tropical regions. For Amazonia, we sampled the occurrence of monodominance in a massive, basin-wide database of forest-inventory plots from the Amazon Tree Diversity Network (ATDN). Utilizing a simple defining metric of at least half of the trees ≥ 10 cm diameter belonging to one species, we found only a few occurrences of monodominance in Amazonia, and the phenomenon was not significantly linked to previously hypothesized life history traits such wood density, seed mass, ectomycorrhizal associations, or Rhizobium nodulation. In our analysis, coppicing (the formation of sprouts at the base of the tree or on roots) was the only trait significantly linked to monodominance. While at specific locales coppicing or ectomycorrhizal associations may confer a considerable advantage to a tree species and lead to its monodominance, very few species have these traits. Mining of the ATDN dataset suggests that monodominance is quite rare in Amazonia, and may be linked primarily to edaphic factors

Geographic patterns of tree dispersal modes in Amazonia and their ecological correlates

Indaga sobre los patrones geográficos y los correlatos ecológicos en la distribución geográfica de los modos de dispersión arbórea más comunes en la Amazonia (endozoocoria, sinzoocoria, anemoocoria e hidrocoria). Se examina si la abundancia proporcional de estos modos de dispersión podría explicarse por la disponibilidad de agentes dispersores (hipótesis de disponibilidad de dispersores) y/o la disponibilidad de recursos para la poducción de frutos zoocorios (hipótesis de disponibilidad de recursos). Para ello se usaron parcelas de inventario de árboles establecidas entre 1934 y 2019, con un diámetro a la altura del pecho (DAP) ≥ 9,55 cm. Ubicados en las selvas tropicales de tierras bajas de la cuenca del río Amazonas y el Escudo Guayanés. Se asignaron modos de dispersión a un total de 5433 especies y morfoespecies en 1877 parcelas de inventario de árboles en bosques de abeto, inundados estacionalmente y permanentemente inundados. Se investigaron los patrones geográficos en la abundancia proporcional de los modos de dispersión. Se realizó una prueba de distancia media entre pares ponderada por abundancia (MPD) y ajustamos modelos lineales generalizados (GLM) para explicar la distribución geográfica de los modos de dispersión. La anemocoria se asoció significativa y positivamente con la velocidad media anual del viento, y la hidrocoria fue significativamente mayor en los bosques inundados. Los modos de dispersión no mostraron consistentemente asociaciones significativas con la disponibilidad de recursos para la construcción de frutos zoochorous. Una menor disimilitud en los modos de dispersión, resultante de una mayor dominancia de la endozoocoria, se produjo en los bosques de abeto (excluyendo los podzoles) en comparación con los bosques inundados. La hipótesis dispersor-disponibilidad fue bien apoyada para los modos de dispersión abióticos (anemochoria e hidrochoria). La disponibilidad de recursos para la construcción de frutos zoocorios parece una explicación poco probable para la distribución de los modos de dispersión en la Amazonia. La asociación entre los frugívoros y la abundancia proporcional de zoocoría requiere más investigación, ya que el reclutamiento de árboles no sólo depende de los vectores de dispersión, sino también de las condiciones que favorecen o limitan el reclutamiento de plántulas en los distintos tipos de bosque.Revisión por pares

Geographic patterns of tree dispersal modes in Amazonia and their ecological correlates

Unidad de excelencia María de Maeztu CEX2019-000940-MAim: To investigate the geographic patterns and ecological correlates in the geographic distribution of the most common tree dispersal modes in Amazonia (endozoochory, synzoochory, anemochory and hydrochory). We examined if the proportional abundance of these dispersal modes could be explained by the availability of dispersal agents (disperser-availability hypothesis) and/or the availability of resources for constructing zoochorous fruits (resource-availability hypothesis). Time period: Tree-inventory plots established between 1934 and 2019. Major taxa studied: Trees with a diameter at breast height (DBH) ≥ 9.55 cm. Location: Amazonia, here defined as the lowland rain forests of the Amazon River basin and the Guiana Shield. Methods: We assigned dispersal modes to a total of 5433 species and morphospecies within 1877 tree-inventory plots across terra-firme, seasonally flooded, and permanently flooded forests. We investigated geographic patterns in the proportional abundance of dispersal modes. We performed an abundance-weighted mean pairwise distance (MPD) test and fit generalized linear models (GLMs) to explain the geographic distribution of dispersal modes. Results: Anemochory was significantly, positively associated with mean annual wind speed, and hydrochory was significantly higher in flooded forests. Dispersal modes did not consistently show significant associations with the availability of resources for constructing zoochorous fruits. A lower dissimilarity in dispersal modes, resulting from a higher dominance of endozoochory, occurred in terra-firme forests (excluding podzols) compared to flooded forests. Main conclusions: The disperser-availability hypothesis was well supported for abiotic dispersal modes (anemochory and hydrochory). The availability of resources for constructing zoochorous fruits seems an unlikely explanation for the distribution of dispersal modes in Amazonia. The association between frugivores and the proportional abundance of zoochory requires further research, as tree recruitment not only depends on dispersal vectors but also on conditions that favour or limit seedling recruitment across forest types