4 research outputs found
Classical Conformal Blocks and Accessory Parameters from Isomonodromic Deformations
Classical conformal blocks naturally appear in the large central charge limit
of 2D Virasoro conformal blocks. In the correspondence, they
are related to classical bulk actions and are used to calculate entanglement
entropy and geodesic lengths. In this work, we discuss the identification of
classical conformal blocks and the Painlev\'e VI action showing how
isomonodromic deformations naturally appear in this context. We recover the
accessory parameter expansion of Heun's equation from the isomonodromic
-function. We also discuss how the expansion of the
-function leads to a novel approach to calculate the 4-point classical
conformal block.Comment: 32+10 pages, 2 figures; v3: upgraded notation, discussion on moduli
space and monodromies, numerical and analytic checks; v2: added refs, fixed
emai
Benchmarking plant diversity of Palaearctic grasslands and other open habitats
Abstract
Aims: Understanding fine-grain diversity patterns across large spatial extents is fundamental for macroecological research and biodiversity conservation. Using the GrassPlot database, we provide benchmarks of fine-grain richness values of Palaearctic open habitats for vascular plants, bryophytes, lichens and complete vegetation (i.e., the sum of the former three groups).
Location: Palaearctic biogeographic realm.
Methods: We used 126,524 plots of eight standard grain sizes from the GrassPlot database: 0.0001, 0.001, 0.01, 0.1, 1, 10, 100 and 1,000 m² and calculated the mean richness and standard deviations, as well as maximum, minimum, median, and first and third quartiles for each combination of grain size, taxonomic group, biome, region, vegetation type and phytosociological class.
Results: Patterns of plant diversity in vegetation types and biomes differ across grain sizes and taxonomic groups. Overall, secondary (mostly semi-natural) grasslands and natural grasslands are the richest vegetation type. The open-access file ”GrassPlot Diversity Benchmarks” and the web tool “GrassPlot Diversity Explorer” are now available online (https://edgg.org/databases/GrasslandDiversityExplorer) and provide more insights into species richness patterns in the Palaearctic open habitats.
Conclusions: The GrassPlot Diversity Benchmarks provide high-quality data on species richness in open habitat types across the Palaearctic. These benchmark data can be used in vegetation ecology, macroecology, biodiversity conservation and data quality checking. While the amount of data in the underlying GrassPlot database and their spatial coverage are smaller than in other extensive vegetation-plot databases, species recordings in GrassPlot are on average more complete, making it a valuable complementary data source in macroecology