On the Geroch-Traschen class of metrics

We compare two approaches to semi-Riemannian metrics of low regularity. The maximally 'reasonable' distributional setting of Geroch and Traschen is shown to be consistently contained in the more general setting of nonlinear distributional geometry in the sense of Colombea

Anthropogenic extinctions conceal widespread evolution of flightlessness in birds

Human-driven extinctions can affect our understanding of evolution, through the nonrandom loss of certain types of species. Here, we explore how knowledge of a major evolutionary transition—the evolution of flightlessness in birds—is biased by anthropogenic extinctions. Adding data on 581 known anthropogenic extinctions to the extant global avifauna increases the number of species by 5%, but quadruples the number of flightless species. The evolution of flightlessness in birds is a widespread phenomenon, occurring in more than half of bird orders and evolving independently at least 150 times. Thus, we estimate that this evolutionary transition occurred at a rate four times higher than it would appear based solely on extant species. Our analysis of preanthropogenic avian diversity shows how anthropogenic effects can conceal the frequency of major evolutionary transitions in life forms and highlights the fact that macroevolutionary studies with only small amounts of missing data can still be highly biased

Plant dispersal characteristics shape the relationship of diversity with area and isolation

Aim The relation of plant dispersal syndromes with insular species richness patters remains one of the challenges in island biogeography, especially as people have affected species distribution patterns. This study disentangles how dispersal syndromes influence the relationship of richness with area and isolation while also accounting for the human impact on island biodiversity. It builds on the potential of islands at the mesoscale and of similar origin to contribute to the ongoing discussion in island biogeography on what determines species richness and filtering. Location Denmark, 54 islands in the North and Baltic Sea. Taxon Vascular plants, including pteridophytes. Methods Generalized linear models (GLMs) and linear regressions are used to analyse how dispersal syndromes influence the relationships of species numbers with island area and isolation, as well as island inhabitation and human density, respectively. Results Species numbers, seed mass and the proportion of zoochore and anemochore species are positively related to island area while the share of water-dispersed species decreases with increasing area. Isolation is weakly related to mean seed mass but has no explaining power for species numbers and the presence of specific dispersal syndrome on the target islands. Species richness and seed mass were positively related to human presence. Main conclusions Human impact for centuries has not overwritten the strong relationship of species richness with area on the Danish Islands but is affecting the shape of this relationship. Island area constitutes a strong filter for different dispersal syndromes and leads to the assumption that heavier and animal-dispersed seeds are positively related to area due to the presence of more bird and mammal species. Human-induced loss of isolation caused by ongoing traffic and the connection of landmasses by bridges and ferries may be a reason for the overall low explanatory power of island isolation.publishedVersio

Plant dispersal characteristics shape the relationship of diversity with area and isolation

Aim This study disentangles how plant dispersal syndromes influence the relationship of species richness with area and isolation while also accounting for the human impact on island biodiversity. It builds on the potential of islands at the mesoscale and of similar origin to contribute to the ongoing discussion in island biogeography on what determines species richness and filtering. Location Denmark, 54 saltwater and brackish water islands in the North and Baltic Sea Taxon Vascular plants, including pteridophytes (ferns, clubmosses and horsetails) Methods Generalized linear models (GLMs) and linear regressions are used to analyse how dispersal syndromes influence the relationships of species numbers with island area and isolation, as well as island inhabitation and human density, respectively. Results Species numbers, as well as mean seed mass and the proportion of zoochore and anemochore species, are positively related to island area while the share of water-dispersed species decreases with increasing area. The slope of the regression line representing the species-area relationship (SAR) was 0.34 and lies within the common range for this relationship. Isolation is weakly related to mean seed mass but has no explaining power for species numbers and the presence of specific dispersal syndrome on the target islands. Species richness and seed mass was positively related to human presence. Main conclusions Human impact for centuries has not overwritten the strong relationship of species richness with area on the Danish Islands but is affecting the shape of this relationship. Island area constitutes a strong filter for different dispersal syndromes and leads to the assumption that heavier and animal-dispersed seeds are positively related to island area due to the presence of more bird and mammal species. Human-induced loss of isolation caused by ongoing traffic and the connection of landmasses by bridges and ferries may be a reason for the overall low explanatory power of island isolation. Higher species richness on inhabited islands may further be linked to higher habitat diversity in human modified landscapes.The data file (.xlsx file) can be opened in Excel or Libre Office. It might be easiest to access the data file in R as it can then be used in combination with the provided R code.The dataset consists of three parts: (I) Environmental data listing the 54 studied Danish Islands including island characteristics, (II) plant species occurrence data (presence/absence data) on these islands, and (III) trait data of vascular plants that form part of the study. Environmental data For all target islands, information on isolation to continental land masses, island area, and the number of island inhabitants were gathered. The exact geographic position and precise boundaries of the 54 target islands were determined in GIS. This allowed us to calculate isolation as the shortest distance to the nearest mainland (species pool; considering the largest islands Saelland, Vendsyssel-Thyto, and Fyn to be part of continental Denmark), and surface area of the individual islands. To account for human alterations we identified inhabited and uninhabited islands and calculated human density (number of island inhabitants per ha). The number of island inhabitants was compiled from Danmarks Statistik (2021) and for smaller islands, we used Google Earth images (© Google Earth 2021) to verify that no houses were present on the island (human density = 0). Danmarks Statistik (2021). www.statbank.dk/BEF4 (last accessed on 25.10.2021). Species occurrence data Species occurrence data was extracted from a comprehensive data set compiled by Erik Wessberg and co-workers since 1979. It became available in 2011 on the homepage of the Danish Botanical Society as a series of commented species lists, one for each of the islands or cluster of islands surveyed in total (Wessberg et al. 2011). Wessberg, E. et al. (2011). Homepage of the Danish Botanical Society, accessed 10 June 2012, https://botaniskforening.dk/botanik/ofloraer/. Trait data Trait information on seed mass (mg) and dispersal syndromes (zoochory, hydrochory, anemochory, and autochory) were gathered for the 1201 species found on 54 Danish islands from a set of databases: mainly Royal Botanic Gardens Kew (2016), LEDA database (Kleyer et al., 2008) and additionally Ecological Flora of The British Isles (Fitter & Peat, 1994), BiolFlor (Klotz, et al., 2002), BROT trait database for plant species of the Mediterranean Basin (Paula et al., 2009), and D³, The Dispersal and Diaspore Database (Hintze, et al. 2013). Gaps in the data (roughly 100 species) were filled, when possible, by interpolation based on the traits of other species of the same genus, and ferns and clubmosses were assigned the smallest seed mass value in the dataset. Fitter, A. H. & Peat, H. J. 1994. The Ecological Flora Database. Journal of Ecology 82, 415-425. Hintze, C., Heydel F, Hoppe C, Cunze S, König A & Tackenberg O. (2013). D³: The Dispersal and Diaspore Database - Baseline data and statistics on seed dispersal. – Perspectives in Plant Ecology and Evolutionary Syst., 15, 180-192. Kleyer, M., Bekker, R., Knevel, I., Bakker, J., Thompson, K., Sonnenschein, M., … Peco, B. (2008). The LEDA Traitbase: A database of life-history traits of Northwest European flora. Journal of Ecology, 96, 1266-1274 Klotz, S., Kühne, I., & Walter, D. S. (2002). BIOLFLOR - Eine Datenbank zu biologisch-ökologischen Merkmalen der Gefäßpflanzen in Deutschland. – Schriftenreihe für Vegetationskunde 38. Bonn: Bundesamt für Naturschutz. Paula, S., Arianoutsou, M., Kazanis, D., Tavsanoglu, Ç., Lloret, F., Buhk, C., Ojeda, F., Luna, B., Moreno, J. M., Rodrigo, A., Espelta, J. M., Palacio, S., Fernández-Santos, B., Fernandes, P. M., & Pausas, J.G. (2009). Fire-related traits for plant species of the Mediterranean Basin. Ecology, 90, 1420 Royal Botanic Gardens Kew. (2016). Seed Information Database (SID). Version 7.1. Available from: http://data.kew.org/sid/ (June 2016)

Loss of functional diversity through anthropogenic extinctions of island birds is not offset by biotic invasions

Human impacts reshape ecological communities through the extinction and introduction of species. The combined impact of these factors depends on whether non-native species fill the functional roles of extinct species, thus buffering the loss of functional diversity. This question has been difficult to address, because comprehensive information about past extinctions and their traits is generally lacking. We combine detailed information about extinct, extant, and established alien birds to quantify historical changes in functional diversity across nine oceanic archipelagos. We found that alien species often equal or exceed the number of anthropogenic extinctions yet apparently perform a narrower set of functional roles as current island assemblages have undergone a substantial and ubiquitous net loss in functional diversity and increased functional similarity among assemblages. Our results reveal that the introduction of alien species has not prevented anthropogenic extinctions from reducing and homogenizing the functional diversity of native bird assemblages on oceanic archipelagos

Coupling a Point-Like Mass to Quantum Gravity with Causal Dynamical Triangulations

We present a possibility of coupling a point-like, non-singular, mass distribution to four-dimensional quantum gravity in the nonperturbative setting of causal dynamical triangulations (CDT). In order to provide a point of comparison for the classical limit of the matter-coupled CDT model, we derive the spatial volume profile of the Euclidean Schwarzschild-de Sitter space glued to an interior matter solution. The volume profile is calculated with respect to a specific proper-time foliation matching the global time slicing present in CDT. It deviates in a characteristic manner from that of the pure-gravity model. The appearance of coordinate caustics and the compactness of the mass distribution in lattice units put an upper bound on the total mass for which these calculations are expected to be valid. We also discuss some of the implementation details for numerically measuring the expectation value of the volume profiles in the framework of CDT when coupled appropriately to the matter source.Comment: 26 pages, 9 figures, updated published versio

A regularisation approach to causality theory for C^{1,1}Lorentzian metrics

We show that many standard results of Lorentzian causality theory remain valid if the regularity of the metric is reduced to C^{1,1}. Our approach is based on regularisations of the metric adapted to the causal structure

Distributional sources for black hole initial data

Black hole initial data is usually produced using Bowen-York type puncture initial data or by applying an excision boundary condition. The benefits of the Bowen-York initial data are the ability to specify the spin and momentum of the system as parameters of the initial data. In an attempt to extend these benefits to other formulations of the Einstein constraints, the puncture method is reformulated using distributions as source terms. It is shown how the Bowen-York puncture black hole initial data and the trumpet variation is generated by distributional sources. A heuristic argument is presented to argue that these sources are the general sources of spin and momentum. In order to clarify the meaning of other distributional sources, an exact family of initial data with generalized sources to the Hamiltonian constraint are studied; spinning trumpet black hole initial data and black hole initial data with higher order momentum sources are also studied.Comment: Code available at https://github.com/SwampWalker/LeapingMonke

Remarks on the distributional Schwarzschild geometry

This work is devoted to a mathematical analysis of the distributional Schwarzschild geometry. The Schwarzschild solution is extended to include the singularity; the energy momentum tensor becomes a delta-distribution supported at r=0. Using generalized distributional geometry in the sense of Colombeau's (special) construction the nonlinearities are treated in a mathematically rigorous way. Moreover, generalized function techniques are used as a tool to give a unified discussion of various approaches taken in the literature so far; in particular we comment on geometrical issues

Symmetries and geodesics in (anti-)de Sitter spacetimes with nonexpanding impulsive waves

We consider a class of exact solutions which represent nonexpanding impulsive waves in backgrounds with nonzero cosmological constant. Using a convenient 5-dimensional formalism it is shown that these spacetimes admit at least three global Killing vector fields. The same geometrical approach enables us to find all geodesics in a simple explicit form and describe the effect of impulsive waves on test particles. Timelike geodesics in the axially-symmetric Hotta-Tanaka spacetime are studied in detail. It is also demonstrated that for vanishing cosmological constant, the symmetries and geodesics reduce to those for well-known impulsive pp-waves.Comment: 16 pages, 3 figures, LaTeX 2e. To appear in Class. Quantum Gra