Superstable manifolds of invariant circles and codimension-one Böttcher functions

Let f : X ⇢ X be a dominant meromorphic self-map, where X is a compact, connected complex manifold of dimension n>1. Suppose that there is an embedded copy of P1 that is invariant under f, with f holomorphic and transversally superattracting with degree a in some neighborhood. Suppose that f restricted to this line is given by z↦zb, with resulting invariant circle S. We prove that if a≥b, then the local stable manifold Wsloc(S) is real analytic. In fact, we state and prove a suitable localized version that can be useful in wider contexts. We then show that the condition a≥b cannot be relaxed without adding additional hypotheses by presenting two examples with a<b for which Wsloc(S) is not real analytic in the neighborhood of any point

Ab initio simulations of liquid systems: Concentration dependence of the electric conductivity of NaSn alloys

Liquid NaSn alloys in five different compositions (20, 40, 50, 57 and 80% sodium) are studied using density functional calculations combined with molecular dynamics(Car-Parrinello method). The frequency-dependent electric conductivities for the systems are calculated by means of the Kubo-Greenwood formula. The extrapolated DC conductivities are in good agreement with the experimental data and reproduce the strong variation with the concentration. The maximum of conductivity is obtained, in agreement with experiment, near the equimolar composition. The strong variation of conductivity, ranging from almost semiconducting up to metallic behaviour, can be understood by an analysis of the densities-of-states.Comment: LaTex 6 pages and 2 figures, to appear in J.Phys. Cond. Ma

Ab initio simulations of liquid NaSn alloys: Zintl anions and network formation

Using the Car-Parrinello technique, ab initio molecular dynamics simulations are performed for liquid NaSn alloys in five different compositions (20, 40, 50, 57 and 80 % sodium). The obtained structure factors agree well with the data from neutron scattering experiments. The measured prepeak in the structure factor is reproduced qualitatively for most compositions. The calculated and measured positions of all peaks show the same trend as function of the composition.\\ The dynamic simulations also yield information about the formation and stability of Sn$_4$ clusters (Zintl anions) in the liquid. In our simulations of compositions with 50 and 57 % sodium we observe the formation of networks of tin atoms. Thus, isolated tin clusters are not stable in such liquids. For the composition with 20 % tin only isolated atoms or dimers of tin appear, ``octet compounds'' of one Sn atom surrounded by 4 Na atoms are not observed.Comment: 12 pages, Latex, 3 Figures on reques

Theoretical investigation of carbon defects and diffusion in α-quartz

The geometries, formation energies, and diffusion barriers of carbon point defects in silica (α-quartz) have been calculated using a charge-self-consistent density-functional based nonorthogonal tight-binding method. It is found that bonded interstitial carbon configurations have significantly lower formation energies (on the order of 5 eV) than substitutionals. The activation energy of atomic C diffusion via trapping and detrapping in interstitial positions is about 2.7 eV. Extraction of a CO molecule requires an activation energy <3.1 eV but the CO molecule can diffuse with an activation energy <0.4 eV. Retrapping in oxygen vacancies is hindered—unlike for O2—by a barrier of about 2 eV

Current and Future Patterns of Global Marine Mammal Biodiversity

Quantifying the spatial distribution of taxa is an important prerequisite for the preservation of biodiversity, and can provide a baseline against which to measure the impacts of climate change. Here we analyse patterns of marine mammal species richness based on predictions of global distributional ranges for 115 species, including all extant pinnipeds and cetaceans. We used an environmental suitability model specifically designed to address the paucity of distributional data for many marine mammal species. We generated richness patterns by overlaying predicted distributions for all species; these were then validated against sightings data from dedicated long-term surveys in the Eastern Tropical Pacific, the Northeast Atlantic and the Southern Ocean. Model outputs correlated well with empirically observed patterns of biodiversity in all three survey regions. Marine mammal richness was predicted to be highest in temperate waters of both hemispheres with distinct hotspots around New Zealand, Japan, Baja California, the Galapagos Islands, the Southeast Pacific, and the Southern Ocean. We then applied our model to explore potential changes in biodiversity under future perturbations of environmental conditions. Forward projections of biodiversity using an intermediate Intergovernmental Panel for Climate Change (IPCC) temperature scenario predicted that projected ocean warming and changes in sea ice cover until 2050 may have moderate effects on the spatial patterns of marine mammal richness. Increases in cetacean richness were predicted above 40° latitude in both hemispheres, while decreases in both pinniped and cetacean richness were expected at lower latitudes. Our results show how species distribution models can be applied to explore broad patterns of marine biodiversity worldwide for taxa for which limited distributional data are available

Predicting the Impact of Climate Change on Threatened Species in UK Waters

Global climate change is affecting the distribution of marine species and is thought to represent a threat to biodiversity. Previous studies project expansion of species range for some species and local extinction elsewhere under climate change. Such range shifts raise concern for species whose long-term persistence is already threatened by other human disturbances such as fishing. However, few studies have attempted to assess the effects of future climate change on threatened vertebrate marine species using a multi-model approach. There has also been a recent surge of interest in climate change impacts on protected areas. This study applies three species distribution models and two sets of climate model projections to explore the potential impacts of climate change on marine species by 2050. A set of species in the North Sea, including seven threatened and ten major commercial species were used as a case study. Changes in habitat suitability in selected candidate protected areas around the UK under future climatic scenarios were assessed for these species. Moreover, change in the degree of overlap between commercial and threatened species ranges was calculated as a proxy of the potential threat posed by overfishing through bycatch. The ensemble projections suggest northward shifts in species at an average rate of 27 km per decade, resulting in small average changes in range overlap between threatened and commercially exploited species. Furthermore, the adverse consequences of climate change on the habitat suitability of protected areas were projected to be small. Although the models show large variation in the predicted consequences of climate change, the multi-model approach helps identify the potential risk of increased exposure to human stressors of critically endangered species such as common skate (Dipturus batis) and angelshark (Squatina squatina)

Postglacial Colonization of Northern Coastal Habitat by Bottlenose Dolphins: A Marine Leading-Edge Expansion?

Oscillations in the Earth’s temperature and the subsequent retreating and advancing of ice-sheets around the polar regions are thought to have played an important role in shaping the distribution and genetic structuring of contemporary high-latitude populations. After the Last Glacial Maximum (LGM), retreating of the ice-sheets would have enabled early colonizers to rapidly occupy suitable niches to the exclusion of other conspecifics, thereby reducing genetic diversity at the leading-edge. Bottlenose dolphins (genus Tursiops) form distinct coastal and pelagic ecotypes, with finer-scale genetic structuring observed within each ecotype. We reconstruct the postglacial colonization of the Northeast Atlantic (NEA) by bottlenose dolphins using habitat modeling and phylogenetics. The AquaMaps model hindcasted suitable habitat for the LGM in the Atlantic lower latitude waters and parts of the Mediterranean Sea. The time-calibrated phylogeny, constructed with 86 complete mitochondrial genomes including 30 generated for this study and created using a multispecies coalescent model, suggests that the expansion to the available coastal habitat in the NEA happened via founder events starting ~15 000 years ago (95% highest posterior density interval: 4 900–26 400). The founders of the 2 distinct coastal NEA populations comprised as few as 2 maternal lineages that originated from the pelagic population. The low effective population size and genetic diversity estimated for the shared ancestral coastal population subsequent to divergence from the pelagic source population are consistent with leading-edge expansion. These findings highlight the legacy of the Late Pleistocene glacial cycles on the genetic structuring and diversity of contemporary populations

Harmful algal blooms and climate change: exploring future distribution changes

Harmful algae can cause death in fish, shellfish, marine mammals, and humans, via their toxins or from effects associated with their sheer quantity. There are many species, which cause a variety of problems around north-west Europe, and the frequency and distribution of algal blooms have altered in the recent past. Species distribution modelling was used to understand how harmful algal species may respond in the future to climate change, by considering environmental preferences and how these may shift. Most distribution studies to date use low resolution global model outputs. In this study, high resolution, downscaled shelf seas climate projections for the north-west European shelf were nested within lower resolution global projections, to understand how the distribution of harmful algae may change by the mid to end of century. Projections suggest that the habitat of most species (defined by temperature, salinity, depth, and stratification) will shift north this century, with suitability increasing in the central and northern North Sea. An increase in occurrence here might lead to more frequent detrimental blooms if wind, irradiance and nutrient levels are also suitable. Prioritizing monitoring of species in these susceptible areas could help in establishing early-warning systems for aquaculture and health protection schemes

Blueprints of Effective Biodiversity and Conservation Knowledge Products That Support Marine Policy

Biodiversity and conservation data are generally costly to collect, particularly in the marine realm. Hence, data collected for a given—often scientific—purpose are occasionally contributed toward secondary needs, such as policy implementation or other types of decision-making. However, while the quality and accessibility of marine biodiversity and conservation data have improved over the past decade, the ways in which these data can be used to develop and implement relevant management and conservation measures and actions are not always explicit. For this reason, there are a number of scientifically-sound datasets that are not used systematically to inform policy and decisions. Transforming these marine biodiversity and conservation datasets into knowledge products that convey the information required by policy- and decision-makers is an important step in strengthening knowledge exchange across the science-policy interface. Here, we identify seven characteristics of a selection of online biodiversity and conservation knowledge products that contribute to their ability to support policy- and decision-making in the marine realm (as measured by e.g., mentions in policy resolutions/decisions, or use for reporting under selected policy instruments; use in high-level screening for areas of biodiversity importance). These characteristics include: a clear policy mandate; established networks of collaborators; iterative co-design of a user-friendly interface; standardized, comprehensive and documented methods with quality assurance; consistent capacity and succession planning; accessible data and value-added products that are fit-for-purpose; and metrics of use collated and reported. The outcomes of this review are intended to: (a) support data creators/owners/providers in designing and curating biodiversity and conservation knowledge products that have greater influence, and hence impact, in policy- and decision-making, and (b) provide recommendations for how decision- and policy-makers can support the development, implementation, and sustainability of robust biodiversity and conservation knowledge products through the framing of marine policy and decision-making frameworks.This is a contribution to the “Building the European Biodiversity Observation Network” (EU BON) project (www.eubon.eu), a 7th Framework Programme funded by the European Union under grant agreement No. 308454. The authors would also like to acknowledge the Proteus Partnership, the European Commission, the CITES Secretariat, UN Environment, the World Conservation Monitoring Centre, the International Union for Conservation of Nature and the national agencies contributing to GBIF core funds for their financial contributions toward developing and maintaining these knowledge products