On Turing dynamical systems and the Atiyah problem

Main theorems of the article concern the problem of M. Atiyah on possible values of l^2-Betti numbers. It is shown that all non-negative real numbers are l^2-Betti numbers, and that "many" (for example all non-negative algebraic) real numbers are l^2-Betti numbers of simply connected manifolds with respect to a free cocompact action. Also an explicit example is constructed which leads to a simply connected manifold with a transcendental l^2-Betti number with respect to an action of the threefold direct product of the lamplighter group Z/2 wr Z. The main new idea is embedding Turing machines into integral group rings. The main tool developed generalizes known techniques of spectral computations for certain random walk operators to arbitrary operators in groupoid rings of discrete measured groupoids.Comment: 35 pages; essentially identical to the published versio

Forest biodiversity, ecosystem functioning and the provision of ecosystem services

Forests are critical habitats for biodiversity and they are also essential for the provision of a wide range of ecosystem services that are important to human well-being. There is increasing evidence that biodiversity contributes to forest ecosystem functioning and the provision of ecosystem services. Here we provide a review of forest ecosystem services including biomass production, habitat provisioning services, pollination, seed dispersal, resistance to wind storms, fire regulation and mitigation, pest regulation of native and invading insects, carbon sequestration, and cultural ecosystem services, in relation to forest type, structure and diversity. We also consider relationships between forest biodiversity and multifunctionality, and trade-offs among ecosystem services. We compare the concepts of ecosystem processes, functions and services to clarify their definitions. Our review of published studies indicates a lack of empirical studies that establish quantitative and causal relationships between forest biodiversity and many important ecosystem services. The literature is highly skewed; studies on provisioning of nutrition and energy, and on cultural services, delivered by mixed-species forests are under-represented. Planted forests offer ample opportunity for optimising their composition and diversity because replanting after harvesting is a recurring process. Planting mixed-species forests should be given more consideration as they are likely to provide a wider range of ecosystem services within the forest and for adjacent land uses. This review also serves as the introduction to this special issue of Biodiversity and Conservation on various aspects of forest biodiversity and ecosystem services

Determinants of Persistence and Tolerance of Carnivores on Namibian Ranches: Implications for Conservation on Southern African Private Lands

Changing land use patterns in southern Africa have potential to dramatically alter the prospects for carnivore conservation. Understanding these influences is essential for conservation planning. We interviewed 250 ranchers in Namibia to assess human tolerance towards and the distribution of large carnivores. Cheetahs (Acinonyx jubatus), leopards (Panthera pardus) and brown hyaenas (Hyaena brunnea) were widely distributed on Namibian farmlands, spotted hyaenas (Crocuta crocuta) had a narrower distribution, and wild dogs (Lycaon pictus) and lions (Panthera leo) are largely limited to areas near source populations. Farmers were most tolerant of leopards and least tolerant of lions, wild dogs and spotted hyaenas. Several factors relating to land use correlated consistently with carnivore-presence and landowner tolerance. Carnivores were more commonly present and/or tolerated where; wildlife diversity and biomass were higher; income from wildlife was higher; income from livestock was lower; livestock biomass was lower; in conservancies; game fencing was absent; and financial losses from livestock depredation were lower. Efforts to create conditions whereby the costs associated with carnivores are lowest, and which confer financial value to them are likely to be the most effective means of promoting carnivore conservation. Such conditions are achieved where land owners pool land to create conservancies where livestock are replaced with wildlife (or where livestock husbandry is improved) and where wildlife generates a significant proportion of ranch income. Additional measures, such as promoting improved livestock husbandry and educational outreach efforts may also help achieve coexistence with carnivores. Our findings provide insights into conditions more conducive to the persistence of and tolerance towards large carnivores might be increased on private (and even communal) lands in Namibia, elsewhere in southern and East Africa and other parts of the world where carnivore conservation is being attempted on private lands

Grizzly Bear conservation in the Foothills Model Forest: appraisal of a collaborative ecosystem management effort

Alberta, Cheviot coal mine, Collaboration, Ecological integrity, Ecosystem-based management, Environmental assessment, Foothills Model Forest, Grizzly bear, Jasper National Park, Policy sciences, Ursus arctos ,