Measuring bee diversity in different European habitats and biogeographical regions

Bee pollinators are currently recorded with many different sampling methods. However, the relative performances of these methods have not been systematically evaluated and compared. In response to the strong need to record ongoing shifts in pollinator diversity and abundance, global and regional pollinator initiatives must adopt standardized sampling protocols when developing large-scale and long-term monitoring schemes. We systematically evaluated the performance of six sampling methods (observation plots, pan traps, standardized and variable transect walks, trap nests with reed internodes or paper tubes) that are commonly used across a wide range of geographical regions in Europe and in two habitat types (agricultural and seminatural). We focused on bees since they represent the most important pollinator group worldwide. Several characteristics of the methods were considered in order to evaluate their performance in assessing bee diversity: sample coverage, observed species richness, species richness estimators, collector biases (identified by subunit-based rarefaction curves), species composition of the samples, and the indication of overall bee species richness (estimated from combined total samples). The most efficient method in all geographical regions, in both the agricultural and seminatural habitats, was the pan trap method. It had the highest sample coverage, collected the highest number of species, showed negligible collector bias, detected similar species as the transect methods, and was the best indicator of overall bee species richness. The transect methods were also relatively efficient, but they had a significant collector bias. The observation plots showed poor performance. As trap nests are restricted to cavity-nesting bee species, they had a naturally low sample coverage. However, both trap nest types detected additional species that were not recorded by any of the other methods. For large-scale and long-term monitoring schemes with surveyors with different experience levels, we recommend pan traps as the most efficient, unbiased, and cost-effective method for sampling bee diversity. Trap nests with reed internodes could be used as a complementary sampling method to maximize the numbers of collected species. Transect walks are the principal method for detailed studies focusing on plant-pollinator associations. Moreover, they can be used in monitoring schemes after training the surveyors to standardize their collection skills.

Copyright and research: an archivangelist's perspective

Conflation of academic copyright issues with respect to books (whether text books, research monographs or popularisations) and research articles, is rife in the academic publishing industry. A charitable interpretation is that this is because to publishers they are all effectively the same: a product produced for commercial benefit. An uncharitable interpretation is that this is a classic Fear Uncertainty and Doubt approach, in an attempt to delay the inevitable move to Open Access (OA) to research articles. To authors, however, research articles and books are generally very different things. Research articles are produced without the expectation of direct financial return, whereas books generally include some consideration of financial return. Taylor’s “Copyright and research: an academic publisher’s perspective” (SCRIPT-ed 4:2) falls wholesale into this mental trap and in particular his lauding of the position paper of the Association of American Professional and Scholarly Publishers, shows a lack of understanding of the continuing huge loss to scholarship of a lack of OA to research articles. It should be regarded as a categorical imperative for scholars to embrace OA to research articles.

Limit operators, collective compactness, and the spectral theory of infinite matrices

In the first half of this memoir we explore the interrelationships between the abstract theory of limit operators (see e.g. the recent monographs of Rabinovich, Roch and Silbermann (2004) and Lindner (2006)) and the concepts and results of the generalised collectively compact operator theory introduced by Chandler-Wilde and Zhang (2002). We build up to results obtained by applying this generalised collectively compact operator theory to the set of limit operators of an operator (its operator spectrum). In the second half of this memoir we study bounded linear operators on the generalised sequence space , where and is some complex Banach space. We make what seems to be a more complete study than hitherto of the connections between Fredholmness, invertibility, invertibility at infinity, and invertibility or injectivity of the set of limit operators, with some emphasis on the case when the operator is a locally compact perturbation of the identity. Especially, we obtain stronger results than previously known for the subtle limiting cases of and . Our tools in this study are the results from the first half of the memoir and an exploitation of the partial duality between and and its implications for bounded linear operators which are also continuous with respect to the weaker topology (the strict topology) introduced in the first half of the memoir. Results in this second half of the memoir include a new proof that injectivity of all limit operators (the classic Favard condition) implies invertibility for a general class of almost periodic operators, and characterisations of invertibility at infinity and Fredholmness for operators in the so-called Wiener algebra. In two final chapters our results are illustrated by and applied to concrete examples. Firstly, we study the spectra and essential spectra of discrete Schrödinger operators (both self-adjoint and non-self-adjoint), including operators with almost periodic and random potentials. In the final chapter we apply our results to integral operators on .