Diagonalization and Jordan Normal Form – motivation through Maple

Following an introduction to the diagonalization of matrices, one of the more difficult topics for students to grasp in linear algebra is the concept of Jordan normal form. In this note, we show how the important notions of diagonalization and Jordan normal form can be introduced and developed through the use of the computer algebra package Maple®.

Later Pleistocene evolution of the Exe valley: a chronostratigraphic model of terrace formation and its implications for Palaeolithic archaeology

This paper presents the first systematic chronostratigraphic study of the river terraces of the Exe catchment in South West England and a new conceptual model for terrace formation in unglaciated basins with applicability to terrace staircase sequences elsewhere. The Exe catchment lay beyond the maximum extent of Pleistocene ice sheets and the drainage pattern evolved from the Tertiary to the Middle Pleistocene, by which time the major valley systems were in place and downcutting began to create a staircase of strath terraces. The higher terraces (8-6) typically exhibit altitudinal overlap or appear to be draped over the landscape, whilst the middle terraces show greater altitudinal separation and the lowest terraces are of a cut and fill form. The terrace deposits investigated in this study were deposited in cold phases of the glacial-interglacial Milankovitch climatic cycles with the lowest four being deposited in the Devensian Marine Isotope Stages (MIS) 4-2. A new cascade process-response model is proposed of basin terrace evolution in the Exe valley, which emphasises the role of lateral erosion in the creation of strath terraces and the reworking of inherited resistant lithological components down through the staircase. The resultant emergent valley topography and the reworking of artefacts along with gravel clasts, have important implications for the dating of hominin presence and the local landscapes they inhabited. Whilst the terrace chronology suggested here is still not as detailed as that for the Thames or the Solent System it does indicate a Middle Palaeolithic hominin presence in the region, probably prior to the late Wolstonian Complex or MIS 6. This supports existing data from cave sites in South West England.

Landscape context and habitat type as drivers of bee diversity in European annual crops

To better understand the dynamics of bee populations in crops, we assessed the effect of landscape context and habitat type on bee communities in annual entomophilous crops in Europe. We quantified bee communities in five pairs of crop-country: buckwheat in Poland, cantaloupe in France, field beans in the UK, spring oilseed rape in Sweden, and strawberries in Germany. For each country, 7-10 study fields were sampled over a gradient of increasing proportion of semi-natural habitats in the surrounding landscape. The CORINE land cover classification was used to characterize the landscape over a 3 km radius around each study field and we used multivariate and regression analyses to quantify the impact of landscape features on bee abundance and diversity at the sub-generic taxonomic level. Neither overall wild bee abundance nor diversity, taken as the number of sub-genera. was significantly affected by the proportion of semi-natural habitat. Therefore, we used the most precise level of the CORINE classification to examine the possible links between specific landscape features and wild bee communities. Bee community composition fell into three distinct groups across Europe: group I included Poland, Germany, and Sweden, group 2 the UK, and group 3 France. Among all three groups, wild bee abundance and sub-generic diversity were affected by 17 landscape elements including some semi-natural habitats (e.g., transitional wood land-shrub), some urban habitats (e.g., sport and leisure facilities) and some crop habitats (e.g., non-irrigated arable land). Some bee taxa were positively affected by urban habitats only, others by semi-natural habitats only, and others by a combination of semi-natural, urban and crop habitats. Bee sub-genera favoured by urban and crop habitats were more resistant to landscape change than those favoured only by semi-natural habitats. In agroecosystems, the agricultural intensification defined as the loss of semi-natural habitats does not necessarily cause a decline in evenness at the local level, but can change community composition towards a bee fauna dominated by common taxa. (C) 2009 Elsevier B.V. All rights reserved.

Landscape gene flow, coexistence and threshold effect: The case of genetically modified herbicide tolerant oilseed rape (Brassica napus)

Globally there have been a number of concerns about the development of genetically modified crops many of which relate to the implications of gene flow at various levels. In Europe these concerns have led the European Union (EU) to promote the concept of 'coexistence' to allow the freedom to plant conventional and genetically modified (GM) varieties but to minimise the presence of transgenic material within conventional crops. Should a premium for non-GM varieties emerge on the market, the presence of transgenes would generate a 'negative externality' to conventional growers. The establishment of maximum tolerance level for the adventitious presence of GM material in conventional crops produces a threshold effect in the external costs. The existing literature suggests that apart from the biological characteristics of the plant under consideration (e.g. self-pollination rates, entomophilous species, anemophilous species, etc.), gene flow at the landscape level is affected by the relative size of the source and sink populations and the spatial arrangement of the fields in the landscape. In this paper, we take genetically modified herbicide tolerant oilseed rape (GM HT OSR) as a model crop. Starting from an individual pollen dispersal function, we develop a spatially explicit numerical model in order to assess the effect of the size of the source/sink populations and the degree of spatial aggregation on the extent of gene flow into conventional OSR varieties under two alternative settings. We find that when the transgene presence in conventional produce is detected at the field level, the external cost will increase with the size of the source area and with the level of spatial disaggregation. on the other hand when the transgene presence is averaged among all conventional fields in the landscape (e.g. because of grain mixing before detection), the external cost will only depend on the relative size of the source area. The model could readily be incorporated into an economic evaluation of policies to regulate adoption of GM HT OSR. (c) 2007 Elsevier B.V. All rights reserved.

Quantifying the effect of buffer zones, crop areas and spatial aggregation on the externalities of genetically modified crops at landscape level

The development of genetically modified (GM) crops has led the European Union (EU) to put forward the concept of 'coexistence' to give fanners the freedom to plant both conventional and GM varieties. Should a premium for non-GM varieties emerge in the market, 'contamination' by GM pollen would generate a negative externality to conventional growers. It is therefore important to assess the effect of different 'policy variables'on the magnitude of the externality to identify suitable policies to manage coexistence. In this paper, taking GM herbicide tolerant oilseed rape as a model crop, we start from the model developed in Ceddia et al. [Ceddia, M.G., Bartlett, M., Perrings, C., 2007. Landscape gene flow, coexistence and threshold effect: the case of genetically modified herbicide tolerant oilseed rape (Brassica napus). Ecol. Modell. 205, pp. 169-180] use a Monte Carlo experiment to generate data and then estimate the effect of the number of GM and conventional fields, width of buffer areas and the degree of spatial aggregation (i.e. the 'policy variables') on the magnitude of the externality at the landscape level. To represent realistic conditions in agricultural production, we assume that detection of GM material in conventional produce might occur at the field level (no grain mixing occurs) or at the silos level (where grain mixing from different fields in the landscape occurs). In the former case, the magnitude of the externality will depend on the number of conventional fields with average transgenic presence above a certain threshold. In the latter case, the magnitude of the externality will depend on whether the average transgenic presence across all conventional fields exceeds the threshold. In order to quantify the effect of the relevant' policy variables', we compute the marginal effects and the elasticities. Our results show that when relying on marginal effects to assess the impact of the different 'policy variables', spatial aggregation is far more important when transgenic material is detected at field level, corroborating previous research. However, when elasticity is used, the effectiveness of spatial aggregation in reducing the externality is almost identical whether detection occurs at field level or at silos level. Our results show also that the area planted with GM is the most important 'policy variable' in affecting the externality to conventional growers and that buffer areas on conventional fields are more effective than those on GM fields. The implications of the results for the coexistence policies in the EU are discussed. (C) 2008 Elsevier B.V. All rights reserved.

Enhancing the selenium content of bovine milk through alteration of the form and concentration of selenium in the diet of the dairy cow

Since estimated dietary selenium intake in the UK has declined steadily from around 60 mug day(-1) in 1975 to 34 mug day(-1) in 1997, there is a need to increase selenium intake from staple foods such as milk and milk products. An experiment was therefore done to investigate the relationship between dietary source and concentration of selenium and the selenium content of bovine milk. In a 3 x 3 factorial design, 90 mid-lactation Holstein dairy cows were supplemented over 8 weeks with either sodium selenite (S), a chelated selenium product (Selenium Metasolate(TM)) (C) or a selenium yeast (Sel-plex(TM)) (Y) at three different dietary inclusion levels of 0.38 (L), 0.76 (M) and 1.14 (H) mg kg(-1) dry matter (DM). Significant increases in milk selenium concentration were observed for all three sources with increasing inclusion level in the diet, but Y gave a much greater response (up to +65 mug l(-1)) than the other two sources of selenium (S and C up to +4 and +6 mug l(-1) respectively). The Y source also resulted in a substantially higher apparent efficiency of transfer of selenium from diet to milk than S or C. Feeding Y at the lowest dietary concentration, and thus within the maximum level permitted under EU regulations, resulted in milk with a selenium concentration of 28 mug l(-1). If the selenium concentration of milk in the UK was increased to this value, it would, at current consumption rates, provide an extra 8.7 mug selenium day(-1), or 11 and 14% of daily recommended national intake for men and women respectively. (C) 2004 Society of Chemical Industry.

Plant-pollinator biodiversity and pollination services in a complex Mediterranean landscape

Mediterranean landscapes comprise a complex mosaic of different habitats that vary in the diversity of their floral communities, pollinator communities and pollination services. Using the Greek Island of Lesvos as a model system, we assess the biodiversity value of six common habitats and measure ecosystemic 'health' using pollen grain deposition in three core flowering plants as a measure of pollination services. Three fire-driven habitats were assessed: freshly burnt areas, fully regenerated pine forests and intermediate age scrub; in addition we examined oak woodlands, actively managed olive groves and groves that had been abandoned from agriculture. Oak woodlands, pine forests and managed olive groves had the highest diversity of bees. The habitat characteristics responsible for structuring bee communities were: floral diversity, floral abundance, nectar energy availability and the variety of nectar resources present. Pollination services in two of our plant species, which were pollinated by a limited sub-set of the pollinator community, indicated that pollination levels were highest in the burnt and mature pine habitats. The third species, which was open to all flower visitors, indicated that oak woodlands had the highest levels of pollination from generalist species. Pollination was always more effective in managed olive groves than in abandoned groves. However, the two most common species of bee, the honeybee and a bumblebee, were not the primary pollinators within these habitats. We conclude that the three habitats of greatest overall value for plant-pollinator communities and provision of the healthiest pollination services are pine forests, oak woodland and managed olive groves. We indicate how the highest value habitats may be maintained in a complex landscape to safeguard and enhance pollination function within these habitats and potentially in adjoining agricultural areas. (c) 2005 Elsevier Ltd. All rights reserved.

Role of nesting resources in organising diverse bee communities in a Mediterranean landscape

1. The habitat components determining the structure of bee communities are well known when considering foraging resources; however, there is little data with respect to the role of nesting resources. 2. As a model system this study uses 21 diverse bee communities in a Mediterranean landscape comprising a variety of habitats regenerating after fire. The findings clearly demonstrate that a variety of nesting substrates and nest building materials have key roles in organising the composition of bee communities. 3. The availability of bare ground and potential nesting cavities were the two primary factors influencing the structure of the entire bee community, the composition of guilds, and also the relative abundance of the dominant species. Other nesting resources shown to be important include availability of steep and sloping ground, abundance of plant species providing pithy stems, and the occurrence of pre-existing burrows. 4. Nesting resource availability and guild structure varied markedly across habitats in different stages of post-fire regeneration; however, in all cases, nest sites and nesting resources were important determinants of bee community structure.

Landscape effects on crop pollination services: are there general patterns?

Pollination by bees and other animals increases the size, quality, or stability of harvests for 70% of leading global crops. Because native species pollinate many of these crops effectively, conserving habitats for wild pollinators within agricultural landscapes can help maintain pollination services. Using hierarchical Bayesian techniques, we synthesize the results of 23 studies - representing 16 crops on five continents - to estimate the general relationship between pollination services and distance from natural or semi-natural habitats. We find strong exponential declines in both pollinator richness and native visitation rate. Visitation rate declines more steeply, dropping to half of its maximum at 0.6 km from natural habitat, compared to 1.5 km for richness. Evidence of general decline in fruit and seed set - variables that directly affect yields - is less clear. Visitation rate drops more steeply in tropical compared with temperate regions, and slightly more steeply for social compared with solitary bees. Tropical crops pollinated primarily by social bees may therefore be most susceptible to pollination failure from habitat loss. Quantifying these general relationships can help predict consequences of land use change on pollinator communities and crop productivity, and can inform landscape conservation efforts that balance the needs of native species and people.