The role of satellite image-processing for national-scale estimates of gene flow from genetically modified crops: rapeseed in the UK as a model.

1. There is concern over the possibility of unwanted environmental change following transgene movement from genetically modified (GM) rapeseed Brassica napus to its wild and weedy relatives. 2. The aim of this research was to develop a remote sensing-assisted methodology to help quantify gene flow from crops to their wild relatives over wide areas. Emphasis was placed on locating sites of sympatry, where the frequency of gene flow is likely to be highest, and on measuring the size of rapeseed fields to allow spatially explicit modelling of wind-mediated pollen-dispersal patterns. 3. Remote sensing was used as a tool to locate rapeseed fields, and a variety of image-processing techniques was adopted to facilitate the compilation of a spatially explicit profile of sympatry between the crop and Brassica rapa. 4. Classified satellite images containing rapeseed fields were first used to infer the spatial relationship between donor rapeseed fields and recipient riverside B. rapa populations. Such images also have utility for improving the efficiency of ground surveys by identifying probable sites of sympatry. The same data were then also used for the calculation of mean field size. 5. This paper forms a companion paper to Wilkinson et al. (2003), in which these elements were combined to produce a spatially explicit profile of hybrid formation over the UK. The current paper demonstrates the value of remote sensing and image processing for large-scale studies of gene flow, and describes a generic method that could be applied to a variety of crops in many countries. 6. Synthesis and applications. The decision to approve or prevent the release of a GM cultivar is made at a national rather than regional level. It is highly desirable that data relating to the decision-making process are collected at the same scale, rather than relying on extrapolation from smaller experiments designed at the plot, field or even regional scale. It would be extremely difficult and labour intensive to attempt to carry out such large-scale investigations without the use of remote-sensing technology. This study used rapeseed in the UK as a model to demonstrate the value of remote sensing in assembling empirical information at a national level.

The elliptic sine-Gordon equation in a half plane

We consider boundary value problems for the elliptic sine-Gordon equation posed in the half plane y > 0. This problem was considered in Gutshabash and Lipovskii (1994 J. Math. Sci. 68 197–201) using the classical inverse scattering transform approach. Given the limitations of this approach, the results obtained rely on a nonlinear constraint on the spectral data derived heuristically by analogy with the linearized case. We revisit the analysis of such problems using a recent generalization of the inverse scattering transform known as the Fokas method, and show that the nonlinear constraint of Gutshabash and Lipovskii (1994 J. Math. Sci. 68 197–201) is a consequence of the so-called global relation. We also show that this relation implies a stronger constraint on the spectral data, and in particular that no choice of boundary conditions can be associated with a decaying (possibly mod 2π) solution analogous to the pure soliton solutions of the usual, time-dependent sine-Gordon equation. We also briefly indicate how, in contrast to the evolutionary case, the elliptic sine-Gordon equation posed in the half plane does not admit linearisable boundary conditions.

Moving boundary value problems for the wave equation

We study certain boundary value problems for the one-dimensional wave equation posed in a time-dependent domain. The approach we propose is based on a general transform method for solving boundary value problems for integrable nonlinear PDE in two variables, that has been applied extensively to the study of linear parabolic and elliptic equations. Here we analyse the wave equation as a simple illustrative example to discuss the particular features of this method in the context of linear hyperbolic PDEs, which have not been studied before in this framework.

The Klein-Gordon equation in a domain with time-dependent boundary

We solve a Dirichlet boundary value problem for the Klein–Gordon equation posed in a time-dependent domain. Our approach is based on a general transform method for solving boundary value problems for linear and integrable nonlinear PDE in two variables. Our results consist of the inversion formula for a generalized Fourier transform, and of the application of this generalized transform to the solution of the boundary value problem.

The Klein-Gordon equation on the half line: a Riemann-Hilbert approach

We solve an initial-boundary problem for the Klein-Gordon equation on the half line using the Riemann-Hilbert approach to solving linear boundary value problems advocated by Fokas. The approach we present can be also used to solve more complicated boundary value problems for this equation, such as problems posed on time-dependent domains. Furthermore, it can be extended to treat integrable nonlinearisations of the Klein-Gordon equation. In this respect, we briefly discuss how our results could motivate a novel treatment of the sine-Gordon equation.

Spectral analysis of the elliptic sine-Gordon equation in the quarter plane

We study the elliptic sine-Gordon equation in the quarter plane using a spectral transform approach. We determine the Riemann-Hilbert problem associated with well-posed boundary value problems in this domain and use it to derive a formal representation of the solution. Our analysis is based on a generalization of the usual inverse scattering transform recently introduced by Fokas for studying linear elliptic problems.

Initial boundary value problems for the nonlinear Schrödinger equation

A new spectral method for solving initial boundary value problems for linear and integrable nonlinear partial differential equations in two independent variables is applied to the nonlinear Schrödinger equation and to its linearized version in the domain {x≥l(t), t≥0}. We show that there exist two cases: (a) if l″(t)<0, then the solution of the linear or nonlinear equations can be obtained by solving the respective scalar or matrix Riemann-Hilbert problem, which is defined on a time-dependent contour; (b) if l″(t)>0, then the Riemann-Hilbert problem is replaced by a respective scalar or matrix problem on a time-independent domain. In both cases, the solution is expressed in a spectrally decomposed form.

A safety evaluation of genetically modified feedstuffs for livestock production; the fate of transgenic DNA and proteins

dTwo genetic constructs used to confer improved agronomic characteristics, namely herbicide tolerance (HT) in maize and soyabean and insect resistance (Bt) in maize, are considered in respect of feeding to farm livestock, animal performance and the nutritional value and safety of animal products. A review of nucleic acid (DNA) and protein digestion in farm livestock concludes that the frequency of intact transgenic DNA and proteins of GM and non-GM crops being absorbed is minimal/non existent, although there is some evidence of the presence of short fragments of rubisco DNA of non-GM soya in animal tissues. It has been established that feed processing (especially heat) prior to feeding causes significant disruption of plant DNA. Studies with ruminant and non-ruminant farm livestock offered GM feeds demonstrated that animal performance and product composition are unaffected and that there is no evidence of transgenic DNA or proteins of current GM in the products of animals consuming such feeds. On this evidence, current HT and Bt constructs represent no threat to the health of animals, or humans consuming the products of such animals. However as new GM constructs become available it will be necessary to subject these to rigorous evaluation.

Explaining contradictory evidence regarding impacts of genetically modified crops in developing countries. Varietal performance of transgenic cotton in India

A study of the commercial growing of different varieties of Bacillus thuringiensis (Bt) cotton compares the performance of growing official and unofficial hybrid varieties of Bt cotton and conventional (non-Bt) hybrids in Gujarat by 622 farmers. Results suggest that the official Bt varieties (MECH 12 and MECH 162) significantly outperform the unofficial varieties. However, unofficial, locally produced Bt hybrids can also perform significantly better than non-Bt hybrids, although second generation (F-2) Bt seed appears to have no yield advantage compared to non-Bt hybrids but can save on insecticide use. Although hybrid vigour is reduced, or even lost, with F-2 seed the Bt gene still confers some advantage. The F-2 seed is regarded as 'GM' by the farmers (and is sold as such), even though its yield performance is little better than the non-GM hybrids. The results help to explain why there is so much confusion arising from GM cotton release in India.

Farm-level economic performance of genetically modified cotton in Maharashtra, India

A study of the commercial growing of Bacillus flutringiensis (Bt) cotton in India, compares the performance of over 9,000 Bt and non-Bt cotton farm plots in Maharashtra over the 2002 and 2003 seasons. Results show that since their commercial release in 2002, Bt cotton varieties have had a significant positive impact on average yields and on the economic performance of cotton growers. Regional variation showed that, in a very few areas, not all farmers had benefited from increased performance of Bt varieties.

The economic impact of genetically modified cotton on South African smallholders: Yield, profit and health effects

Results of a large-scale survey of resource-poor smallholder cotton farmers in South Africa over three years conclusively show that adopters of Bt cotton have benefited in terms of higher yields, lower pesticide use, less labour for pesticide application and substantially higher gross margins per hectare. These benefits were clearly related to the technology, and not to preferential adoption by farmers who were already highly efficient. The smallest producers are shown to have benefited from adoption of the Bt variety as much as, if not more than, larger producers. Moreover, evidence from hospital records suggests a link between declining pesticide poisonings and adoption of the Bt variety.

Environmental and human health impacts of growing genetically modified herbicide-tolerant sugar beet: a life-cycle assessment

There is ongoing debate concerning the possible environmental and human health impacts of growing genetically modified (GM) crops. Here, we report the results of a life-cycle assessment (LCA) comparing the environmental and human health impacts of conventional sugar beet growing regimes in the UK and Germany with those that might be expected if GM herbicide-tolerant (to glyphosate) sugar beet is commercialized. The results presented for a number of environmental and human health impact categories suggest that growing the GM herbicide-tolerant crop would be less harmful to the environment and human health than growing the conventional crop, largely due to lower emissions from herbicide manufacture, transport and field operations. Emissions contributing to negative environmental impacts, such as global warming, ozone depletion, ecotoxicity of water and acidification and nutrification of soil and water, were much lower for the herbicide-tolerant crop than for the conventional crop. Emissions contributing to summer smog, toxic particulate matter and carcinogenicity, which have negative human health impacts, were also substantially lower for the herbicide-tolerant crop. The environmental and human health impacts of growing GM crops need to be assessed on a case-by-case basis using a holistic approach. LCA is a valuable technique for helping to undertake such assessments.