Shadow lines in the arithmetic of elliptic curves

Let E/Q be an elliptic curve and p a rational prime of good ordinary reduction. For every imaginary quadratic field K/Q satisfying the Heegner hypothesis for E we have a corresponding line in E(K)\otimes Q_p, known as a shadow line. When E/Q has analytic rank 2 and E/K has analytic rank 3, shadow lines are expected to lie in E(Q)\otimes Qp. If, in addition, p splits in K/Q, then shadow lines can be determined using the anticyclotomic p-adic height pairing. We develop an algorithm to compute anticyclotomic p-adic heights which we then use to provide an algorithm to compute shadow lines. We conclude by illustrating these algorithms in a collection of examples.

High-throughput phenotyping (HTP) identifies seedling root traits linked to variation in seed yield and nutrient capture in field-grown oilseed rape (Brassica napusL.)

Background and Aims Root traits can be selected for crop improvement. Techniques such as soil excavations can be used to screen root traits in the field, but are limited to genotypes that are well-adapted to field conditions. The aim of this study was to compare a low-cost, high-throughput root phenotyping (HTP) technique in a controlled environment with field performance, using oilseed rape (OSR; Brassica napus) varieties. Methods Primary root length (PRL), lateral root length and lateral root density (LRD) were measured on 14-d-old seedlings of elite OSR varieties (n = 32) using a ‘pouch and wick’ HTP system (∼40 replicates). Six field experiments were conducted using the same varieties at two UK sites each year for 3 years. Plants were excavated at the 6- to 8-leaf stage for general vigour assessments of roots and shoots in all six experiments, and final seed yield was determined. Leaves were sampled for mineral composition from one of the field experiments. Key Results Seedling PRL in the HTP system correlated with seed yield in four out of six (r = 0·50, 0·50, 0·33, 0·49; P < 0·05) and with emergence in three out of five (r = 0·59, 0·22, 0·49; P < 0·05) field experiments. Seedling LRD correlated positively with leaf concentrations of some minerals, e.g. calcium (r = 0·46; P < 0·01) and zinc (r = 0·58; P < 0·001), but did not correlate with emergence, general early vigour or yield in the field. Conclusions Associations between PRL and field performance are generally related to early vigour. These root traits might therefore be of limited additional selection value, given that vigour can be measured easily on shoots/canopies. In contrast, LRD cannot be assessed easily in the field and, if LRD can improve nutrient uptake, then it may be possible to use HTP systems to screen this trait in both elite and more genetically diverse, non-field-adapted OSR.

The influence of different artificial soil types on the acute toxicity of carbendazim to the earthworm Eisenia fetida in laboratory toxicity tests

Field populations of earthworms have shown a varied response in mortality to the fungicide carbendazim, the toxic reference substance used in agrochemical field trials. The aim of this study was to determine the influence of soil conditions as a potential cause of this variation. Laboratory acute toxicity tests were conducted using a range of artificial soils with varying soil components (organic matter, clay, pH and moisture). Batch adsorption/desorption studies were run to determine the influence of the soil properties on carbendazim behaviour. Adsorption was shown to be correlated with organic matter content and pH and this in turn could be linked to Eisenia fetida mortality, with lower mortality occurring with increased adsorption. Overall while E.fetida mortality did vary significantly between several of the soils the calculated LC50 values in the different soils did not cover a wide range (6.04-16.00 mg kg(-1)), showing that under these laboratory conditions soil components did not greatly influence carbendazim toxicity to E.fietida. (c) 2007 Elsevier Masson SAS. All rights reserved.

Poor survival on an artificial diet of two genotypes of the aphid Myzus persicae: a fitness cost of insecticide resistance?

A fully susceptible genotype (4106A) of Myzus persicae survived the longest on an artificial diet and, in several of the eight replicates, monitoring was terminated when the culture was still thriving. A genotype with elevated carboxylesterase FE4 at the R3 level (800F) had a mean survival of only 98.13 days, whereas 794J, which combines R3 E4 carboxylesterase with target-site resistance (knockdown resistance), survived for the even shorter mean time of 84.38 days. The poorer survival of the two genotypes with extremely elevated carboxylesterase-resistance was not the result of a reluctance to transfer to new diet at each diet change. Although available for only two replicates, a revertant clone of 794J (794Jrev), which has the same genotype as 794J but the amplified E4 genes are not expressed leading to a fully susceptible phenotype, did not appear to survive any better than this clone. This suggests that the poor survival on an artificial diet of the extreme-carboxylesterase genotypes is not the result of the cost of over-producing the enzyme. The frequency of insecticide-resistant genotypes is low in the population until insecticide is applied, indicating that they have reduced fitness, although this does not necessarily reflect a direct cost of expressing the resistance mechanism.

Moderating mycorrhizas: arbuscular mycorrhizas modify rhizosphere chemistry and maintain plant phosphorus status within narrow boundaries

Pastures often experience a pulse of phosphorus (P) when fertilized. We examined the role of arbuscular mycorrhizal fungi (AMF) in the uptake of P from a pulse. Five legumes (Kennedia prostrata, Cullen australasicum, Bituminaria bituminosa, Medicago sativa and Trifolium subterraneum) were grown in a moderate P, sterilized field soil, either with (+AMF) or without (−AMF) addition of unsterilized field soil. After 9–10 weeks, half the pots received 15 mg P kg−1 of soil. One week later, we measured: shoot and root dry weights; percentage of root length colonized by AMF; plant P, nitrogen and manganese (Mn) concentrations; and rhizosphere carboxylates, pH and plant-available P. The P pulse raised root P concentration by a similar amount in uncolonized and colonized plants, but shoot P concentration increased by 143% in uncolonized plants and 53% in colonized plants. Inoculation with AMF decreased the amount of rhizosphere carboxylates by 52%, raised rhizosphere pH by ∼0.2–0.7 pH units and lowered shoot Mn concentration by 38%. We conclude that AMF are not simply a means for plants to enhance P uptake when P is limiting, but also act to maintain shoot P within narrow boundaries and can affect nutrient uptake through their influence on rhizosphere chemistry.

A calibrated, non-invasive method for measuring the internal interface height field at high resolution in the rotating, two-layer annulus

We describe a remote sensing method for measuring the internal interface height field in a rotating, two-layer annulus laboratory experiment. The method is non-invasive, avoiding the possibility of an interaction between the flow and the measurement device. The height fields retrieved are accurate and highly resolved in both space and time. The technique is based on a flow visualization method developed by previous workers, and relies upon the optical rotation properties of the working liquids. The previous methods returned only qualitative interface maps, however. In the present study, a technique is developed for deriving quantitative maps by calibrating height against the colour fields registered by a camera which views the flow from above. We use a layer-wise torque balance analysis to determine the equilibrium interface height field analytically, in order to derive the calibration curves. With the current system, viewing an annulus of outer radius 125 mm and depth 250 mm from a distance of 2 m, the inferred height fields have horizontal, vertical and temporal resolutions of up to 0.2 mm, 1 mm and 0.04 s, respectively.

Field trials to assess the uptake of arsenic by vegetables from contaminated soils and soil remediation with iron oxides

The uptake of arsenic (As) by plants from contaminated soils presents a health hazard that may affect the use of agricultural and former industrial land. Methods for limiting the hazard are desirable. A proposed remediation treatment comprises the precipitation of iron (Fe) oxides in the contaminated soil by adding ferrous sulfate and lime. The effects on As bioavailability were assessed using a range of vegetable crops grown in the field. Four UK locations were used, where soil was contaminated by As from different sources. At the most contaminated site, a clay loam containing a mean of 748 mg As kg(-1) soil, beetroot, calabrese, cauliflower, lettuce, potato, radish and spinach were grown. For all crops except spinach, ferrous sulfate treatment caused a significant reduction in the bioavailability of As in some part of the crop. Application of ferrous sulfate in solution, providing 0.2% Fe oxides in the soil (0-10 cm), reduced As uptake by a mean of 22%. Solid ferrous sulfate was applied to give concentrations of 0.5% and 1% Fe oxides: the 0.5% concentration reduced As uptake by a mean of 32% and the 1% concentration gave no significant additional benefit. On a sandy loam containing 65 mg As kg(-1) soil, there was tentative evidence that ferrous sulfate treatment up to 2% Fe oxides caused a significant reduction in lettuce As, but calabrese did not respond. At the other two sites, the effects of ferrous sulfate treatment were not significant, but the uptake of soil As was low in treated and untreated soils. Differences between sites in the bioavailable fraction of soil As may be related to the soil texture or the source of As. The highest bioavailability was found on the soil which had been contaminated by aerial deposition and had a high sand content. (C) 2003 Elsevier Science B.V. All rights reserved.

Response of organically managed grassland to available phosphorus and potassium in the soil and supplementary fertilization: field trials using grass-clover leys cut for silage

Effective use and recycling of manures together with occasional and judicious use of supplementary fertilizing materials forms the basis for management of phosphorus (P) and potassium (K) within organic farming systems. Replicated field trials were established at three sites across the UK to compare the supply of P and K to grass-clover swards cut for silage from a range of fertilizing materials, and to assess the usefulness of routine soil tests for P and K in organic farming systems. None of the fertilizing materials (farmyard manure, rock phosphate, Kali vinasse, volcanic tuff) significantly increased silage yields, nor was P offtake increased. However, farmyard manure and Kali vinasse proved effective sources of K to grass and clover in the short to medium term. Available P (measured as Olsen-P) showed no clear relationship with crop P offtake in these trials. In contrast, available K (measured by ammonium nitrate extraction) proved a useful measurement to predict K availability to crops and support K management decisions.

Effects of manure and fertilizer on grain yield, soil carbon and phosphorus in a 13-year field trial in semi-arid Kenya

Long-term indicators of soil fertility were assessed by measuring grain yield, soil organic carbon (SOC) and soil Olsen phosphorous for a P-deficient soil. In one set of treatments, goat manure was applied annually for 13 years at 0, 5 and 10 t ha(-1), and intercrops of sorghum/cowpea, millet/green gram and maize/pigeonpea were grown. Yield depended on rainfall and trends with time were not identifiable. Manure caused an upward trend in SOC, but 10 t ha(-1) manure did not give significantly more SOC than 5 t ha(-1). Only 10 t ha(-1) manure increased Olsen P. Measurements of both SOC and Olsen P are recommended. In another set of treatments, manure was applied for four years; the residual effect lasted another seven to eight years when assessed by yield, SOC and Olsen P Treatment with mineral fertilizers provided the same rates of N and P as 5 t hat manure and yields from manure and fertilizer were similar. Fertilizer increased Olsen P but not SOC. Management systems with occasional manure application and intermediate fertilizer applications should be assessed. Inputs and offtakes of C, N and P were measured for three years. Approximately 16, 25 and 11% of C, N and P respectively were stabilized into soil organic matter from 5 t ha(-1) a(-1) manure. The majority of organic P was fixed as soil inorganic P.