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Dive into the research topics where Alice E. Milne is active.

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Featured researches published by Alice E. Milne.


Philosophical Transactions of the Royal Society A | 1996

Symmetries and exact solutions of a (2+1)-dimensional sine-Gordon system

Peter A. Clarkson; Elizabeth L. Mansfield; Alice E. Milne

We investigate the classical and non-classical reductions of the (2 + 1)-dimensional sine-Gordon system of Konopelchenko and Rogers, which is a strong generalization of the sine-Gordon equation. A family of solutions obtained as a non-classical reduction involves a decoupled sum of solutions of a generalized, real, pumped Maxwell-Bloch system. This implies the existence of families of solutions, all occurring as a decoupled sum, expressible in terms of the second, third and fifth Painlevé transcendents, and the sine-Gordon equation. Indeed, hierarchies of such solutions are found, and explicit transformations connecting members of each hierarchy are given. By applying a known Bäcklund transformation for the system to the new solutions found, we obtain further families of exact solutions, including some which are expressed as the argument and modulus of sums of products of Bessel functions with arbitrary coefficients. Finally, we show that the sine-Gordon system satisfies the necessary conditions of the Painlevé PDE test due to Weiss et al which requires the usual test to be modified, and derive a non-isospectral Lax pair for the generalized, real, pumped Maxwell-Bloch system.


Soil Research | 2013

Spectral and wavelet analysis of gilgai patterns from air photography.

Alice E. Milne; R. Webster; R.M. Lark

Gilgais form repeating patterns that seem to be regular to some degree. We have analysed the patterns of gilgais as they appear on aerial photographs of the Bland Plain of New South Wales to discover to what degree they exhibit regularity and to estimate the spatial frequencies of the repeating patterns. We digitised rectangular sections of the photographs to produce grids of pixels at 0.063-mm intervals, equivalent to 1.3 m on the ground, with the optical density of each pixel recorded as a level of grey in the range 0 (black) to 255 (white). From the data we computed autocorrelograms and power spectra in both 1 and 2 dimensions and wavelet coefficients and wavelet packet coefficients and their variances. Spectra of many of the individual rows of the grids contained peaks corresponding to wavelengths of ≈32 m (at Caragabal) and ≈52 m (at Back Creek). The 2-dimensional spectra have rings of relatively large power corresponding to these wavelengths in addition to their central peaks. The 1-dimensional wavelet variances have pronounced peaks at the 16–32 pixel scale, corresponding to 20–40 m on the ground. The 2-dimensional wavelet analyses revealed peaks in the variances in the same range. Back Creek has in addition a low-frequency feature caused by the much darker than average gilgais in one corner of the digitised rectangle, and this is equally evident in the 1-dimensional analyses of rows that cross this corner, where the largest contribution to wavelet packet variation is at wavelength 84–167 m. Where this feature is absent, the best wavelet packet basis indicates that variation at frequencies at or below the repeating pattern is consistent with an underlying stationary random variable, while higher-frequency components show more complex (non-stationary) behaviour. We conclude that the gilgai patterns we have examined have a regularity with wavelengths in the range 30–50 m.


Ecology Letters | 2012

Putting the brakes on a cycle: bottom-up effects damp cycle amplitude

James R. Bell; E. C. Burkness; Alice E. Milne; David W. Onstad; Mark Abrahamson; Krista L. Hamilton; W. D. Hutchison

Pest population density oscillations have a profound effect on agroecosystem functioning, particularly when pests cycle with epidemic persistence. Here, we ask whether landscape-level manipulations can be used to restrict the cycle amplitude of the European corn borer moth [Ostrinia nubilalis (Hübner)], an economically important maize pest. We analysed time series from Minnesota (1963-2009) and Wisconsin (1964-2009) to quantify the extent of regime change in the US Corn Belt where rates of transgenic Bt maize adoption varied. The introduction of Bt maize explained cycle damping when the adoption of the crop was high (Minnesota); oscillations were damped but continued to persist when Bt maize was used less intensely (Wisconsin). We conclude that host plant quality is key to understanding both epidemic persistence and the success of intervention strategies. In particular, the dichotomy in maize management between states is thought to limit the spatial autocorrelation of O. nubilalis.


Journal of Ecology | 2017

Resilience and food security: rethinking an ecological concept

James M. Bullock; Kiran L. Dhanjal‐Adams; Alice E. Milne; Tom H. Oliver; Lindsay C. Todman; Andrew P. Whitmore; Richard F. Pywell

Summary Focusing on food production, in this paper we define resilience in the food security context as maintaining production of sufficient and nutritious food in the face of chronic and acute environmental perturbations. In agri-food systems, resilience is manifest over multiple spatial scales: field, farm, regional and global. Metrics comprise production and nutritional diversity as well as socio-economic stability of food supply. Approaches to enhancing resilience show a progression from more ecologically based methods at small scales to more socially based interventions at larger scales. At the field scale, approaches include the use of mixtures of crop varieties, livestock breeds and forage species, polycultures and boosting ecosystem functions. Stress-tolerant crops, or with greater plasticity, provide technological solutions. At the farm scale, resilience may be conferred by diversifying crops and livestock and by farmers implementing adaptive approaches in response to perturbations. Biodiverse landscapes may enhance resilience, but the evidence is weak. At regional to global scales, resilient food systems will be achieved by coordination and implementation of resilience approaches among farms, advice to farmers and targeted research. Synthesis. Threats to food production are predicted to increase under climate change and land degradation. Holistic responses are needed that integrate across spatial scales. Ecological knowledge is critical, but should be implemented alongside agronomic solutions and socio-economic transformations.


Ecology Letters | 2012

Putting the brakes on a cycle

James R. Bell; E. C. Burkness; Alice E. Milne; David W. Onstad; Mark Abrahamson; Krista L. Hamilton; W. D. Hutchison

Pest population density oscillations have a profound effect on agroecosystem functioning, particularly when pests cycle with epidemic persistence. Here, we ask whether landscape-level manipulations can be used to restrict the cycle amplitude of the European corn borer moth [Ostrinia nubilalis (Hübner)], an economically important maize pest. We analysed time series from Minnesota (1963-2009) and Wisconsin (1964-2009) to quantify the extent of regime change in the US Corn Belt where rates of transgenic Bt maize adoption varied. The introduction of Bt maize explained cycle damping when the adoption of the crop was high (Minnesota); oscillations were damped but continued to persist when Bt maize was used less intensely (Wisconsin). We conclude that host plant quality is key to understanding both epidemic persistence and the success of intervention strategies. In particular, the dichotomy in maize management between states is thought to limit the spatial autocorrelation of O. nubilalis.


PLOS Computational Biology | 2015

The Effect of Farmers’ Decisions on Pest Control with Bt Crops: A Billion Dollar Game of Strategy

Alice E. Milne; James R. Bell; W. D. Hutchison; Frank van den Bosch; Paul D. Mitchell; David W. Crowder; Stephen Parnell; Andrew P. Whitmore

A farmer’s decision on whether to control a pest is usually based on the perceived threat of the pest locally and the guidance of commercial advisors. Therefore, farmers in a region are often influenced by similar circumstances, and this can create a coordinated response for pest control that is effective at a landscape scale. This coordinated response is not intentional, but is an emergent property of the system. We propose a framework for understanding the intrinsic feedback mechanisms between the actions of humans and the dynamics of pest populations and demonstrate this framework using the European corn borer, a serious pest in maize crops. We link a model of the European corn borer and a parasite in a landscape with a model that simulates the decisions of individual farmers on what type of maize to grow. Farmers chose whether to grow Bt-maize, which is toxic to the corn borer, or conventional maize for which the seed is cheaper. The problem is akin to the snow-drift problem in game theory; that is to say, if enough farmers choose to grow Bt maize then because the pest is suppressed an individual may benefit from growing conventional maize. We show that the communication network between farmers’ and their perceptions of profit and loss affects landscape scale patterns in pest dynamics. We found that although adoption of Bt maize often brings increased financial returns, these rewards oscillate in response to the prevalence of pests.


Journal of Physics A | 1996

ALGORITHMS FOR SPECIAL INTEGRALS OF ORDINARY DIFFERENTIAL EQUATIONS

David W. Albrecht; Elizabeth L. Mansfield; Alice E. Milne

We give new, conceptually simple procedures for calculating special integrals of polynomial type (also known as Darboux polynomials, algebraic invariant curves, or eigenpolynomials), for ordinary differential equations. In principle, the method requires only that the given ordinary differential equation be itself of polynomial type of degree one and any order. The method is algorithmic, is suited to the use of computer algebra, and does not involve solving large nonlinear algebraic systems. To illustrate the method, special integrals of the second, fourth and sixth Painleve equations, and a third-order ordinary differential equation of Painleve type are investigated. We prove that for the second Painleve equation, the known special integrals are the only ones possible.


Weed Research | 2016

Designing a sampling scheme to reveal correlations between weeds and soil properties at multiple spatial scales

Helen Metcalfe; Alice E. Milne; R. Webster; R.M. Lark; A. J. Murdoch; Jonathan Storkey

Summary Weeds tend to aggregate in patches within fields, and there is evidence that this is partly owing to variation in soil properties. Because the processes driving soil heterogeneity operate at various scales, the strength of the relations between soil properties and weed density would also be expected to be scale‐dependent. Quantifying these effects of scale on weed patch dynamics is essential to guide the design of discrete sampling protocols for mapping weed distribution. We developed a general method that uses novel within‐field nested sampling and residual maximum‐likelihood (reml) estimation to explore scale‐dependent relations between weeds and soil properties. We validated the method using a case study of Alopecurus myosuroides in winter wheat. Using reml, we partitioned the variance and covariance into scale‐specific components and estimated the correlations between the weed counts and soil properties at each scale. We used variograms to quantify the spatial structure in the data and to map variables by kriging. Our methodology successfully captured the effect of scale on a number of edaphic drivers of weed patchiness. The overall Pearson correlations between A. myosuroides and soil organic matter and clay content were weak and masked the stronger correlations at >50 m. Knowing how the variance was partitioned across the spatial scales, we optimised the sampling design to focus sampling effort at those scales that contributed most to the total variance. The methods have the potential to guide patch spraying of weeds by identifying areas of the field that are vulnerable to weed establishment.


The Journal of Agricultural Science | 2015

Exploring the spatial variation in the fertilizer-nitrogen requirement of wheat within fields

Daniel Kindred; Alice E. Milne; R. Webster; B.P. Marchant; R. Sylvester-Bradley

The fertilizer-nitrogen (N) requirement for wheat grown in the UK varies from field to field. Differences in the soil type, climate and cropping history result in differences in (i) the crops’ demands for N, (ii) the supply of N from the soil (SNS) and (iii) the recovery of the fertilizer by the crops. These three components generally form the basis of systems for N recommendation. Three field experiments were set out to investigate the variation of the N requirement for wheat within fields and to explore the importance of variation in the crops’ demands for N, SNS and fertilizer recovery in explaining the differences in the economic optima for N. The N optima were found to vary by >100 kg N/ha at two of the sites. At the other site, the yield response to N was small. Yields at the optimum rate of N varied spatially by c. 4 t/ha at each site. Soil N supply, which was estimated by the unfertilized crops’ harvested N, varied spatially by 120, 75 and 60 kg/ha in the three experiments. Fertilizer recovery varied spatially from 30% to >100% at each of the sites. There were clear relationships between the SNS and the N optima at all the three sites. The expected relationship between the crops demand for N and N optima was evident at only one of the three sites. There was no consistent relationship between the N recovery and the N optima. A consistent relationship emerged, however, between the optimal yield and SNS; areas with a greater yield potential tending to also supply more N from the soil. This moderated the expected effect of the SNS and the crops demand for N on the N optima.


Science of The Total Environment | 2017

The landscape model: a model for exploring trade-offs between agricultural production and the environment

K. Coleman; Shibu E. Muhammed; Alice E. Milne; Lindsay C. Todman; A. Gordon Dailey; Margaret J. Glendining; Andrew P. Whitmore

We describe a model framework that simulates spatial and temporal interactions in agricultural landscapes and that can be used to explore trade-offs between production and environment so helping to determine solutions to the problems of sustainable food production. Here we focus on models of agricultural production, water movement and nutrient flow in a landscape. We validate these models against data from two long-term experiments, (the first a continuous wheat experiment and the other a permanent grass-land experiment) and an experiment where water and nutrient flow are measured from isolated catchments. The model simulated wheat yield (RMSE 20.3–28.6%), grain N (RMSE 21.3–42.5%) and P (RMSE 20.2–29% excluding the nil N plots), and total soil organic carbon particularly well (RMSE 3.1 − 13.8 %), the simulations of water flow were also reasonable (RMSE 180.36 and 226.02%). We illustrate the use of our model framework to explore trade-offs between production and nutrient losses.

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R.M. Lark

British Geological Survey

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