Three-level main-effects designs exploiting prior information about model uncertainty

To explore the projection efficiency of a design, Tsai, et al [2000. Projective three-level main effects designs robust to model uncertainty. Biometrika 87, 467-475] introduced the Q criterion to compare three-level main-effects designs for quantitative factors that allow the consideration of interactions in addition to main effects. In this paper, we extend their method and focus on the case in which experimenters have some prior knowledge, in advance of running the experiment, about the probabilities of effects being non-negligible. A criterion which incorporates experimenters' prior beliefs about the importance of each effect is introduced to compare orthogonal, or nearly orthogonal, main effects designs with robustness to interactions as a secondary consideration. We show that this criterion, exploiting prior information about model uncertainty, can lead to more appropriate designs reflecting experimenters' prior beliefs. (c) 2006 Elsevier B.V. All rights reserved.

The effects of photoperiod and light spectrum on stock plant growth and rooting of cuttings of Cotinus coggygria 'Royal Purple'

Extending the season of production and improving the scheduling of ornamental crops are key commercial objectives for nurserymen. In some woody species, the period in which cuttings can be rooted successfully is transient, thus limiting the opportunities for scheduled production. Optimum rooting often occurs in early- to mid-summer coinciding with periods of active shoot growth. The relationship between this shoot activity and root initiation was investigated in Cotinus coggygria 'Royal Purple'. Shoot growth on stock plants was manipulated by altering the photoperiod or light quality. Results indicated there were seasonal effects on rooting, but the importance of shoot activity varied with harvest time. Cuttings harvested in August had high rooting percentages, irrespective of photoperiod, and despite shoot growth terminating in response to the short-day treatment. In contrast, by September, rooting percentage was highest in cuttings from plants under long-days, which had maintained greatest shoot growth activity. Cotinus shoots grown in vitro under 16 h days showed reduced shoot growth and increased rooting competence compared with shoots grown under 8 h days. Growing stock plants under polythene films, which altered the amount and quality of the incident light, influenced the rooting of cuttings harvested in August, but no consistent relationship with shoot activity was apparent. From a practical viewpoint, maintaining shoot activity late in the season may prolong the period for propagation by cuttings; but, from a scientific viewpoint, processes associated with an active shoot apex do not provide a complete explanation of seasonal variation in rooting.

Some new three-level orthogonal main effects plans robust to model uncertainty

In this paper, we list some new orthogonal main effects plans for three-level designs for 4, 5 and 6 factors in IS runs and compare them with designs obtained from the existing L-18 orthogonal array. We show that these new designs have better projection properties and can provide better parameter estimates for a range of possible models. Additionally, we study designs in other smaller run-sizes when there are insufficient resources to perform an 18-run experiment. Plans for three-level designs for 4, 5 and 6 factors in 13 to 17 runs axe given. We show that the best designs here are efficient and deserve strong consideration in many practical situations.

Rooting cuttings of Syringa vulgaris cv. Charles Joly and Corylus avellana cv. Aurea: the influence of stock plant pruning and shoot growth

The relationship between shoot growth and rooting was examined in two, 'difficult-to root' amenity trees, Syringa vulgaris L. cv. Charles Joly and Corylus avellana L. cv. Aurea. A range of treatments reflecting severity of pruning was imposed on field-grown stock prior to bud break. To minimise variation due to the numbers of buds that developed under different treatments, bud number was restricted to 30 per plant. Leafy cuttings were harvested at different stages of the active growth phase of each species. With Syringa, rooting decreased with later harvests, but loss of rooting potential was delayed in cuttings collected from the most severe pruning treatment. Rooting potential was associated with the extent of post-excision shoot growth on the cutting but regression analyses indicated that this relationship could not entirely explain the loss of rooting with time, nor the effects due to pruning. Similarly, in Corylus rooting was promoted by severe pruning, but the relationship between apical growth on the cutting and rooting was weaker than in Syringa, and only at the last harvest did growth play a critical role in determining rooting. Another unusual factor of the last harvest of Corylus was a bimodal distribution of roots per cutting, with very few rooted cuttings having less than five roots. This implies that, for this harvest at least, the potential of an individual cutting to root is probably not limited by the number of potential rooting sites.

Farming and food production and development in the Shropshire Hills Environmentally Sensitive Area, 1997-2008

European agricultural and environmental policy has evolved considerably over the last 15 years. In this paper the changes in farm businesses in an Environmentally Sensitive Area in England are evaluated based on two surveys with the same farmers at the start and end of this period. The rate of participation in the environmental scheme had increased significantly at a time when Government led goals in this area had developed and become more output focussed. A combination of policy, market and animal health status changes had encouraged a number to leave cattle production, and though remaining with stock and grass they had decided against any extensive development in the direction of pluriactivity – with or without Government encouragement. This left the future of this group in some uncertainty given that two significant forms of financial support, the environmental scheme and the Hill Farm Allowance, were due to close.

A simple, coherent framework for partitioning uncertainty in climate predictions

A simple and coherent framework for partitioning uncertainty in multi-model climate ensembles is presented. The analysis of variance (ANOVA) is used to decompose a measure of total variation additively into scenario uncertainty, model uncertainty and internal variability. This approach requires fewer assumptions than existing methods and can be easily used to quantify uncertainty related to model-scenario interaction - the contribution to model uncertainty arising from the variation across scenarios of model deviations from the ensemble mean. Uncertainty in global mean surface air temperature is quantified as a function of lead time for a subset of the Coupled Model Intercomparison Project phase 3 ensemble and results largely agree with those published by other authors: scenario uncertainty dominates beyond 2050 and internal variability remains approximately constant over the 21st century. Both elements of model uncertainty, due to scenario-independent and scenario-dependent deviations from the ensemble mean, are found to increase with time. Estimates of model deviations that arise as by-products of the framework reveal significant differences between models that could lead to a deeper understanding of the sources of uncertainty in multi-model ensembles. For example, three models are shown diverging pattern over the 21st century, while another model exhibits an unusually large variation among its scenario-dependent deviations.