Johannes Forkman

Estimator and Tests for Common Coefficients of Variation in Normal Distributions

Inference for the coefficient of variation in normal distributions is considered. An explicit estimator of a coefficient of variation that is shared by several populations with normal distributions is proposed. Methods for making confidence intervals and statistical tests, based on McKays approximation for the coefficient of variation, are provided. Exact expressions for the first two moments of McKays approximation are given. An approximate F-test for equality of a coefficient of variation that is shared by several normal distributions and a coefficient of variation that is shared by several other normal distributions is introduced.

Parametric bootstrap methods for testing multiplicative terms in GGE and AMMI models.

The genotype main effects and genotype-by-environment interaction effects (GGE) model and the additive main effects and multiplicative interaction (AMMI) model are two common models for analysis of genotype-by-environment data. These models are frequently used by agronomists, plant breeders, geneticists and statisticians for analysis of multi-environment trials. In such trials, a set of genotypes, for example, crop cultivars, are compared across a range of environments, for example, locations. The GGE and AMMI models use singular value decomposition to partition genotype-by-environment interaction into an ordered sum of multiplicative terms. This article deals with the problem of testing the significance of these multiplicative terms in order to decide how many terms to retain in the final model. We propose parametric bootstrap methods for this problem. Models with fixed main effects, fixed multiplicative terms and random normally distributed errors are considered. Two methods are derived: a full and a simple parametric bootstrap method. These are compared with the alternatives of using approximate F-tests and cross-validation. In a simulation study based on four multi-environment trials, both bootstrap methods performed well with regard to Type I error rate and power. The simple parametric bootstrap method is particularly easy to use, since it only involves repeated sampling of standard normally distributed values. This method is recommended for selecting the number of multiplicative terms in GGE and AMMI models. The proposed methods can also be used for testing components in principal component analysis.

Regeneration capacity from buds on roots and rhizomes in five herbaceous perennials as affected by time of fragmentation.

Variation in seasonal sprouting pattern from roots and rhizomes of perennial herbaceous plants influence the success of plant proliferation ability, invasiveness and escape from weed control measures. The latter often rely on methods, which repeatedly fragment the underground system, thereby trigger adventitious and axillary buds to sprout, and consequently reduce the amount of stored energy. If carried out at times when no re-growth occurs, treatments will have little effect on weed populations, but cost much in terms of labour and energy. The purpose of this experiment was to determine the seasonal variation in bud sprouting capacity after fragmentation. Five troublesome perennial weed species, collected in northern and southern Sweden, were grown outdoors in Uppsala, Sweden (N 59°49′, E 17°39′), from May 2009 to January 2010. Cut root and rhizome fragments, taken at two weeks intervals from July to January, were used to evaluate bud sprouting capacity, which was statistically analyzed using generalized additive models. In Elytrigia repens from southern Sweden and Sonchus arvensis sprouting capacity was significantly impaired during a period from September to November. In Equisetum arvense and Tussilago farfara sprouting was low between July and November where after it increased. In contrast, Cirsium arvense and E. repens from northern Sweden sprouted readily throughout the period. Except for E. repens, a model by populations was significantly better than one based on latitudinal origin. The result suggests a species-specific timing of treatments in weed management, avoiding the non-effective autumn period for E. arvense, S. arvensis and T. farfara, and in some cases in E. repens.

Performance of empirical BLUP and Bayesian prediction in small randomized complete block experiments

The model for analysis of randomized complete block (RCB) experiments usually includes two factors: block and treatment. If treatment is modelled as fixed, best linear unbiased estimation (BLUE) is used, and treatment means estimate expected means. If treatment is modelled as random, best linear unbiased prediction (BLUP) shrinks the treatment means towards the overall mean, which results in smaller root-mean-square error (RMSE) in prediction of means. This theoretical result holds provided the variance components are known, but in practice the variance components are estimated. BLUP using estimated variance components is called empirical best linear unbiased prediction (EBLUP). In small experiments, estimates can be unreliable and the usefulness of EBLUP is uncertain. The present paper investigates, through simulation, the performance of EBLUP in small RCB experiments with normally as well as non-normally distributed random effects. The methods of Satterthwaite (1946) and of Kenward & Roger (1997, 2009), as implemented in the SAS System, were studied. Performance was measured by RMSE, in prediction of means, and coverage of prediction intervals. In addition, a Bayesian approach was used for prediction of treatment differences and computation of credible intervals. EBLUP performed better than BLUE with regard to RMSE, also when the number of treatments was small and when the treatment effects were non-normally distributed. The methods of Satterthwaite and of Kenward & Roger usually produced approximately correct coverage of prediction intervals. The Bayesian method gave the smallest RMSE and usually more accurate coverage of intervals than the other methods.

A Method for Designing Nonlinear Univariate Calibration

A method is proposed for designing nonlinear univariate calibration of measuring instruments. The problem addressed is how to select a set of design points (standards or calibrators) to minimize the errors in the inverse predictions. The curve parameters are assumed to vary randomly between calibrations, with known expected value and known covariance matrix. A design criterion is suggested for analytical procedures, according to which the coefficient of variation and the area under the precision profile are minimized.

Radiation-use efficiency in leys: influences of growth period and clover proportion

Abstract Acquisition of carbohydrates and their partitioning to storage organs are decisive attributes for the persistence of perennial leys. It was therefore of interest to analyse radiation-use efficiency (RUE) and root allocation (br) in one-, two-, and three-year-old red clover–grass leys as functions of growth period (first and second growth, ley age), proportion of clover, and site properties (location, soil type, humus content). By calibrating RUE and br, the ley yields simulated with a growth model were adjusted to the values observed during two consecutive years at 33 organic farms located in the southern and the northwestern coastal regions of Finland. Driving variables of the simulations were daily measurements of weather. RUE declined from the first to the second growth and further with ley age, while its variability increased. The value of br decreased from the first to the second growth, and was positively correlated with RUE. The high variability of RUE between different sites, and the absence of correlations between site properties and RUE, were mainly attributable to differences in overwintering and regrowth conditions. Early measurements of above-ground biomass subsequent to overwintering and cutting, and the inclusion of site-specific measurements of soil properties would have increased the general validity of the calibrated parameter values. RUE correlated positively with proportion of clover. However, the increase of the proportion of clover from the first to the second growth was not strong enough to balance the concurrent decline of RUE. With increasing ley age there were two concurrent and reinforcing patterns, namely a decrease in proportion of clover and in RUE. Thus, both symbiotic N fixation and vigour of perennial red clover–grass leys declined with ley age. With regards to RUE, however, three-year-old leys were still productive.

Population dynamics and nitrogen allocation of Sonchus arvensis L. in relation to initial root size

To develop better mechanical management strategies, more information on the impact of root partitioning on changes in the population dynamics of Sonchus arvensis is needed. Therefore, the effects of root fragmentation of S. arvensis on shoot height frequency distributions, biomass production and nitrogen allocation were studied in an outdoor experiment in Sweden in 2008. Three artificial populations of S. arvensis of different initial root lengths but with the same total root length per area were planted. Shoot heights were measured at the onset of flowering and dry weight and nitrogen content of leaves, stems, buds and roots were quantified twice during the season. Height frequency distributions of the populations were bimodal, indicating the existence of two generations distinctly different in height growth pattern. Shorter root fragments produced shoots with a lower mean height compared to longer fragments. Plants originating from longer root fragments had higher dry weight and more nitrogen compared to plants from shorter root fragments. Dry matter production per square meter did not differ between the populations. The proportion of dry matter and nitrogen allocated to the different plant components (leaves, stems, buds and roots) at harvest did not differ between the populations. Over time, nitrogen was reallocated from leaves and stems to roots. Our results show that initial root length of S. arvensis per square meter, rather than the number of root fragments per square meter, is a good predictor of biomass at harvest, and that the degree of root fragmentation does not affect nitrogen allocation patterns. Root fragmentation, however, leads to a lower average canopy height for S. arvensis, and thus may be an effective weed control measure in combination with a crop which is competitive for light.

The use of a reference variety for comparisons in incomplete series of crop variety trials

In a series of crop variety trials, ‘test varieties’ are compared with one another and with a ‘reference’ variety that is included in all trials. The series is typically analyzed with a linear mixed model and the method of generalized least squares. Usually, the estimates of the expected differences between the test varieties and the reference variety are presented. When the series is incomplete, i.e. when all test varieties were not included in all trials, the method of generalized least squares may give estimates of expected differences to the reference variety that do not appear to accord with observed differences. The present paper draws attention to this phenomenon and explores the recurrent idea of comparing test varieties indirectly through the use of the reference. A new ‘reference treatment method’ was specified and compared with the method of generalized least squares when applied to a five-year series of 85 spring wheat trials. The reference treatment method provided estimates of differences to the reference variety that agreed with observed differences, but was considerably less efficient than the method of generalized least squares.

Effect of region on the uncertainty in crop variety trial programs with a reduced number of trials

Results from crop variety trials may vary between geographical regions because of differences in climate and soil types. Results are usually presented at regional level. To evaluate the importance of the regions used in the Swedish variety trial programs, we examined which regions produced similar levels of yield and similar ratios in yield between cultivars; the amount by which variance could be reduced by division into regions or clusters of regions; and the amount of trials per region and year, replicates per trial, and trials per year required in order to fulfill specifications on the precision of results. Yield data from spring barley and winter wheat trials performed during 1997–2006 were studied using cluster analysis and variance component estimation. The objectives were (1) to discuss the effects of regions on precision when the number of trials has decreased; (2) to demonstrate the method; and (3) to report the results obtained. In spring barley, clusters of regions produced different levels of yield, but similar yield ratios between cultivars. In winter wheat, clusters of regions giving different yield ratios were identified. When the option of a single analysis was compared with that of region-wise analysis, the reduction in variance with the former, due to the larger number of trials, outweighed the reduction in variance with the latter due to decreased random interaction between trials and cultivars.

Effects of root fragmentation on generative reproduction of Sonchus arvensis

ABSTRACT To develop better mechanical management strategies, more information on the impact of root partitioning on generative reproduction of Sonchus arvensis L. is needed. Therefore, an outdoor experiment was performed in Sweden in 2008, to evaluate the effect of root fragmentation on generative reproduction of S. arvensis. Two artificial populations of S. arvensis with the same total root length per area but with different initial root lengths and different numbers of root fragments were planted. Cumulative numbers of flower receptacles which had shed mature seeds over the season were assessed. Changes in the number of seeds per flower receptacle and average seed weight were monitored over time during the late season. Plants from long root fragments produced more flower receptacles than plants from short ones. Per area, however, the number of mature flower receptacles did not differ. The number of seeds per flower receptacle and individual seed weight were not affected by initial root length for the first cohort of shoots which sprouted from the initially planted roots. A second cohort, from roots produced during the season, resulted, irrespective of its initial root length, in fewer flower receptacles per plant and per area, with less seeds per receptacle, but with the same average seed weight as the first cohort. The number of seeds per flower receptacle was higher in mid-September than earlier or later. Average seed weight slightly decreased over time. The weight of seeds produced in early September was inversely related to the number of seeds per receptacle, but this trade-off disappeared over time. Root fragmentation alone in pure populations of S. arvensis does not impede generative reproduction, but is likely to decrease input of seeds to the seed bank, when combined with crop competition.