Some vocabulary and grammar for the analysis of multi-environment trials, as applied to the analysis of FPB and PPB trials

For the improvement of genetic material suitable for on farm use under low-input conditions, participatory and formal plant breeding strategies are frequently presented as competing options. A common frame of reference to phrase mechanisms and purposes related to breeding strategies will facilitate clearer descriptions of similarities and differences between participatory plant breeding and formal plant breeding. In this paper an attempt is made to develop such a common framework by means of a statistically inspired language that acknowledges the importance of both on farm trials and research centre trials as sources of information for on farm genetic improvement. Key concepts are the genetic correlation between environments, and the heterogeneity of phenotypic and genetic variance over environments. Classic selection response theory is taken as the starting point for the comparison of selection trials (on farm and research centre) with respect to the expected genetic improvement in a target environment (low-input farms). The variance-covariance parameters that form the input for selection response comparisons traditionally come from a mixed model fit to multi-environment trial data. In this paper we propose a recently developed class of mixed models, namely multiplicative mixed models, also called factor-analytic models, for modelling genetic variances and covariances (correlations). Mixed multiplicative models allow genetic variances and covariances to be dependent on quantitative descriptors of the environment, and confer a high flexibility in the choice of variance-covariance structure, without requiring the estimation of a prohibitively high number of parameters. As a result detailed considerations regarding selection response comparisons are facilitated. ne statistical machinery involved is illustrated on an example data set consisting of barley trials from the International Center for Agricultural Research in the Dry Areas (ICARDA). Analysis of the example data showed that participatory plant breeding and formal plant breeding are better interpreted as providing complementary rather than competing information.

Modern scientific methods and their potential in wastewater science and technology

Application of novel analytical and investigative methods such as fluorescence in situ hybridization, confocal laser scanning microscopy (CLSM), microelectrodes and advanced numerical simulation has led to new insights into micro-and macroscopic processes in bioreactors. However, the question is still open whether or not these new findings and the subsequent gain of knowledge are of significant practical relevance and if so, where and how. To find suitable answers it is necessary for engineers to know what can be expected by applying these modern analytical tools. Similarly, scientists could benefit significantly from an intensive dialogue with engineers in order to find out about practical problems and conditions existing in wastewater treatment systems. In this paper, an attempt is made to help bridge the gap between science and engineering in biological wastewater treatment. We provide an overview of recently developed methods in microbiology and in mathematical modeling and numerical simulation. A questionnaire is presented which may help generate a platform from which further technical and scientific developments can be accomplished. Both the paper and the questionnaire are aimed at encouraging scientists and engineers to enter into an intensive, mutually beneficial dialogue. (C) 2002 Elsevier Science Ltd. All rights reserved.

Steiner trades that give rise to completely decomposable latin interchanges

In this paper we focus on the representation of Steiner trades of volume less than or equal to nine and identify those for which the associated partial latin square can be decomposed into six disjoint latin interchanges.

On the Hamilton-Waterloo problem

The Hamilton-Waterloo problem asks for a 2-factorisation of K-v in which r of the 2-factors consist of cycles of lengths a(1), a(2),..., a(1) and the remaining s 2-factors consist of cycles of lengths b(1), b(2),..., b(u) (where necessarily Sigma(i)(=1)(t) a(i) = Sigma(j)(=1)(u) b(j) = v). In thus paper we consider the Hamilton-Waterloo problem in the case a(i) = m, 1 less than or equal to i less than or equal to t and b(j) = n, 1 less than or equal to j less than or equal to u. We obtain some general constructions, and apply these to obtain results for (m, n) is an element of {(4, 6)1(4, 8), (4, 16), (8, 16), (3, 5), (3, 15), (5, 15)}.

The three-way intersection problem for latin squares

The set of integers k for which there exist three latin squares of order n having precisely k cells identical, with their remaining n(2) - k cells different in all three latin squares, denoted by I-3[n], is determined here for all orders n. In particular, it is shown that I-3[n] = {0,...,n(2) - 15} {n(2) - 12,n(2) - 9,n(2)} for n greater than or equal to 8. (C) 2002 Elsevier Science B.V. All rights reserved.

The metamorphosis of lambda-fold K-3,K-3-designs into lambda-fold 6-cycle systems

In this paper necessary and sufficient conditions are given for the metamorphosis of a lambda-fold K-3,K-3-design of order n into a lambda-fold 6-cycle system of order n, by retaining one 6-cycle subgraph from each copy of K-3,K-3, and then rearranging the set of all the remaining edges, three from each K-3,K-3, into further 6-cycles so that the result is a lambda-fold 6-cycle system.

Trade spectra of complete partite graphs

The trade spectrum of a graph G is essentially the set of all integers t for which there is a graph H whose edges can be partitioned into t copies of G in two entirely different ways. In this paper we determine the trade spectrum of complete partite graphs, in all but a few cases.