2005). Testing for adventitious presence of transgenic material in conventional seed or grain lots using quantitative laboratory methods: statistical procedures and their implementation. AbstractWhen the laboratory methods employed are qualitative, the statistical methodologies used in testing for the adventitious presence (AP) of transgenic material in conventional seed and grain lots are well defined. However, when the response from the method used by the laboratory is quantitative (e.g. percent transgenic DNA), the statistical methodologies developed for qualitative laboratory methods are not fully appropriate. In this paper, we present the details of procedures specific to quantitative laboratory methods. In particular we consider: (1) the assessment of quantitative laboratory method errors using linear modelling; and (2) the process of deciding whether or not a lot meets pre-specified purity standards, including the development of probability calculations needed to develop operating characteristic curves and estimate consumer and producer risks for a given lower quality limit (LQL), acceptable quality limit (AQL) and testing plan. We also describe implementation of this approach in a useful spreadsheet application.

Plant variety protection (PVP), or plant breeders’ rights, provides intellectual property protection (IPP) for cultivars. Technical requirements are distinctness, uniformity, and stable (DUS) reproduction. However, field trials are increasingly resource demanding and potentially inconclusive for soybean (Glycine max [L.] Merr.). Our objective was to establish methodologies using molecular markers to facilitate DUS testing while maintaining current IPP levels. We determined that DNA from 10–15 bulked plants represented cultivar genotype. Single nucleotide polymorphism (SNP) data were highly robust in the face of missing and mistyped data; concordances among five laboratories were >.9888. We used SNP, morphological, physiological, and pedigree information to examine 322 publicly available cultivars including 187 with PVPs. Associations among cultivars following multivariate analyses of genetic distances from SNP data and from pedigree kinship data were very similar. A SNP similarity of 98.6% was the maximum at which cultivars also differed for morphological characteristics. Many (38%) cultivar pairs with members >90% SNP similarity expressed different morphologies with SNP similarities ranging 96–98.6%. Of cultivars <96% SNP similar, only a single pair differed by a single morphological difference; all others differed by more than two morphological characteristics. A SNP similarity of 96% between soybean cultivars represents an initial and conservative point of demarcation between cultivars that have morphological differences and those that do not. Chronological monitoring of pedigree–kinship and SNP similarities showed little evidence that a lack of genetic diversity in F2 breeding populations contributed to challenges in DUS among U.S. soybean cultivars.

Biplots have been widely used in recent years for the analysis of multi‐environment trials through the genotype plus genotype × environment (GGE) biplot analysis or through the additive main effects and multiplicative interaction analysis. Sometimes the environments are structured in blocks of environments, for example, regions or years. In this paper, we propose a new biplot technique for describing genotype × environment interactions that takes into account this additional information. We call it a GGB biplot for genotype plus genotype × block of environments biplot. This biplot has interesting geometrical properties that will be covered in this paper. Similarly to what was done for the GGE biplot (Laffont et al., 2007), we also establish a link between the partitioning of the total sum of squares provided by the GGB biplot and the partitioning provided by the analysis of variance. Simulated and real data are used to illustrate this new biplot.

The genotype + genotype‐by‐environment (GGE) biplot technique has been widely used in the recent years for the analysis of multienvironment trials, as is evident by the large number of articles published where there is a reference to this technique. One question often raised by the users of this technique is how much of genotype and/or genotype‐by‐environment variability is captured by the GGE biplot axes. This article provides an answer to this question by establishing a link between the partitioning of the total sum of squares (TSS) of the genotype‐by‐environment‐centered matrix provided by singular value decomposition and the partitioning of this TSS provided by the analysis of variance technique. An artificial dataset is used to illustrate this link, which is visualized through a mosaic plot. This new GGE biplot interpretation tool is found to be useful and is discussed in contrast with other interpretation tools.

Many seed quality tests are conducted by first randomly assigning seeds into replicates of a given size. The replicate results are then used to check whether or not any problems occur in the realization of the test. The two main tools developed for this verification are the ratio of the observed variance of the replicate results to a theoretical variance and the tolerance for the range of the results. In this paper, we derive the theoretical distribution and its related properties of the sequence of numbers of seeds with a given quality attribute present in the replicates. From these theoretical results, we revisit the two quality checking tools widely used for the germination test. We show a precaution to be taken when relying on the variance ratio to check for under- or over-dispersion of the replicate results. This has led to the development of tables providing credible intervals of the variance ratio. The International Seed Testing Association tolerance tables for the range of the results are also compared with tolerances computed from the exact theoretical distribution of the range, leading us to recommend a revision of these tables.