Abstract. For the foreseeable future, plant breeding methodology will continue to unfold as a practical application of the scaling of quantitative biology. These efforts to increase the effective scale of breeding programs will focus on the immediate and long-term needs of society. The foundations of the quantitative dimension will be integration of quantitative genetics, statistics, gene-to-phenotype knowledge of traits embedded within crop growth and development models. The integration will be enabled by advances in quantitative genetics methodology and computer simulation. The foundations of the biology dimension will be integrated experimental and functional gene-to-phenotype modelling approaches that advance our understanding of functional germplasm diversity, and gene-to-phenotype trait relationships for the native and transgenic variation utilised in agricultural crops. The trait genetic knowledge created will span scales of biology, extending from molecular genetics to multi-trait phenotypes embedded within evolving genotype-environment systems. The outcomes sought and successes achieved by plant breeding will be measured in terms of sustainable improvements in agricultural production of food, feed, fibre, biofuels and other desirable plant products that meet the needs of society. In this review, examples will be drawn primarily from our experience gained through commercial maize breeding. Implications for other crops, in both the private and public sectors, will be discussed.

Complex quantitative traits of plants as measured on collections of genotypes across multiple environments are the outcome of processes that depend in intricate ways on genotype and environment simultaneously. For a better understanding of the genetic architecture of such traits as observed across environments, genotype-by-environment interaction should be modeled with statistical models that use explicit information on genotypes and environments. The modeling approach we propose explains genotype-by-environment interaction by differential quantitative trait locus (QTL) expression in relation to environmental variables. We analyzed grain yield and grain moisture for an experimental data set composed of 976 F 5 maize testcross progenies evaluated across 12 environments in the U.S. corn belt during 1994 and 1995. The strategy we used was based on mixed models and started with a phenotypic analysis of multienvironment data, modeling genotype-by-environment interactions and associated genetic correlations between environments, while taking into account intraenvironmental error structures. The phenotypic mixed models were then extended to QTL models via the incorporation of marker information as genotypic covariables. A majority of the detected QTL showed significant QTL-by-environment interactions (QEI). The QEI were further analyzed by including environmental covariates into the mixed model. Most QEI could be understood as differential QTL expression conditional on longitude or year, both consequences of temperature differences during critical stages of the growth.T HE incidence of genotype-by-environment interactions (GEI) for quantitative traits has important implications for any attempts to understand the genetic architecture of these traits by mapping quantitative trait loci (QTL) and also for the effectiveness of attempts to improve these traits by both conventional and markerassisted selection (MAS) breeding strategies. The literature on GEI and QTL-by-environment interactions (QEI) for quantitative traits in maize is ambiguous, with evidence in favor (Moreau et al. 2004) and against (Ledeaux et al. 2006) their importance. The diversity of the results for the importance of QEI for quantitative traits in crop plants observed in the literature strongly suggests that explicit testing for their presence, magnitude, and form is a critical step in any attempt to understand the genetic architecture of these traits. Further, theoretical considerations of the impact of different forms of QEI on the outcomes of MAS in plant breeding (Podlich et al. 2004;Cooper et al. 2002Cooper et al. , 2005Cooper et al. , 2006 motivate the development of methods for explicitly studying the importance of QEI as a component of the genetic architecture of quantitative traits.When QEI occurs and environmental covariables derived from geographical and weather information are available, QTL effects across environments can be tested for dependence on particular environmental covariables (Crossa et al. 1999;Malosetti et al. 2004;Varga...

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It is often of interest to find the maximum or near maxima among a set of vector‐valued parameters in a statistical model; in the case of disease mapping, for example, these correspond to relative‐risk “hotspots” where public‐health intervention may be needed. The general problem is one of estimating nonlinear functions of the ensemble of relative risks, but biased estimates result if posterior means are simply substituted into these nonlinear functions. The authors obtain better estimates of extrema from a new, weighted ranks squared error loss function. The derivation of these Bayes estimators assumes a hidden‐Markov random‐field model for relative risks, and their behaviour is illustrated with real and simulated data.

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.

We have assessed the impact of 13 different data transformation methods on the performance of four types of clustering methods (partitioning (K-mean), hierarchical distance (Average Linkage), multivariate normal mixture, and non-parametric kernel density) and four cluster number determination statistics (CNDS) (Pseudo F, Pseudo t 2 , Cubic Clustering Criterion (CCC), and Bayesian Information Criterion (BIC», using both simulated and real gene expression profile data. We found that Square Root, Cubic Root, and Spacing transformations have mostly positive impacts on the performance of the four types of clustering methods whereas Tukey's Bisquare and Interquantile Range have mostly negative impacts. The impacts from other transformation methods are clustering method-specific and data type-specific. The performance of CNDS improves with appropriately transformed data. Multivariate Mixture Clustering and Kernel Density Clustering perform better than K-mean and Average Linkage in grouping both simulated and real gene expression profile data.

Determining parentage is a fundamental problem in biology and in applications such as identifying pedigrees. Difficulties inferring parentage derive from extensive inbreeding within the population, whether natural or planned; using an insufficient number of hypervariable loci; and from allele mismatches caused by mutation or by laboratory errors that generate false exclusions. Many studies of parentage have been limited to comparisons of small numbers of specific parent-progeny triplets. There have been few large-scale surveys of candidates in which there is no prior knowledge of parentage. We present an algorithm that determines the probability of parentage in circumstances where there is no prior knowledge of pedigree and that is robust in the face of missing data and mistyped data. The focus is parentage of an inbred line having uncertain ancestry. The algorithm is a variation of a previously published hybrid-focused algorithm. We describe the algorithm and demonstrate its performance in determining parentage of 43 inbred varieties of soybean that have been profiled using 236 SSR loci and from seven inbred varieties of maize that were profiled using 70 SSR loci. We include simulations of additional levels of missing and mistyped data to show the algorithm's utility and flexibility.