Mixed model approaches for the identification of QTLs within a maize hybrid breeding program.

Two outlines for mixed model based approaches to quantitative trait locus (QTL) mapping in existing maize hybrid selection programs are presented: a restricted maximum likelihood (REML) and a Bayesian Markov Chain Monte Carlo (MCMC) approach. The methods use the in-silico-mapping procedure developed by Parisseaux and Bernardo (2004) as a starting point. The original single-point approach is extended to a multi-point approach that facilitates interval mapping procedures. For computational and conceptual reasons, we partition the full set of relationships from founders to parents of hybrids into two types of relations by defining so-called intermediate founders. QTL effects are defined in terms of those intermediate founders. Marker based identity by descent relationships between intermediate founders define structuring matrices for the QTL effects that change along the genome. The dimension of the vector of QTL effects is reduced by the fact that there are fewer intermediate founders than parents. Furthermore, additional reduction in the number of QTL effects follows from the identification of founder groups by various algorithms. As a result, we obtain a powerful mixed model based statistical framework to identify QTLs in genetic backgrounds relevant to the elite germplasm of a commercial breeding program. The identification of such QTLs will provide the foundation for effective marker assisted and genome wide selection strategies. Analyses of an example data set show that QTLs are primarily identified in different heterotic groups and point to complementation of additive QTL effects as an important factor in hybrid performance.

A mixed-model quantitative trait loci (QTL) analysis for multiple-environment trial data using environmental covariables for QTL-by-environment interactions, with an example in maize.

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 multi-environment 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.

Using molecular sizes of simple sequence repeats vs. discrete binned data in assessing probability of ancestry: application to maize hybrids.

Most inferential methods for profiling genotypes based upon the use of DNA fragments use molecular-size data transcribed into discrete bins, which are intervals of DNA fragment sizes. Categorizing into bins is labor intensive with inevitable arbitrariness that may vary between laboratories. We describe and evaluate an algorithm for determining probabilities of parentage based on raw molecular-size data without establishing bins. We determine the standard deviation of DNA fragment size and assess the association of standard deviation with fragment size. We consider a pool of potential ancestors for an index line that is a hybrid with unknown pedigree. We evaluate the identification of inbred parents of maize hybrids with simple sequence repeat data in the form of actual molecular sizes received from two laboratories. We find the standard deviation to be essentially constant over the molecular weight. We compare these results with those of parallel analyses based on these same data that had been transcribed into discrete bins by the respective laboratories. The conclusions were quite similar in the two cases, with excellent performance using either binned or molecular-size data. We demonstrate the algorithm's utility and robustness through simulations of levels of missing and misscored molecular-size data.

Assessing probability of ancestry using simple sequence repeat profiles: applications to maize inbred lines and soybean varieties.

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.

Assessing probability of ancestry using simple sequence repeat profiles: applications to maize hybrids and inbreds.

Determination of parentage is fundamental to the study of biology and to applications such as the identification of pedigrees. Limitations to studies of parentage have stemmed from the use of an insufficient number of hypervariable loci and mismatches of alleles that can be caused by mutation or by laboratory error and that can generate false exclusions. Furthermore, most studies of parentage have been limited to comparisons of small numbers of specific parent-progeny triplets thereby precluding large-scale surveys of candidates where there may be no prior knowledge of parentage. We present an algorithm that can determine probability of parentage in circumstances where there is no prior knowledge of pedigree and that is robust in the face of missing data or mistyped data. We present data from 54 maize hybrids and 586 maize inbreds that were profiled using 195 SSR loci including simulations of additional levels of missing and mistyped data to demonstrate the utility and flexibility of this algorithm.