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.

The E(NK) model: extending the NK model to incorporate gene-by-environment interactions and epistasis for diploid genomes

The haploid NK model developed by Kauffman can be extended to diploid genomes and to incorporate gene-by-environment interaction effects in combination with epistasis. To provide the flexibility to include a wide range of forms of gene-by-environment interactions, a target population of environment types (TPE) is defined. The TPE consists of a set of E different environment types, each with their own frequency of occurrence. Each environment type conditions a different NK gene network structure or series of gene effects for a given network structure, providing the framework for defining gene-by-environment interactions. Thus, different NK models can be partially or completely nested within the E environment types of a TPE, giving rise to the E(NK) model for a biological system. With this model it is possible to examine how populations of genotypes evolve in context with properties of the environment that influence the contributions of genes to the fitness values of genotypes. We are using the E(NK) model to investigate how both epistasis and gene-by-environment interactions influence the genetic improvement of quantitative traits by plant breeding strategies applied to agricultural systems. © 2002 Wiley Periodicals, Inc.

Environment-dependent microevolution in a Mediterranean pine (Pinus pinaster Aiton).

BACKGROUND: A central question for understanding the evolutionary responses of plant species to rapidly changing environments is the assessment of their potential for short-term (in one or a few generations) genetic change. In our study, we consider the case of Pinus pinaster Aiton (maritime pine), a widespread Mediterranean tree, and (i) test, under different experimental conditions (growth chamber and semi-natural), whether higher recruitment in the wild from the most successful mothers is due to better performance of their offspring; and (ii) evaluate genetic change in quantitative traits across generations at two different life stages (mature trees and seedlings) that are known to be under strong selection pressure in forest trees. RESULTS: Genetic control was high for most traits (h2 = 0.137-0.876) under the milder conditions of the growth chamber, but only for ontogenetic change (0.276), total height (0.415) and survival (0.719) under the more stressful semi-natural conditions. Significant phenotypic selection gradients were found in mature trees for traits related to seed quality (germination rate and number of empty seeds). Moreover, female relative reproductive success was significantly correlated with offspring performance for specific leaf area (SLA) in the growth chamber experiment, and stem mass fraction (SMF) in the experiment under semi-natural conditions, two adaptive traits related to abiotic stress-response in pines. Selection gradients based on genetic covariance of seedling traits and responses to selection at this stage involved traits related to biomass allocation (SMF) and growth (as decomposed by a Gompertz model) or delayed ontogenetic change, depending also on the testing environment. CONCLUSIONS: Despite the evidence of microevolutionary change in adaptive traits in maritime pine, directional or disruptive changes are difficult to predict due to variable selection at different life stages and environments. At mature-tree stages, higher female effective reproductive success can be explained by differences in their production of offspring (due to seed quality) and, to a lesser extent, by seemingly better adapted seedlings. Selection gradients and responses to selection for seedlings also differed across experimental conditions. The distinct processes involved at the two life stages (mature trees or seedlings) together with environment-specific responses advice caution when predicting likely evolutionary responses to environmental change in Mediterranean forest trees.

Studying the genetic basis of drought tolerance in sorghum by managed stress trials and adjustments for phenological and plant height differences

Managed environments in the form of well watered and water stressed trials were performed to study the genetic basis of grain yield and stay green in sorghum with the objective of validating previously detected QTL. As variations in phenology and plant height may influence QTL detection for the target traits, QTL for flowering time and plant height were introduced as cofactors in QTL analyses for yield and stay green. All but one of the flowering time QTL were detected near yield and stay green QTL. Similar co-localization was observed for two plant height QTL. QTL analysis for yield, using flowering time/plant height cofactors, led to yield QTL on chromosomes 2, 3, 6, 8 and 10. For stay green, QTL on chromosomes 3, 4, 8 and 10 were not related to differences in flowering time/plant height. The physical positions for markers in QTL regions projected on the sorghum genome suggest that the previously detected plant height QTL, Sb-HT9-1, and Dw2, in addition to the maturity gene, Ma5, had a major confounding impact on the expression of yield and stay green QTL. Co-localization between an apparently novel stay green QTL and a yield QTL on chromosome 3 suggests there is potential for indirect selection based on stay green to improve drought tolerance in sorghum. Our QTL study was carried out with a moderately sized population and spanned a limited geographic range, but still the results strongly emphasize the necessity of corrections for phenology in QTL mapping for drought tolerance traits in sorghum.

Contribution and perspectives of quantitative genetics to plant breeding in Brazil

The purpose of this article is to show how quantitative genetics has contributed to the huge genetic progress obtained in plant breeding in Brazil in the last forty years. The information obtained through quantitative genetics has given Brazilian breeders the possibility of responding to innumerable questions in their work in a much more informative way, such as the use or not of hybrid cultivars, which segregating population to use, which breeding method to employ, alternatives for improving the efficiency of selection programs, and how to handle the data of progeny and/or cultivars evaluations to identify the most stable ones and thus improve recommendations.

Analysis of 16S rRNA and mxaF genes revealing insights into Methylobacterium niche-specific plant association

The genus Methylobacterium comprises pink-pigmented facultative methylotrophic (PPFM) bacteria, known to be an important plant-associated bacterial group. Species of this group, described as plant-nodulating, have the dual capacity of producing cytokinin and enzymes, such as pectinase and cellulase, involved in systemic resistance induction and nitrogen fixation under specific plant environmental conditions. The aim hereby was to evaluate the phylogenetic distribution of Methylobacterium spp. isolates from different host plants. Thus, a comparative analysis between sequences from structural (16S rRNA) and functional mxaF (which codifies for a subunit of the enzyme methanol dehydrogenase) ubiquitous genes, was undertaken. Notably, some Methylobacterium spp. isolates are generalists through colonizing more than one host plant, whereas others are exclusively found in certain specific plant-species. Congruency between phylogeny and specific host inhabitance was higher in the mxaF gene than in the 16S rRNA, a possible indication of function-based selection in this niche. Therefore, in a first stage, plant colonization by Methylobacterium spp. could represent generalist behavior, possibly related to microbial competition and adaptation to a plant environment. Otherwise, niche-specific colonization is apparently impelled by the host plant.

Analysis of 16S rRNA and mxaF genes reveling insights into Methylobacterium niche-specific plant association

The genus Methylobacterium comprises pink-pigmented facultative methylotrophic (PPFM) bacteria, known to be an important plant-associated bacterial group. Species of this group, described as plant-nodulating, have the dual capacity of producing cytokinin and enzymes, such as pectinase and cellulase, involved in systemic resistance induction and nitrogen fixation under specific plant environmental conditions. The aim hereby was to evaluate the phylogenetic distribution of Methylobacterium spp. isolates from different host plants. Thus, a comparative analysis between sequences from structural (16S rRNA) and functional mxaF (which codifies for a subunit of the enzyme methanol dehydrogenase) ubiquitous genes, was undertaken. Notably, some Methylobacterium spp. isolates are generalists through colonizing more than one host plant, whereas others are exclusively found in certain specific plant-species. Congruency between phylogeny and specific host inhabitance was higher in the mxaF gene than in the 16S rRNA, a possible indication of function-based selection in this niche. Therefore, in a first stage, plant colonization by Methylobacterium spp. could represent generalist behavior, possibly related to microbial competition and adaptation to a plant environment. Otherwise, niche-specific colonization is apparently impelled by the host plant.

BAYESIAN STATISTICAL METHODS IN GENE-ENVIRONMENT AND GENE-GENE INTERACTION STUDIES

Complex diseases such as cancer result from multiple genetic changes and environmental exposures. Due to the rapid development of genotyping and sequencing technologies, we are now able to more accurately assess causal effects of many genetic and environmental factors. Genome-wide association studies have been able to localize many causal genetic variants predisposing to certain diseases. However, these studies only explain a small portion of variations in the heritability of diseases. More advanced statistical models are urgently needed to identify and characterize some additional genetic and environmental factors and their interactions, which will enable us to better understand the causes of complex diseases. In the past decade, thanks to the increasing computational capabilities and novel statistical developments, Bayesian methods have been widely applied in the genetics/genomics researches and demonstrating superiority over some regular approaches in certain research areas. Gene-environment and gene-gene interaction studies are among the areas where Bayesian methods may fully exert its functionalities and advantages. This dissertation focuses on developing new Bayesian statistical methods for data analysis with complex gene-environment and gene-gene interactions, as well as extending some existing methods for gene-environment interactions to other related areas. It includes three sections: (1) Deriving the Bayesian variable selection framework for the hierarchical gene-environment and gene-gene interactions; (2) Developing the Bayesian Natural and Orthogonal Interaction (NOIA) models for gene-environment interactions; and (3) extending the applications of two Bayesian statistical methods which were developed for gene-environment interaction studies, to other related types of studies such as adaptive borrowing historical data. We propose a Bayesian hierarchical mixture model framework that allows us to investigate the genetic and environmental effects, gene by gene interactions (epistasis) and gene by environment interactions in the same model. It is well known that, in many practical situations, there exists a natural hierarchical structure between the main effects and interactions in the linear model. Here we propose a model that incorporates this hierarchical structure into the Bayesian mixture model, such that the irrelevant interaction effects can be removed more efficiently, resulting in more robust, parsimonious and powerful models. We evaluate both of the 'strong hierarchical' and 'weak hierarchical' models, which specify that both or one of the main effects between interacting factors must be present for the interactions to be included in the model. The extensive simulation results show that the proposed strong and weak hierarchical mixture models control the proportion of false positive discoveries and yield a powerful approach to identify the predisposing main effects and interactions in the studies with complex gene-environment and gene-gene interactions. We also compare these two models with the 'independent' model that does not impose this hierarchical constraint and observe their superior performances in most of the considered situations. The proposed models are implemented in the real data analysis of gene and environment interactions in the cases of lung cancer and cutaneous melanoma case-control studies. The Bayesian statistical models enjoy the properties of being allowed to incorporate useful prior information in the modeling process. Moreover, the Bayesian mixture model outperforms the multivariate logistic model in terms of the performances on the parameter estimation and variable selection in most cases. Our proposed models hold the hierarchical constraints, that further improve the Bayesian mixture model by reducing the proportion of false positive findings among the identified interactions and successfully identifying the reported associations. This is practically appealing for the study of investigating the causal factors from a moderate number of candidate genetic and environmental factors along with a relatively large number of interactions. The natural and orthogonal interaction (NOIA) models of genetic effects have previously been developed to provide an analysis framework, by which the estimates of effects for a quantitative trait are statistically orthogonal regardless of the existence of Hardy-Weinberg Equilibrium (HWE) within loci. Ma et al. (2012) recently developed a NOIA model for the gene-environment interaction studies and have shown the advantages of using the model for detecting the true main effects and interactions, compared with the usual functional model. In this project, we propose a novel Bayesian statistical model that combines the Bayesian hierarchical mixture model with the NOIA statistical model and the usual functional model. The proposed Bayesian NOIA model demonstrates more power at detecting the non-null effects with higher marginal posterior probabilities. Also, we review two Bayesian statistical models (Bayesian empirical shrinkage-type estimator and Bayesian model averaging), which were developed for the gene-environment interaction studies. Inspired by these Bayesian models, we develop two novel statistical methods that are able to handle the related problems such as borrowing data from historical studies. The proposed methods are analogous to the methods for the gene-environment interactions on behalf of the success on balancing the statistical efficiency and bias in a unified model. By extensive simulation studies, we compare the operating characteristics of the proposed models with the existing models including the hierarchical meta-analysis model. The results show that the proposed approaches adaptively borrow the historical data in a data-driven way. These novel models may have a broad range of statistical applications in both of genetic/genomic and clinical studies.

Effect of environment and genotype on bread-making quality of spring-sown spring wheat cultivars in China

Improvement of end-use quality in bread wheat depends on a thorough understanding of current wheat quality and the influences of genotype (G), environment (E), and genotype by environment interaction (G x E) on quality traits. Thirty-nine spring-sown spring wheat (SSSW) cultivars and advanced lines from China were grown in four agro-ecological zones comprising seven locations during the 1998 and 1999 cropping seasons. Data on 12 major bread-making quality traits were used to investigate the effect of G, E, and G x E on these traits. Wide range variability for protein quantity and quality, starch quality parameters and milling quality in Chinese SSSW was observed. Genotype and environment were found to significantly influence all quality parameters as major effects. Kernel hardness, flour yield, Zeleny sedimentation value and mixograph properties were mainly influenced by the genetic variance components, while thousand kernel weight, test weight, and falling number were mostly influenced by the environmental variance components. Genotype, environment, and their interaction had important effects on test weight, mixing development time and RVA parameters. Cultivars originating from Zone VI (northeast) generally expressed high kernel hardness, good starch quality, but poor milling and medium to weak mixograph performance; those from Zone VII (north) medium to good gluten and starch quality, but low milling quality; those from Zone VIII (central northwest) medium milling and starch quality, and medium to strong mixograph performance; those from Zone IX (western/southwestern Qinghai-Tibetan Plateau) medium milling quality, but poor gluten strength and starch parameters; and those from Zone X (northwest) high milling quality, strong mixograph properties, but low protein content. Samples from Harbin are characterized by good gluten and starch quality, but medium to poor milling quality; those from Hongxinglong by strong mixograph properties, medium to high milling quality, but medium to poor starch quality and medium to low protein content; those from Hohhot by good gluten but poor milling quality; those from Linhe by weak gluten quality, medium to poor milling quality; those from Lanzhou by poor bread-making and starch quality; those from Yongning by acceptable bread-making and starch quality and good milling quality; and those from Urumqi by good milling quality, medium gluten quality and good starch pasting parameters. Our findings suggest that Chinese SSSW quality could be greatly enhanced through genetic improvement for targeted well-characterized production environments.

Mixed model formulations for multi-environment trials

When studying genotype X environment interaction in multi-environment trials, plant breeders and geneticists often consider one of the effects, environments or genotypes, to be fixed and the other to be random. However, there are two main formulations for variance component estimation for the mixed model situation, referred to as the unconstrained-parameters (UP) and constrained-parameters (CP) formulations. These formulations give different estimates of genetic correlation and heritability as well as different tests of significance for the random effects factor. The definition of main effects and interactions and the consequences of such definitions should be clearly understood, and the selected formulation should be consistent for both fixed and random effects. A discussion of the practical outcomes of using the two formulations in the analysis of balanced data from multi-environment trials is presented. It is recommended that the CP formulation be used because of the meaning of its parameters and the corresponding variance components. When managed (fixed) environments are considered, users will have more confidence in prediction for them but will not be overconfident in prediction in the target (random) environments. Genetic gain (predicted response to selection in the target environments from the managed environments) is independent of formulation.

Analysis of line x environment interactions for yield in navy beans. 2. Pattern analysis of lines and environment within years

Seven years of multi-environment yield trials of navy bean (Phaseolus vulgaris L.) grown in Queensland were examined. As is common with plant breeding evaluation trials, test entries and locations varied between years. Grain yield data were analysed for each year using cluster and ordination analyses (pattern analyses). These methods facilitate descriptions of genotype performance across environments and the discrimination among genotypes provided by the environments. The observed trends for genotypic yield performance across environments were partly consistent with agronomic and disease reactions at specific environments and also partly explainable by breeding and selection history. In some cases, similarities in discrimination among environments were related to geographic proximity, in others management practices, and in others similarities occurred between geographically widely separated environments which differed in management practices. One location was identified as having atypical line discrimination. The analysis indicated that the number of test locations was below requirements for adequate representation of line x environment interaction. The pattern analyses methods used were an effective aid in describing the patterns in data for each year and illustrated the variations in adaptive patterns from year to year. The study has implications for assessing the number and location of test sites for plant breeding multi-environment trials, and for the understanding of genetic traits contributing to line x environment interactions.

Transgenic tobacco revealing altered bacterial diversity in the rhizosphere during early plant development

The rhizosphere constitutes a complex niche that may be exploited by a wide variety of bacteria. Bacterium-plant interactions in this niche can be influenced by factors such as the expression of heterologous genes in the plant. The objective of this work was to describe the bacterial communities associated with the rhizosphere and rhizoplane regions of tobacco plants, and to compare communities from transgenic tobacco lines (CAB1, CAB2 and TRP) with those found in wild-type (WT) plants. Samples were collected at two stages of plant development, the vegetative and flowering stages (1 and 3 months after germination). The diversity of the culturable microbial community was assessed by isolation and further characterization of isolates by amplified ribosomal RNA gene restriction analysis (ARDRA) and 16S rRNA sequencing. These analyses revealed the presence of fairly common rhizosphere organisms with the main groups Alphaproteobacteria, Betaproteobacteria, Actinobacteria and Bacilli. Analysis of the total bacterial communities using PCR-DGGE (denaturing gradient gel electrophoresis) revealed that shifts in bacterial communities occurred during early plant development, but the reestablishment of original community structure was observed over time. The effects were smaller in rhizosphere than in rhizoplane samples, where selection of specific bacterial groups by the different plant lines was demonstrated. Clustering patterns and principal components analysis (PCA) were used to distinguish the plant lines according to the fingerprint of their associated bacterial communities. Bands differentially detected in plant lines were found to be affiliated with the genera Pantoea, Bacillus and Burkholderia in WT, CAB and TRP plants, respectively. The data revealed that, although rhizosphere/rhizoplane microbial communities can be affected by the cultivation of transgenic plants, soil resilience may be able to restore the original bacterial diversity after one cycle of plant cultivation.

Correlation between carbon isotope discrimination and transpiration efficiency in lines of the C-4 species Sorghum bicolor in the glasshouse and the field

Transpiration efficiency, W, the ratio of plant carbon produced to water transpired and carbon isotope discrimination of leaf dry matter, Delta(d)' were measured together on 30 lines of the C-4 species, Sorghum bicolor in the glasshouse and on eight lines grown in the field. In the glasshouse, the mean W observed was 4.9 mmol C mol(-1) H2O and the range was 0.8 mmol C mol(-1) H2O The mean Delta(d) was 3.0 parts per thousand and the observed range was 0.4 parts per thousand. In the field, the mean W was lower at 2.8 mmol C mol H2O and the mean Delta(d) was 4.6 parts per thousand. Significant positive correlations between W and Delta(d) were observed for plants grown in the glasshouse and in the field. The observed correlations were consistent with theory, opposite to those for C-4 species, and showed that variation in Delta(d) was an integrated measure of long-term variation in the ratio of intercellular to ambient CO2 partial pressure, p(i)/p(a). Detailed gas exchange measurements of carbon isotope discrimination during CO2 uptake, Delta(A) and p(i)/p(a) were made on leaves of eight S. bicolor lines. The observed relationship between Delta(A) and p(i)/p(a) was linear with a negative slope of 3.7 parts per thousand in Delta(A) for a unit change in p(i)/p(a). The slope of this linear relationship between Delta(A) and p(i)/p(a) in C-4 species is dependent on the leakiness of the CO2 concentrating mechanism of the C pathway, We estimated the leakiness (defined as the fraction of CO2 released in the bundle sheath by C-4 acid decarboxylations, which is lost by leakage) to be 0.2. We conclude that, although variation in Delta(d) observed in the 30 lines of S. bicolor is smaller than that commonly observed in C-4 species, it also reflects variation in transpiration efficiency, W. Among the eight lines examined in detail and in the environments used, there was considerable genotype x environment interaction.

Genotype-by-management interactions for grain yield and grain protein concentration of wheat

The magnitude of genotype-by-management (G x M) interactions for grain yield and grain protein concentration was examined in a multi-environment trial (MET) involving a diverse set of 272 advanced breeding lines from the Queensland wheat breeding program. The MET was structured as a series of management-regimes imposed at 3 sites for 2 years. The management-regimes were generated at each site-year as separate trials in which planting time, N fertiliser application rate, cropping history, and irrigation were manipulated. irrigation was used to simulate different rainfall regimes. From the combined analysis of variance, the G x M interaction variance components were found to be the largest source of G x E interaction variation for both grain yield (0.117 +/- 0.005 t(2) ha(-2); 49% of total G x E 0.238 +/- 0.028 t(2) ha(-2)) and grain protein concentration (0.445 +/- 0.020%(2); 82% of total G x E 0.546 +/- 0.057%(2)), and in both cases this source of variation was larger than the genotypic variance component (grain yield 0.068 +/- 0.014 t(2) ha(-2) and grain protein 0.203 +/- 0.026%(2)). The genotypic correlation between the traits varied considerably with management-regime, ranging from -0.98 to -0.31, with an estimate of 0.0 for one trial. Pattern analysis identified advanced breeding lines with improved grain yield and grain protein concentration relative to the cultivars Hartog, Sunco and Meteor. It is likely that a large component of the previously documented G x E interactions for grain yield of wheat in the northern grains region are in part a result of G x M interactions. The implications of the strong influence of G x M interactions for the conduct of wheat breeding METs in the northern region are discussed. (C) 2001 Elsevier Science B.V. All rights reserved.