Linear, bilinear, and linear-bilinear fixed and mixed models for analyzing genotype × environment interaction in plant breeding and agronomy

2010 ◽  
Vol 90 (5) ◽  
pp. 561-574 ◽  
Author(s):  
J. Crossa ◽  
M. Vargas ◽  
A K Joshi
Keyword(s):  
Plant Breeding ◽  
Least Squares ◽  
Statistical Models ◽  
Fixed Effects ◽  
Linear Models ◽  
Environment Interaction ◽  
Bilinear Models ◽  
Genotype Environment Interaction ◽  
Effect Model ◽  
Value Decomposition

The purpose of this manuscript is to review various statistical models for analyzing genotype × environment interaction (GE). The objective is to present parsimonious approaches other than the standard analysis of variance of the two-way effect model. Some fixed effects linear-bilinear models such as the sites regression model (SREG) are discussed, and a mixed effects counterpart such as the factorial analytic (FA) model is explained. The role of these linear-bilinear models for assessing crossover interaction (COI) is explained. One class of linear models, namely factorial regression (FR) models, and one class of bilinear models, namely partial least squares (PLS) regression, allows incorporating external environmental and genotypic covariables directly into the model. Examples illustrating the use of various statistical models for analyzing GE in the context of plant breeding and agronomy are given. Key words: Least squares, singular value decomposition, environmental and genotypic covariables

Statistical models for genotype by environment data: from conventional ANOVA models to eco-physiological QTL models

2005 ◽  
Vol 56 (9) ◽  
pp. 883 ◽  
Author(s):  
Fred A. van Eeuwijk ◽  
Marcos Malosetti ◽  
Xinyou Yin ◽  
Paul C. Struik ◽  
Piet Stam
Keyword(s):  
Statistical Models ◽  
Regression Models ◽  
Physiological Model ◽  
Environment Interaction ◽  
Response Curves ◽  
Physiological Models ◽  
Factorial Regression ◽  
Multiple Quantitative Trait Locus ◽  
Bilinear Models ◽  
Genotype Environment Interaction

To study the performance of genotypes under different growing conditions, plant breeders evaluate their germplasm in multi-environment trials. These trials produce genotype × environment data. We present statistical models for the analysis of such data that differ in the extent to which additional genetic, physiological, and environmental information is incorporated into the model formulation. The simplest model in our exposition is the additive 2-way analysis of variance model, without genotype × environment interaction, and with parameters whose interpretation depends strongly on the set of included genotypes and environments. The most complicated model is a synthesis of a multiple quantitative trait locus (QTL) model and an eco-physiological model to describe a collection of genotypic response curves. Between those extremes, we discuss linear-bilinear models, whose parameters can only indirectly be related to genetic and physiological information, and factorial regression models that allow direct incorporation of explicit genetic, physiological, and environmental covariables on the levels of the genotypic and environmental factors. Factorial regression models are also very suitable for the modelling of QTL main effects and QTL × environment interaction. Our conclusion is that statistical and physiological models can be fruitfully combined for the study of genotype × environment interaction.

scholarly journals Cultivating response: Peasant seed and plant–human collaboration in an agro-industrial heartland

2021 ◽  
pp. 251484862110224
Author(s):  
Leila Rezvani
Keyword(s):  
Plant Breeding ◽  
Environmental Changes ◽  
F1 Hybrids ◽  
Vegetable Production ◽  
Environment Interaction ◽  
Peasant Farmer ◽  
Genotype Environment Interaction ◽  
Seed Saving ◽  
Peasant Farmers ◽  
Ways Of Being

Using Donna Haraway’s notion of “response-ability”, or the cultivation of the capacity for response, this paper seeks to understand seed saving and plant breeding as politically and ethically charged modes of interspecies communication. In Brittany, France, a region known for its industrial-scale fresh vegetable production, peasant farmers and organic plant breeders question the modernist plant breeding and agro-industrial paradigm, cross-pollinating ideas to produce new understandings of genotype-environment interaction, biodiversity and heredity. Plant liveliness is understood as politically transformative, constitutive of an agriculture that supports peasant farmer and crop plant creativity and self-determination. In contrast to F1 hybrids, open-pollinated semences paysannes (peasant seed) retain the ability to respond to environmental changes, adapt and evolve over (human and plant) generations. Farmers must in turn engage specific modes of attention, interpreting plant expressions and shaping future generations through rouging and crossing, selecting and saving, watching and learning from their crops. Mutual response is the foundation of interdependence, in which nonconspecific partners adjust to one another’s ways of being and doing in order to labor together. In remaining response-able, farmers reckon with the liveliness and agential capacities of plants, qualities that work against their subsumption into factory-like methods of cultivation. These communicative practices hint at the radical potential for interspecies resistance to monoculture within plant breeding and cultivation, practices that are so often molded by the interests of agro-industrial capital.

scholarly journals Genotype-environment interaction, genetic trends, and performance dissimilarity of Nellore herds raised in three different environmental gradients

2018 ◽  
Vol 39 (1) ◽  
pp. 349
Author(s):  
Julio Cesar de Souza ◽  
Fabio Rafael Leão Fialho ◽  
Marcos Paulo Gonçalves Rezende ◽  
Carlos Henrique Cavallari Machado ◽  
Mariana Pereira Alencar ◽  
...  
Keyword(s):  
Weight Gain ◽  
Fixed Effects ◽  
Genetic Parameters ◽  
Environmental Gradients ◽  
Superior Performance ◽  
Environment Interaction ◽  
Genotype Environment Interaction ◽  
And Performance ◽  
Main Components ◽  
Genetic Trends

The objectives of this work were to evaluate the genotype-environment interaction, and estimate genetic parameters, genetic trends, and performance dissimilarity-weight gain from birth to weaning (WGBW), adjusted weight to 205 days (W205), weight gain from weaning to 18 months of age (WG18), and adjusted weight to 550 days (W550)-in Nellore animals born between 1986 and 2012, and raised in pasture-based system in three different environmental gradients in Brazil. Data of 62,001 animals-11,729 raised in the Alto Taquari/Bolsão region (ATBR), 21,143 raised in the Campo Grande/Dourados region (CGDR) and 29,129 raised in the western São Paulo/Paraná region (SPPR) in Brazil-were used. The contemporary groups were defined by sex, location, and birth year and season, with at least nine individuals, two different environments, and breeding bulls with at least five progenies. The statistical model contained the direct additive and residual genetic effects (random effects), and environmental and contemporary group effects (fixed effects). Genetic parameters, genotype-environment interaction and genetic trends were estimates using animal model (uni- and/or bi- traits). The level of similarity between regions was evaluated using principal components. The animals raised in the CGDR had superior performance regarding the traits evaluated. The direct heritability estimates ranged from 0.39 to 0.44 (WGBW), 0.41 to 0.45 (W205), 0.42 to 0.55 (WG18) and 0.60 to 0.62 (W550). The maternal heritability of the traits ranged from 0.20 (WGBW), 0.12 to 0.18 (W205), 0.00 to 0.06 (WG18) and 0.02 to 0.22 (W550). According to the Spearman correlation, the ranking of the breeding bulls in the regions evaluated were different. The mean of Euclidean distance indicated low similarity between ATBR and CGDR (43.20), and ATBR and SPPR (29.24). CGDR and SPPR presented similarity of 17.84. The breed values increased over the years in the traits evaluated. The cumulative variance percentage of the first two main components explained 99.99% variation among the regions, and the weight gains of the animals were the most important to differentiate the regions. A genotype-environment interaction was found for the traits evaluated, thus, the breeding bull selected with superior genetic merit for one region might not be the best for others.

Genotype-environment interaction – a challenge for plant breeding

1975 ◽  
Vol 85 (3) ◽  
pp. 477-493 ◽  
Author(s):  
J. Hill
Keyword(s):  
Plant Breeding ◽  
Environment Interaction ◽  
Genotype Environment Interaction

Much has been written and said about genotype-environment (GE) interactions and the particular problems which they pose for plant breeders. It is not the purpose of this article to dwell upon every aspect of this story, but rather to discuss how these problems came to be recognized, to comment upon the various techniques which have been employed in seeking a solution to them and to suggest what developments might lie ahead.

scholarly journals Selection in several environments by BLP as an alternative to pooled anova in crop breeding

2009 ◽  
Vol 33 (5) ◽  
pp. 1342-1350 ◽  
Author(s):  
Júlio Sílvio de Sousa Bueno Filho ◽  
Roland Vencovsky
Keyword(s):  
Plant Breeding ◽  
Random Effects ◽  
Fixed Effects ◽  
Mixed Model ◽  
Linear Models ◽  
Minimum Variance ◽  
Pooled Analysis ◽  
Balanced Designs ◽  
Best Linear Unbiased ◽  
Combine Information

Plant breeders often carry out genetic trials in balanced designs. That is not always the case with animal genetic trials. In plant breeding is usual to select progenies tested in several environments by pooled analysis of variance (ANOVA). This procedure is based on the global averages for each family, although genetic values of progenies are better viewed as random effects. Thus, the appropriate form of analysis is more likely to follow the mixed models approach to progeny tests, which became a common practice in animal breeding. Best Linear Unbiased Prediction (BLUP) is not a "method" but a feature of mixed model estimators (predictors) of random effects and may be derived in so many ways that it has the potential of unifying the statistical theory of linear models (Robinson, 1991). When estimates of fixed effects are present is possible to combine information from several different tests by simplifying BLUP, in these situations BLP also has unbiased properties and this lead to BLUP from straightforward heuristics. In this paper some advantages of BLP applied to plant breeding are discussed. Our focus is on how to deal with estimates of progeny means and variances from many environments to work out predictions that have "best" properties (minimum variance linear combinations of progenies' averages). A practical rule for relative weighting is worked out.

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