The model, Yij = μ1 + β1Ij + δij, defines stability parameters that may be used to describe the performance of a variety over a series of environments. Yij is the variety mean of the ith variety at the jth environment, µ1 is the ith variety mean over all environments, β1 is the regression coefficient that measures the response of the ith variety to varying environments, δij is the deviation from regression of the ith variety at the jth environment, and Ij is the environmental index.

The data from two single-cross diallels and a set of 3-way crosses were examined to see whether genetic differences could be detected. Genetic differences among lines were indicated for the regression of the lines on the environmental index with no evidence of nonadditive gene action. The estimates of the squared deviations from regression for many hybrids were near zero, whereas extremely large estimates were obtained for other hybrids.

Stability Parameters for Comparing Varieties

SUMMARY To define a likelihood we have to specify the form of distribution of the observations, but to define a quasi-likelihood function we need only specify a relation between the mean and variance of the observations and the quasi-likelihood can then be used for estimation. For a one-parameter exponential family the log likelihood is the same as the quasi-likelihood and it follows that assuming a one-paramet'er exponential family is the weakest sort of distributional assumption t'hat can be made. The Gauss-Newton method for calculating nonlinear least squares estimates generalizes easily to deal wit'h maximum quasi-likelihood estimates, and a rearrangement of this produces a generalization of the method described by Nelder & Wedderburn (1972). This paper is mainly concerned wit'h fitting regression models, linear or nonlinear, in which the variance of each observation is specified to be either equal to, or proportional to, some function of its expectat'ion. If the form of distribution of the observations were specified, t'he method of maximum likelihood would give estimates of t'he parameters in t'he model. For instance, if it is specified that the observations have normally distributed errors with constant variance, then the method of least squares provides expressions for the variances and covariances of the estimates, exact for linear models and approximate for nonlinear ones, and these estimates and the expressions for their errors remain valid even if the observations are not normally distributed but merely have a fixed variance; thus, with linear models and a given error variance, the variance of least squares estimat'es is not affected by the distribution of the errors, and the same holds approximately for nonlinear ones. A more general situation is considered in this paper, namely the situation when there is a given relation between the variance and mean of the observations, possibly with an unknown constant of proportionality. A similar problem was considered from a Bayesian viewpoint by Hartigan (1969).We define a quasi-likelihood function, which can be used for estimation in the same way as a likelihood function. With constant variance this again leads to least squares estimation. When other mean-variance relationships are specified, the quasilikelihood sometimes turns out to be a recognizable likelihood function; for instance, for a constant coefficient of variation the quasi-likelihood function is the same as the likelihood obtained by treating the observations as if they had a gamma distribution.

https://www.jstor.org/stable/info/2334725

Quasi-likelihood functions, generalized linear models, and the Gauss-Newton method

GENES is a software package used for data analysis and processing with different biometric models and is essential in genetic studies applied to plant and animal breeding It allows parameter estimation to analyze biological phenomena and is fundamental for the decision-making process and predictions of success and viability of selection strategies The program can be downloaded from the Internet (http://wwwufvbr/dbg/genes/geneshtm or http://wwwufvbr/dbg/biodatahtm) and is available in Portuguese, English and Spanish Specific literature (http://wwwlivrariaufvbr/) and a set of sample files are also provided, making GENES easy to use The software is integrated into the programs MS Word, MS Excel and Paint, ensuring simplicity and effectiveness in data import and export of results, figures and data It is also compatible with the free software R and Matlab, through the supply of useful scripts available for complementary analyses in different areas, including genome wide selection, prediction of breeding values and use of neural networks in genetic improvement

/pdf/genes-a-software-package-for-analysis-in-experimental-59l7e5v1pc.pdf

GENES: a software package for analysis in experimental statistics and quantitative genetics

Phenotypic plasticity is the ability of an individual organism to alter its physiology/morphology in response to changes in environmental conditions. This ability is particularly important in plants, whose sessile life-style requires them to deal with ambient conditions. This review focuses on issues related to the evolution of phenotypic plasticity in plants-factors responsible for differences in plasticity between populations or species (e.g. selection, drift), the presence of plasticity variation among taxa, the relationship between character correlations and character plasticities, and the assessment of the ecological role of phenotypic plasticity. In addition, a section is provided to introduce methods and problems of analyzing data from plasticity experiments. As a general rule, references are provided as an entrance to the literature and do not represent an exhaustive list. Bradshaw's review (20) remains the best introduction to the subject; this review is intended to complement his, not to replace it. The notion that plants respond morphologically to changes in their environment has a long tradition. Work by Turesson (139), Clausen et al (27), and others (see 20 for review) firmly documented the nature and extent of phenotypic responses to varied environments. Classic examples such as sun vs shade leaves (143), heterophylly (29, 30, 35), environmental control of cleistogamy (153), and the responses to herbivory (58, 84), mowing (147), and competition (140) all represent cases of phenotypic plasticity. These and other good examples support the notion that plastic responses are adaptive. Note, however, that the definition of phenotypic plasticity does not imply that such responses are necessarily adaptive. Plant response to an environmental

https://www.jstor.org/stable/pdfplus/2097012.pdf

The Evolution of Phenotypic Plasticity in Plants

Drought tolerance improvement in crop plants: An integrated view from breeding to genomics

The adaptation of barley varieties was studied by the use of grain yields of a randomly chosen group of 277 varieties from a world collection, grown in replicated trials for several seasons at three sites in South Australia For each variety a linear regression of yield on the mean yield of all varieties for each site and season was computed to measure variety adaptation In these calculations the basic yields were measured on a logarithmic scale, as it was found that a high degree of linearity was thereby induced The mean yield of all varieties for each site and season provided a quantitative grading of the environments; and from the analysis described, varieties specifically adapted to good or poor seasons and those showing general adaptability may be identified The study of the adaptation of the whole population of varieties was facilitated by the use of a two-dimensional plot (scatter diagram), with mean yield and regression coefficient as coordinates for each variety Though wide variation was evident in both mean yield and sensitivity to environment as characterized by the regression coefficient, the variation in sensitivity was proportionately less among varieties with higher mean yield, and the varieties with highest mean yield exhibited, within very narrow limits (regression coefficients close to 08), a similar degree of adaptation to all environments over the wide range, especially of seasonal conditions, typical of the South Australian cereal belt Varieties from particular geographic regions of the world showed a similarity in type of adaptation, which provides a useful basis for plant introduction Phenotypic stability and physiological and morphological characteristics of groups of varieties with specific or general adaptability are discussed in relation to plant introduction and breeding

/pdf/the-analysis-of-adaptation-in-a-plant-breeding-programme-1q9gvqtr3z.pdf

The analysis of adaptation in a plant-breeding programme

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The analysis of adaptation in a plant-breeding programme