To achieve a coherent evolutionary theory, it is necessary to account for the effects of the environment on the process of development. Phenotypic plasticity is the change in the expressed phenotype of a genotype as a function of the environment. Various measures of plasticity exist, many of which can be united within the framework of a polynomial function. This function is the norm of reaction. For the special case of a linear reaction norm, genetic variation can be partitioned into portions that are independent and dependent on the environment. From this partition two heritability measures are derived which can be used, alternatively, to compare populations or make predictions about the response to selection. Genetically, plasticity is likely due both to differences in allelic expression across environments and to changes in interactions among loci; plasticity is not a function of heterozygosity. Plasticity responds to both artificial and natural selection. The evolution of plasticity is modeled in thre...

Genetics and Evolution of Phenotypic Plasticity

The Analysis of Variance.

Following the recognition of the importance of dealing with the effects of genotype-by-environment (G ×E) interaction in multi-environment testing of genotypes in plant breeding programs, there has been substantial development in the area of analytical methodology to quantify and describe these interactions Three major areas where there have been developments are the analysis of variance, indirect selection, and pattern analysis methodologies This has resulted in a wide range of analytical methods each with their own advocates There is little doubt that the development of these methodologies has greatly contributed to an enhanced understanding of the magnitude and form ofG ×E interactions and our ability to quantify their presence in a multi-environment experiment However, our understanding of the environmental and physiological bases of the nature ofG ×E interactions in plant breeding has not improved commensurably with the availability of these methodologies This may in part be due to concentration on the statistical aspects of the analytical methodologies rather than on the complementary resolution of the biological basis of the differences in genotypic adaptation observed in plant breeding experiments There are clear relationships between many of the analytical methodologies used for studying genotypic variation andG ×E interaction in plant breeding experiments However, from the numerous discussions on the relative merits of alternative ways of analysingG ×E interactions which can be found in the literature, these relationships do not appear to be widely appreciated This paper outlines the relevant theoretical relationships between the analysis of variance, indirect selection and pattern analysis methodologies, and their practical implications for the plant breeder interested in assessing the effects ofG ×E interaction on the response to selection The variance components estimated from the combined analysis of variance can be used to judge the relative magnitude of genotypic andG ×E interaction variance Where concern is on the effect of lack of correlation among environments, theG ×E interaction component can be partitioned into a component due to heterogeneity of genotypic variance among environments and another due to the lack of correlation among environments In addition, the pooled genetic correlation among all environments can be estimated as the intraclass correlation from the variance components of the combined analysis of variance WhereG ×E interaction accounts for a large proportion of the variation among genotypes, the individual genetic correlations between environments could be investigated rather than the pooled genetic correlation Indirect selection theory can be applied to the case where the same character is measured on the same genotypes in different environments Where there are no correlations of error effects among environments, the phenotypic correlation between environments may be used to investigate indirect response to selection Pattern analysis (classification and ordination) methods based on standardised data can be used to summarise the relationships among environments in terms of the scope to exploit indirect selection With the availability of this range of analytical methodology, it is now possible to investigate the results of more comprehensive experiments which attempt to understand the nature of differences in genotypic adaptation Hence a greater focus of interest on understanding the causes of the interaction can be achieved

Relationships among analytical methods used to study genotypic variation and genotype-by-environment interaction in plant breeding multi-environment experiments

We present a general quantitative genetic model for the evolution of reaction norms. This model goes beyond previous models by simultaneously permitting any shaped reaction norm and allowing for the imposition of genetic constraints. Earlier models are shown to be special cases of our general model; we discuss in detail models involving just two macroenvironments, linear reaction norms, and quadratic reaction norms. The model predicts that, for the case of a temporally varying environment, a population will converge on (1) the genotype with the maximum mean geometric fitness over all environments, (2) a linear reaction norm whose slope is proportional to the covariance between the environment of development and the environment of selection, and (3) a linear reaction norm even if nonlinear reaction norms are possible. An examination of experimental studies finds some limited support for these predictions. We discuss the limitations of our model and the need for more realistic gametic models and additional data on the genetic and developmental bases of plasticity.

https://onlinelibrary.wiley.com/doi/pdf/10.1046/j.1420-9101.1993.6010031.x

The genetics of phenotypic plasticity. V. Evolution of reaction norm shape

Participatory plant breeding (PPB) has been suggested as an effective alternative to formal plant breeding (FPB) as a breeding strategy for achieving productivity gains under low input conditions. With genetic progress through PPB and FPB being determined by the same genetic variables, the likelihood of success of PPB approaches applied in low input target conditions was analyzed using two case studies from FPB that have resulted in significant productivity gains under low input conditions: (1) breeding tropical maize for low input conditions by CIMMYT, and (2) breeding of spring wheat for the highly variable low input rainfed farming systems in Australia. In both cases, genetic improvement was an outcome of long-term investment in a sustained research effort aimed at understanding the detail of the important environmental constraints to productivity and the plant requirements for improved adaptation to the identified constraints, followed up by the design and continued evaluation of efficient breeding strategies. The breeding strategies used differed between the two case studies but were consistent in their attention to the key determinants of response to selection: (1) ensuring adequate sources of genetic variation and high selection pressures for the important traits at all stages of the breeding program, (2) use of experimental procedures to achieve high levels of heritability in the breeding trials, and (3) testing strategies that achieved a high genetic correlation between performance of germplasm in the breeding trials and under on-farm conditions. The implications of the outcomes from these FPB case studies for realizing the positive motivations for adopting PPB strategies are discussed with particular reference for low input target environment conditions.

Breeding for low input conditions and consequences for participatory plant breeding: examples from tropical maize and wheat

Relationships between genotype x environment interaction and genetic correlation of the same trait measured in different fixed environments are derived by comparing the variance-covariance structures of observations between a one-way multiple-trait linear model and a two-way single-trait mixed linear model. In the latter model, heterogeneity of interaction variances among environments and non-zero covariances among interactions are assumed, in addition to the heterogeneity of error variances and non-zero covariances between genetic-group effects and interactions that were accommodated in earlier work. The results are applicable to more than two environments and to unbalanced data. This paper is a generalization and a correction of earlier works.

Relationships between genotype x environment interaction and genetic correlation of the same trait measured in different environments.

Two methods of deriving linear selection indices for non-linear profit functions have been proposed. One is by linear approximation of profit, and another is the graphical method of Moav and Hill (1966). When profit is defined as the function of population means, the graphical method is optimal. In this paper, profit is defined as the function of the phenotypic values of individual animals; it is then shown that the graphical method is not generally optimal. We propose new methods for constructing selection indices. First, a numerical method equivalent to the graphical method is proposed. Furthermore, we propose two other methods using quadratic approximation of profit: one is based on Taylor series about means before selection, and the other is based on Tayler series about means after selection. Among these different methods, it is shown that the method using quadratic approximation based on Taylor series about means after selection is the most efficient.

Linear selection indices for non-linear profit functions

Parametric relationships between the genotype x environment interaction and the genetic correlation of the same attribute measured in two different environments are derived. It is shown that the criticism by Fernando et al. (1984) of Yamada's method (1962) in the case of unbalanced data is irrelevant.

Parametric relationships between genotype x environment interaction and genetic correlation when two environments are involved.

A selection index which maximizes genetic gains in a desired direction has been previously suggested. We extend this index to the case where desired relative genetic gains are constrained to be not less or not greater than pre-specified levels. Further, we suggest an index for desired relative genetic gains constrained to be between certain levels. All these indices are obtained using quadratic programming techniques.

Y. Itoh

Papers

Relationships between genotype x environment interaction and genetic correlation of the same trait measured in different environments.

Linear selection indices for non-linear profit functions

Parametric relationships between genotype x environment interaction and genetic correlation when two environments are involved.

Selection indices for desired relative genetic gains with inequality constraints