Norms of reaction and physiological response functions are deterministic forms of genotype expressions in variable environments. Several methods of analyses have been developed that either express genotypes as functions of known or estimated environmental effects, or as phenotypes described as joint functions of genotypes and environments. However, lacking either condition, the analysis developed by Gregorius, is a more general approach to understanding norms of reaction. An extension of that analysis is to obtain a conditional genotypic separability by transformation of the environmental variable. Analysis of the transformation rule may then reveal the form of the conditional joint genotypic and environmental "effects". Also, if the effects of several environmental variables can be separated, the transformations may then be most easily analyzed in terms of those multiple variables. The genotypic response function may then be approximated by a complicated function of several variables, and characterized by a series of coefficients for the set of variables.
A second extension is to consider genotypes as multiple trait systems of reaction and hence, to consider the norms of reaction as multivariate functions. In that case, the genotypic responses could be characterized by a matrix of an expanded series of coefficients. While more difficult to estimate and analyze, the matrix characterization of genotypes provides a more integrated view of organisms and of joint genotypic and environmental effects.
Key words: genotype, environment, interaction, reaction norm.