Many plant traits are phenotypically plastic in response to resource levels that vary continuously among environments. To be able to predict phenotypes in new environments, it is useful to model reaction norms as functions, rather than as a collection of discrete character states. Flowering date and rosette leaf number were measured in 100 recombinant inbred lines of Arabidopsis thaliana, grown on a gradient of light intensity. The results show that there is genetic variation among the recombinant inbred lines for parameters of the reaction norm functions. Genetic variances for leaf number and flowering date are highest under low light conditions. Underlying quantitative trait loci (QTLs) affecting the shape of the reaction norm functions were mapped by modifying Haley & Knott (1992) regressions to include polynomial effects of the environment. Quantitative trait loci of large effect were generally insensitive to the resource gradient. Seven QTLs affecting flowering date and eight QTLs for rosette leaf number were identified, of which only two had significant effects on the linear and quadratic components of the reaction norm function. These results suggest that the genotype-environment interactions for flowering time are controlled by many minor genes, whose effects are below the detection limit in most mapping experiments.