Although fan-shaped and crossover interactions are theoretically different, in practice, they can be quite difficult to differentiate. In looking at Figures 1a and b, one can imagine several “variations on the theme” for both fan-shaped and crossover interactions. In general for a fan-shaped interaction, a main effect of genotype will be present as well as a main effect of the environment. In the fan-shaped interaction shown in Figure 1a, there is a main effect of genotype at both environmental extremes; it is simply far stronger in environment 2 (far right side of the graph) as compared to environment–2 (far left side). But one could imagine a fan-shaped interaction where there was no genotypic effect at one extreme (e.g., the lines converge to the same phenotypic mean at environment–2). Further, fan-shaped interactions can differ in the slope of the lines for each genotype, which indicate how much the environment is modifying genetic effects. In the crossover interaction shown in Figure 1b, the lines cross at environment 0 (i.e., in the middle). But crossover interactions can vary in the location of the
