between the environments when there is only VG). Environmental variation only (VE; Fig. 9.6b) means that the four genotypes have identical phenotypes but the phenotype changes between the two environments (the four genotype lines are not drawn exactly on top of each other so each can be seen). A combination of both genotypic (VG) and environmental (VE) variation in phenotype means that the genotypes have different phenotypes and the phenotypes also change between environments (Fig. 9.6c). Notice that with VG and VE the lines are parallel, showing that each genotype has an identical change in phenotype caused by the change in environment.

Two types of genotype-by-environment interaction are shown in Fig. 9.6. Both examples illustrate the hallmark of genotype-by-environment interaction: different genotypes vary in their response to changes in their environment. One example shows that the range of genotypic values of the four genotypes depends on the environment (Fig. 9.6d). In environment A there is less variation in genotypic values and in environment B there is more variation in genotypic values. When the lines connecting genotypes are not parallel in a norm-of-reaction plot, then geno-typic variance changes with environment. Another example shows different environmental sensitivity of genotypes that causes a change of phenotypic ranks between the two environments (Fig. 9.6e). Three of the genotypes respond to the change in environment and demonstrate increased genotypic values in environment B. The genotype with a value of 5 in environment A experiences the largest change in phenotype, showing a value of 11 in environment B. In contrast, the genotype indicated by the solid line is completely insensitive to the environmental change. Crossing lines indicate genotype-by-environment interactions as changes in rank order of genotypic values in norm-of-reaction plots.

An early and still classic example of a genotype-by-environment interaction comes from Clausen, Keck, and Hiesey (1948; see Nunez-Farfan & Schlichting 2001). These researchers sampled a group of plants in the genus Achillea at a single location in Aspen Valley, California (elevation 1950 m). They then sprouted vegetative cuttings of each Aspen Valley plant to create multiple individuals of each genotype for the numerous sampled genotypes. The newly sprouted cuttings were planted at three sites with increasing elevations between sea level (Stanford) and high in the mountains above the treeline (Timberline). The sprouted cuttings of each of the original Aspen Valley plants were genetically identical, so plants with identical genotypes could be transplanted at each elevation.

The transplanted cuttings were monitored and their phenotypes were measured over several years. Figure 9.7 shows the values of two phenotypes (longest stem and number of stems) measured for seven different genotypes grown at each of the three elevations.

Genotypic, environmental, and genotype-by-environment interaction all contributed to phenotypic variation in Achillea. VG is evident because the pheno-types for the different genotypes within an environment were clearly not identical. VE was evident because the average phenotype varied across the environments, being highest at Mather, intermediate at Stanford, and lowest at Timberline. VGxE was also evident because the ranks of the phenotypic values for each genotype clearly changed across the three environments. In other words, genotypes that demonstrated phenotypic values above the mean in one environment had a below average phenotypic value in another environment and vice versa. Therefore, in Achillea the pheno-typic variation seen across these three environments had three causes. It was due to a combination of differences in phenotypic values among genotypes, differences in phenotypic values among environments, and differences in the change in phenotypic value of genotypes across the three environments.

Genotype-by-environment interaction has been observed for diverse phenotypes and a wide range of organisms. An example related to human health involves the risk of colorectal adenoma, a disease characterized by pre-cancerous tumors of the colon, genotypes at the UGT1A6 (UDP glycosyltransferase 1 family, polypeptide A6) locus, and use of aspirin. Regular aspirin intake reduces the risk of colorectal adenoma for individuals with all UGT1A6 genotypes compared to no use of aspirin. However, individuals homozygous or heterozygous for the "slow" UGT1A6 allele, a variant that leads to slower aspirin metabolism, show significantly reduced risk of colorectal adenoma when individuals are taking aspirin compared with other UGT1A6 genotypes (Bigler et al. 2001; Chan et al. 2005; Hubner et al. 2006). Thus, individual risk of colorectal adenoma depends on combinations of UGT1A6 genotype and aspirin "environments." Additional examples of genotype-by-environment interactions in human disease are reviewed by Hunter (2005). See many more examples of genotype-by-environment interactions in Pigliucci (2001) and DeWitt and Scheiner (2004).

The genotype-by-environment interaction can also be thought of as a correlation between genotypic value and environmental impact on the phenotype. The decomposition of VP = VG + VE without any contribution of VGxE makes the assumption that the

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