Biplot analysis of genotype by trait data

From a genotype by environment by trait three-way table, genotype-by-trait tables in any single environment, across all environments, or across a subset of the environments can be generated and visually studied using biplots. Biplot analysis of genotype by trait tables is a typical example of biplot analysis of multivariate data. The model for biplot analysis of genotype by trait data is SVD of trait-standardized two-way table, i.e., equation [15] with s_j being the standard deviation for trait j. A genotype by trait biplot can help understand the relationships among traits (breeding objectives) and help identify traits that are positively or negatively associated, traits that are redundantly measured, and traits that can be used in indirect selection for another trait.  It also helps to visualize the trait profiles (strength and weakness) of genotypes, which is important for parent as well as variety selection (Yan and Kang 2003). Most of the functions described in previous sections for biplot analysis of genotype by environment tables are applicable to genotype by trait data. To avoid unnecessary duplications, we will only present an example on how a genotype by trait biplot can assist in parent selection in breeding and genetics research.

Figure 15.  Genotype by trait biplot. 18 spring oat genotypes measured for four traits.  Data from 2004 Ontario Oat Performance trails, averaged across locations.

The biplot in Fig. 15 presents data of 18 covered spring oat varieties determined for four traits in the 2004 Ontario oat performance trials: yield, groat percentage, oil, and protein concentration. It is trait-metric preserving (SVP = 2) and is, therefore, appropriate for visualizing the relationships among the traits. With the knowledge that higher yield, groat, and protein and lower oil are desirable for milling oat varieties, the purpose of this exercise is to formulate crosses for breeding better milling oat varieties as well as for studying the genetics of groat and oil content. The following can be seen from Fig. 15:

1)     Across the 18 tested genotypes, yield and groat were positively associated (an acute angle). These two traits were negatively correlated with oil concentration (obtuse angles); and they were independent of protein concentration (near right angles). Oil and protein were negatively correlated (an obtuse angle). These relationships suggest that it is possible to combine higher yield, higher groat, higher protein, and lower oil in a single genotype.

2)     AC Goslin, a proven good milling variety, had the highest yield and groat, lower than average oil, and lower than average protein. It would be more ideal if Goslin had higher protein content. Fig. 15 indicates that “OA1021-1” combined all favorable attributes: it had similar yield and groat as Goslin but had higher protein and lower oil than Goslin.

3)     AC Rigodon was located opposite from the origin to OA1021-1 relative to the biplot origin because its trait profile was opposite to that of OA1021-1: it had the highest oil, the lowest yield and groat, and intermediate protein. It is, therefore, highly undesirable for milling. However, it might be a good parent for studying the genetic determination of oil and groat in oat. Therefore, OA1021-1 ´ AC Rigodon may make a good cross for this purpose.

4)     AC Stewart had the highest protein content, intermediate groat and yield, and lower-than-average oil. If it is desirable to further improve the protein level of Goslin and OA1021-1, crosses of Stewart ´ Goslin and Stewart ´ OA1021-1 may be useful.

5)     In addition, many other relationships can be revealed from Fig. 15. For example, Cultivars AC Stewart, Ida, and Irish constitute a group of genotypes with similar trait profiles; QO685.43 and QO685.48 form another group with similar trait profiles, etc. It would be rational to guess that the genotypes within each group share similar origins/parentages.