A further challenge facing breeders is the interaction between genotypes and environments (GEI) which reduces the association between the genotype and phenotype. Sweetpotato is known to be very sensitive to environmental changes (Bacusmo et al., 1988). It is grown in diverse environments especially by small-scale resource poor farmers who use degraded soils with low use of agricultural inputs. Despite being grown in such diverse environments, it has been observed that the performance of different sweetpotato cultivars depends on the environment (Nasayao and Saladaga, 1988). This change in sweetpotato performance is a result of the complex phenomenon of GEI which may lead to a change in the relative ranking of the genotypes from one environment to another. The sensitivity of sweetpotato to environmental changes has been studied for several important traits (Collins et al., 1987; Bacusmo et al., 1988; Kanua and Floyd, 1988; Martin et al., 1988; Nasayao and Saladaga, 1988; Naskar and
Singh, 1992; Ngeve, 1993; Manrique and Hermann, 2000) and in all cases the GEI has been observed to complicate sweetpotato breeding and genotype selection.
Genotype x environment interaction has a significant effect on yield and yield components of sweetpotato (Bacusmo et al., 1988), thus it is important to determine the most suitable cultivar for a certain site (Caliskan et al., 2007a,b). Root mass, one of the most important traits, crude protein, and percentage dry mass exhibited significant variation under different environments (Collins et al., 1987). Studies by Osiru et al. (2009) in Uganda, Mbwaga et al. (2007) in Tanzania, Caliskan et al. (2007a) in Turkey and Moussa et al. (2011) in Egypt showed significant GEI among sweetpotato cultivars grown in different agro-ecological zones as well as over seasons. In a related study, Caliskan et al. (2007b) recorded significant differences in percentage dry mass (DM%) among cultivars across sites. Furthermore, Kanua and Floyd (1988) also reported significant GEI among sweetpotato cultivars in Papua New Guinea but in addition they observed that exotic cultivars had greater interaction with the environment than the local ones.
In a study to determine the GEI for a set of sweetpotato genotypes across several eco- geological conditions in Peru, Grüneberg et al. (2005) observed three categories of high yielding genotypes: those that were high yielding with wide adaptation; those that were high yielding with specific adaptation to medium and high yielding environments; and those that were high yielding with specific adaptation to low yielding environments. Therefore, it is possible to breed sweetpotato for high yield and wide adaptation.
A genotype is considered to be stable if it shows consistent performance across different sites or years (Fernandez, 1991). Several statistical methods have been used to determine stability in sweetpotato over a wide range of environments. Ngeve (1993) carried out studies to determine if there were significant differences in the yield potential, total yield, marketable yield, and number of storage roots in both the local and improved genotypes. He observed significant differences due to site and year. However, the regression methods of Eberhart and Russell (1966) and Shukla (1972) ranked the genotypes differently with some genotypes ranked as stable by the one method and as unstable by the other. Bacusmo et al. (1988) compared the effectiveness of different stability methods in determining the stability and adaptability of 14 sweetpotato genotypes. The results indicated that the Eberhart and Russell (1966) and Tai (1971) methods are related and did not effectively separate the genotypes according to their stability. Shukla’s (1972) stability method had a good association with the Eberhart and Russell (1966) and Tai (1971) methods but Shukla’s method provides a means of assigning a variance component due to individual genotypes and a test of significance of the variance components. It is the variance component and the trait mean of each genotype that are used for selecting superior and stable genotypes. These observed inconsistencies in identifying stable genotypes
by different methods show that choice of method is crucial in identifying stable genotype and more than one method should be used in determining the stability of genotypes.
All the above methods have been widely used in GEI studies. However, the Additive Main effects and Multiplicative Interaction (AMMI) analysis method has gained popularity and is now widely preferred for GEI studies in sweetpotato (Manrique and Hermann, 2000; Grüneberg et al., 2005; Mbwaga et al., 2007; Mwololo et al., 2009; Osiru et al., 2009). The AMMI analysis gives a more appropriate statistical analysis of trials that may exhibit GEI. It incorporates both additive and multiplicative components into an integrated, powerful, least squares analysis and is the most appropriate when both the main effects and interactions are important (Freeman, 1985).
For graphical examination of the relationship among genotypes, test environments and GEI, AMMI biplots for interaction principal component analysis 1 (IPCA1) scores (y-axis) versus the genotype and environmental means (x-axis) or IPCA2 (y-axis) versus IPCA1 (x-axis) (Zobel et al., 1988) and the GGE (genotype main effect plus genotype by environment interaction) biplots (Yan et al., 2000) can be used. These are effective tools for (i) mega-environment analysis (“which won where” pattern) whereby specific genotypes can be recommended for specific mega environments (Yan and Kang, 2003; Yan and Tinker, 2006), and (ii) genotype evaluation (the mean performance and stability) and environment evaluation (the power to discriminate among genotypes in the target environments) (Ding et al., 2007).
1.11.1 AMMI stability value
Since the AMMI model does not directly make provision for a quantitative stability measure, Purchase et al. (2000) developed the AMMI stability value (ASV) based on the IPCA1 and IPCA2 scores for each genotype. The ASV is the distance from zero to each co-ordinate point (i.e. the hypotenuse) in a two dimension scattergram of IPCA1 versus IPCA2 scores and is determined using the Pythagoras’ theorem. Due to the higher contribution of the IPCA1 axis to the GEI SS than the IPCA2 axis, the IPCA1 score is weighted by the ratio of IPCA1 SS to IPCA2 SS in the calculation of the ASV. The lower the ASV, the higher the stability ranking of the genotype. However, in selecting preferred cultivars, stability per se is not the only parameter considered since the most stable cultivars are not necessarily the best performers for the trait of interest. Therefore, the genotype selection index (GSI) was developed.
1.11.2 Genotype selection index
The genotype selection index (GSI) incorporates both the mean performance and stability of a cultivar for a particular trait into a single index (Farshadfar, 2008). The GSI combines the ASV rank for a particular genotype and the mean performance rank of the genotype in each
environment. For example, a genotype with the lowest ASV for a trait is ranked one and a genotype with the best mean performance for a trait (e.g. yield) is ranked one. The ranks for each genotype are added together providing a single selection index, the GSI, for trait performance and stability. The genotype with the smallest GSI is considered the most desirable combining stability and high mean performance for the trait.